---
_id: '63656'
article_number: '012220'
article_type: original
author:
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Julien
full_name: Pinske, Julien
last_name: Pinske
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Ares L, Pinske J, Hinrichs B, Kolb M, Sperling J. Restricted Monte Carlo wave-function
method and Lindblad equation for identifying entangling open-quantum-system dynamics.
Physical Review A. 2026;113(1). doi:10.1103/hcj7-8zlg
apa: Ares, L., Pinske, J., Hinrichs, B., Kolb, M., & Sperling, J. (2026). Restricted
Monte Carlo wave-function method and Lindblad equation for identifying entangling
open-quantum-system dynamics. Physical Review A, 113(1), Article
012220. https://doi.org/10.1103/hcj7-8zlg
bibtex: '@article{Ares_Pinske_Hinrichs_Kolb_Sperling_2026, title={Restricted Monte
Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system
dynamics}, volume={113}, DOI={10.1103/hcj7-8zlg},
number={1012220}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Ares, Laura and Pinske, Julien and Hinrichs, Benjamin and Kolb,
Martin and Sperling, Jan}, year={2026} }'
chicago: Ares, Laura, Julien Pinske, Benjamin Hinrichs, Martin Kolb, and Jan Sperling.
“Restricted Monte Carlo Wave-Function Method and Lindblad Equation for Identifying
Entangling Open-Quantum-System Dynamics.” Physical Review A 113, no. 1
(2026). https://doi.org/10.1103/hcj7-8zlg.
ieee: 'L. Ares, J. Pinske, B. Hinrichs, M. Kolb, and J. Sperling, “Restricted Monte
Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system
dynamics,” Physical Review A, vol. 113, no. 1, Art. no. 012220, 2026, doi:
10.1103/hcj7-8zlg.'
mla: Ares, Laura, et al. “Restricted Monte Carlo Wave-Function Method and Lindblad
Equation for Identifying Entangling Open-Quantum-System Dynamics.” Physical
Review A, vol. 113, no. 1, 012220, American Physical Society (APS), 2026,
doi:10.1103/hcj7-8zlg.
short: L. Ares, J. Pinske, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A
113 (2026).
date_created: 2026-01-18T18:08:18Z
date_updated: 2026-01-18T18:15:01Z
department:
- _id: '799'
doi: 10.1103/hcj7-8zlg
external_id:
arxiv:
- '2412.08735'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Restricted Monte Carlo wave-function method and Lindblad equation for identifying
entangling open-quantum-system dynamics
type: journal_article
user_id: '99427'
volume: 113
year: '2026'
...
---
_id: '63657'
article_number: L010403
article_type: letter_note
author:
- first_name: Julien
full_name: Pinske, Julien
last_name: Pinske
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Pinske J, Ares L, Hinrichs B, Kolb M, Sperling J. Separability Lindblad equation for
dynamical open-system entanglement. Physical Review A. 2026;113(1). doi:10.1103/kd3b-bfxq
apa: Pinske, J., Ares, L., Hinrichs, B., Kolb, M., & Sperling, J. (2026). Separability
Lindblad equation for dynamical open-system entanglement. Physical Review A,
113(1), Article L010403. https://doi.org/10.1103/kd3b-bfxq
bibtex: '@article{Pinske_Ares_Hinrichs_Kolb_Sperling_2026, title={Separability Lindblad
equation for dynamical open-system entanglement}, volume={113}, DOI={10.1103/kd3b-bfxq},
number={1L010403}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Pinske, Julien and Ares, Laura and Hinrichs, Benjamin and Kolb,
Martin and Sperling, Jan}, year={2026} }'
chicago: Pinske, Julien, Laura Ares, Benjamin Hinrichs, Martin Kolb, and Jan Sperling.
“Separability Lindblad Equation for Dynamical Open-System Entanglement.” Physical
Review A 113, no. 1 (2026). https://doi.org/10.1103/kd3b-bfxq.
ieee: 'J. Pinske, L. Ares, B. Hinrichs, M. Kolb, and J. Sperling, “Separability
Lindblad equation for dynamical open-system entanglement,” Physical Review
A, vol. 113, no. 1, Art. no. L010403, 2026, doi: 10.1103/kd3b-bfxq.'
mla: Pinske, Julien, et al. “Separability Lindblad Equation for Dynamical Open-System
Entanglement.” Physical Review A, vol. 113, no. 1, L010403, American Physical
Society (APS), 2026, doi:10.1103/kd3b-bfxq.
short: J. Pinske, L. Ares, B. Hinrichs, M. Kolb, J. Sperling, Physical Review A
113 (2026).
date_created: 2026-01-18T18:11:27Z
date_updated: 2026-01-18T18:15:26Z
department:
- _id: '799'
doi: 10.1103/kd3b-bfxq
external_id:
arxiv:
- '2412.08724'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Separability Lindblad equation for dynamical open-system entanglement
type: journal_article
user_id: '99427'
volume: 113
year: '2026'
...
---
_id: '47534'
abstract:
- lang: eng
text: "In this proceeding we consider a translation invariant Nelson type model
in\r\ntwo spatial dimensions modeling a scalar relativistic particle in interaction\r\nwith
a massive radiation field. As is well-known, the corresponding Hamiltonian\r\ncan
be defined with the help of an energy renormalization. First, we review a\r\nFeynman-Kac
formula for the semigroup generated by this Hamiltonian proven by\r\nthe authors
in a recent preprint (where several matter particles and exterior\r\npotentials
are treated as well). After that, we employ a few technical key\r\nrelations and
estimates obtained in our preprint to present an otherwise\r\nself-contained derivation
of new Feynman-Kac formulas for the fiber\r\nHamiltonians attached to fixed total
momenta of the translation invariant\r\nsystem. We conclude by inferring an alternative
derivation of the Feynman-Kac\r\nformula for the full translation invariant Hamiltonian."
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Oliver
full_name: Matte, Oliver
last_name: Matte
citation:
ama: 'Hinrichs B, Matte O. Feynman-Kac formula for fiber Hamiltonians in the relativistic
Nelson model in two spatial dimensions. In: Hiroshima F, ed. Proceedings of
the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics.”
Vol 2310. RIMS Kôkyûroku. ; 2025.'
apa: Hinrichs, B., & Matte, O. (2025). Feynman-Kac formula for fiber Hamiltonians
in the relativistic Nelson model in two spatial dimensions. In F. Hiroshima (Ed.),
Proceedings of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields
and Related Topics” (Vol. 2310, Issue 3).
bibtex: '@inproceedings{Hinrichs_Matte_2025, series={RIMS Kôkyûroku}, title={Feynman-Kac
formula for fiber Hamiltonians in the relativistic Nelson model in two spatial
dimensions}, volume={2310}, number={3}, booktitle={Proceedings of the 2023 RIMS
Workshop “Mathematical Aspects of Quantum Fields and Related Topics”}, author={Hinrichs,
Benjamin and Matte, Oliver}, editor={Hiroshima, Fumio}, year={2025}, collection={RIMS
Kôkyûroku} }'
chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians
in the Relativistic Nelson Model in Two Spatial Dimensions.” In Proceedings
of the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related
Topics,” edited by Fumio Hiroshima, Vol. 2310. RIMS Kôkyûroku, 2025.
ieee: B. Hinrichs and O. Matte, “Feynman-Kac formula for fiber Hamiltonians in the
relativistic Nelson model in two spatial dimensions,” in Proceedings of the
2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”
2025, vol. 2310, no. 3.
mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians
in the Relativistic Nelson Model in Two Spatial Dimensions.” Proceedings of
the 2023 RIMS Workshop “Mathematical Aspects of Quantum Fields and Related Topics,”
edited by Fumio Hiroshima, vol. 2310, no. 3, 2025.
short: 'B. Hinrichs, O. Matte, in: F. Hiroshima (Ed.), Proceedings of the 2023 RIMS
Workshop “Mathematical Aspects of Quantum Fields and Related Topics,” 2025.'
date_created: 2023-10-02T06:21:37Z
date_updated: 2026-01-16T08:55:19Z
department:
- _id: '799'
- _id: '623'
editor:
- first_name: Fumio
full_name: Hiroshima, Fumio
last_name: Hiroshima
external_id:
arxiv:
- '2309.09005'
intvolume: ' 2310'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2310.html
project:
- _id: '266'
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
publication: Proceedings of the 2023 RIMS Workshop 'Mathematical Aspects of Quantum
Fields and Related Topics'
series_title: RIMS Kôkyûroku
status: public
title: Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model
in two spatial dimensions
type: conference
user_id: '99427'
volume: 2310
year: '2025'
...
---
_id: '63642'
abstract:
- lang: eng
text: We prove absence of ground states in the infrared-divergent spin boson model
at large coupling. Our key argument reduces the proof to verifying long range
order in the dual one-dimensional continuum Ising model, i.e., to showing that
the respective two point function is lower bounded by a strictly positive constant.
We can then use known results from percolation theory to establish long range
order at large coupling. Combined with the known existence of ground states at
small coupling, our result proves that the spin boson model undergoes a phase
transition with respect to the coupling strength. We also present an expansion
for the vacuum overlap of the spin boson ground state in terms of the Ising $n$-point
functions, which implies that the phase transition is unique, i.e., that there
is a critical coupling constant below which a ground state exists and above which
none can exist.
author:
- first_name: Volker
full_name: Betz, Volker
last_name: Betz
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Mino Nicola
full_name: Kraft, Mino Nicola
last_name: Kraft
- first_name: Steffen
full_name: Polzer, Steffen
last_name: Polzer
citation:
ama: Betz V, Hinrichs B, Kraft MN, Polzer S. On the Ising Phase Transition in the
Infrared-Divergent Spin Boson Model. arXiv:250119362. Published online
2025.
apa: Betz, V., Hinrichs, B., Kraft, M. N., & Polzer, S. (2025). On the Ising
Phase Transition in the Infrared-Divergent Spin Boson Model. In arXiv:2501.19362.
bibtex: '@article{Betz_Hinrichs_Kraft_Polzer_2025, title={On the Ising Phase Transition
in the Infrared-Divergent Spin Boson Model}, journal={arXiv:2501.19362}, author={Betz,
Volker and Hinrichs, Benjamin and Kraft, Mino Nicola and Polzer, Steffen}, year={2025}
}'
chicago: Betz, Volker, Benjamin Hinrichs, Mino Nicola Kraft, and Steffen Polzer.
“On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model.” ArXiv:2501.19362,
2025.
ieee: V. Betz, B. Hinrichs, M. N. Kraft, and S. Polzer, “On the Ising Phase Transition
in the Infrared-Divergent Spin Boson Model,” arXiv:2501.19362. 2025.
mla: Betz, Volker, et al. “On the Ising Phase Transition in the Infrared-Divergent
Spin Boson Model.” ArXiv:2501.19362, 2025.
short: V. Betz, B. Hinrichs, M.N. Kraft, S. Polzer, ArXiv:2501.19362 (2025).
date_created: 2026-01-16T08:56:45Z
date_updated: 2026-01-16T08:57:21Z
department:
- _id: '799'
external_id:
arxiv:
- '2501.19362'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2501.19362
status: public
title: On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63644'
abstract:
- lang: eng
text: We study the ultraviolet problem for models of a finite-dimensional quantum
mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin
boson model or its rotating-wave approximation. If the state change of the system
upon emission or absorption of a boson is either given by a normal matrix or by
a 2-nilpotent one, which is the case for the previously named examples, we prove
an optimal renormalization result. We complement it, by proving the norm resolvent
convergence of appropriately regularized models to the renormalized one. Our method
consists of a dressing transformation argument in the normal case and an appropriate
interior boundary condition for the 2-nilpotent case.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: Javier
full_name: Valentín Martín, Javier
last_name: Valentín Martín
citation:
ama: Hinrichs B, Lampart J, Valentín Martín J. Ultraviolet Renormalization of Spin
Boson Models I. Normal and 2-Nilpotent Interactions. arXiv:250204876. Published
online 2025.
apa: Hinrichs, B., Lampart, J., & Valentín Martín, J. (2025). Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions. In arXiv:2502.04876.
bibtex: '@article{Hinrichs_Lampart_Valentín Martín_2025, title={Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions}, journal={arXiv:2502.04876},
author={Hinrichs, Benjamin and Lampart, Jonas and Valentín Martín, Javier}, year={2025}
}'
chicago: Hinrichs, Benjamin, Jonas Lampart, and Javier Valentín Martín. “Ultraviolet
Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions.”
ArXiv:2502.04876, 2025.
ieee: B. Hinrichs, J. Lampart, and J. Valentín Martín, “Ultraviolet Renormalization
of Spin Boson Models I. Normal and 2-Nilpotent Interactions,” arXiv:2502.04876.
2025.
mla: Hinrichs, Benjamin, et al. “Ultraviolet Renormalization of Spin Boson Models
I. Normal and 2-Nilpotent Interactions.” ArXiv:2502.04876, 2025.
short: B. Hinrichs, J. Lampart, J. Valentín Martín, ArXiv:2502.04876 (2025).
date_created: 2026-01-16T08:58:25Z
date_updated: 2026-01-16T08:59:03Z
department:
- _id: '799'
external_id:
arxiv:
- '2502.04876'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2502.04876
status: public
title: Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent
Interactions
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63645'
abstract:
- lang: eng
text: In this paper we construct the non-trivial, renormalized Hamiltonian for a
class of spin-boson models with supercritical form factors, including the one
describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed
through both a self-energy and mass renormalization, in the so-called Hamiltonian
formalism of constructive quantum field theory, implemented by a non-unitary dressing
transformation. This solves the problem of triviality for unitarily-renormalized
supercritical spin-boson models.
author:
- first_name: Marco
full_name: Falconi, Marco
last_name: Falconi
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Javier
full_name: Valentín Martín, Javier
last_name: Valentín Martín
citation:
ama: Falconi M, Hinrichs B, Valentín Martín J. Non-Trivial Renormalization of Spin-Boson
Models with Supercritical Form Factors. arXiv:250800805. Published online
2025.
apa: Falconi, M., Hinrichs, B., & Valentín Martín, J. (2025). Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors. In arXiv:2508.00805.
bibtex: '@article{Falconi_Hinrichs_Valentín Martín_2025, title={Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors}, journal={arXiv:2508.00805},
author={Falconi, Marco and Hinrichs, Benjamin and Valentín Martín, Javier}, year={2025}
}'
chicago: Falconi, Marco, Benjamin Hinrichs, and Javier Valentín Martín. “Non-Trivial
Renormalization of Spin-Boson Models with Supercritical Form Factors.” ArXiv:2508.00805,
2025.
ieee: M. Falconi, B. Hinrichs, and J. Valentín Martín, “Non-Trivial Renormalization
of Spin-Boson Models with Supercritical Form Factors,” arXiv:2508.00805.
2025.
mla: Falconi, Marco, et al. “Non-Trivial Renormalization of Spin-Boson Models with
Supercritical Form Factors.” ArXiv:2508.00805, 2025.
short: M. Falconi, B. Hinrichs, J. Valentín Martín, ArXiv:2508.00805 (2025).
date_created: 2026-01-16T08:59:11Z
date_updated: 2026-01-16T09:01:45Z
department:
- _id: '799'
external_id:
arxiv:
- '2508.00805'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2508.00805
status: public
title: Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63646'
abstract:
- lang: eng
text: We study the behavior of a probability measure near the bottom of its support
in terms of time averaged quotients of its Laplace transform. We discuss how our
results are connected to both rank-one perturbation theory as well as renewal
theory. We further apply our results in order to derive criteria for the existence
and non-existence of ground states for a finite dimensional quantum system coupled
to a bosonic field.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Steffen
full_name: Polzer, Steffen
last_name: Polzer
citation:
ama: Hinrichs B, Polzer S. Wiener-Type Theorems for the Laplace Transform. With
Applications to Ground State Problems. arXiv:251102867. Published online
2025.
apa: Hinrichs, B., & Polzer, S. (2025). Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems. In arXiv:2511.02867.
bibtex: '@article{Hinrichs_Polzer_2025, title={Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems}, journal={arXiv:2511.02867},
author={Hinrichs, Benjamin and Polzer, Steffen}, year={2025} }'
chicago: Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems.” ArXiv:2511.02867,
2025.
ieee: B. Hinrichs and S. Polzer, “Wiener-Type Theorems for the Laplace Transform.
With Applications to Ground State Problems,” arXiv:2511.02867. 2025.
mla: Hinrichs, Benjamin, and Steffen Polzer. “Wiener-Type Theorems for the Laplace
Transform. With Applications to Ground State Problems.” ArXiv:2511.02867,
2025.
short: B. Hinrichs, S. Polzer, ArXiv:2511.02867 (2025).
date_created: 2026-01-16T08:59:45Z
date_updated: 2026-01-16T09:01:02Z
department:
- _id: '799'
external_id:
arxiv:
- '2511.02867'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2511.02867
status: public
title: Wiener-Type Theorems for the Laplace Transform. With Applications to Ground
State Problems
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '63647'
abstract:
- lang: eng
text: We study the convergence rate of translation-invariant discrete-time quantum
dynamics on a one-dimensional lattice. We prove that the cumulative distributions
function of the ballistically scaled position $\mathbb X(n)/{n}$ after $n$ steps
converges at a rate of $n^{-1/3}$ in the Lévy metric as $n\to\infty$. In the special
case of step-coin quantum walks with two-dimensional coin space, we recover the
same convergence rate for the supremum distance and prove optimality.
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Pascal
full_name: Mittenbühler, Pascal
last_name: Mittenbühler
citation:
ama: Hinrichs B, Mittenbühler P. On the Optimal Rate of Convergence for Translation-Invariant
1D Quantum Walks. arXiv:251113409. Published online 2025.
apa: Hinrichs, B., & Mittenbühler, P. (2025). On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks. In arXiv:2511.13409.
bibtex: '@article{Hinrichs_Mittenbühler_2025, title={On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks}, journal={arXiv:2511.13409}, author={Hinrichs,
Benjamin and Mittenbühler, Pascal}, year={2025} }'
chicago: Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks.” ArXiv:2511.13409, 2025.
ieee: B. Hinrichs and P. Mittenbühler, “On the Optimal Rate of Convergence for Translation-Invariant
1D Quantum Walks,” arXiv:2511.13409. 2025.
mla: Hinrichs, Benjamin, and Pascal Mittenbühler. “On the Optimal Rate of Convergence
for Translation-Invariant 1D Quantum Walks.” ArXiv:2511.13409, 2025.
short: B. Hinrichs, P. Mittenbühler, ArXiv:2511.13409 (2025).
date_created: 2026-01-16T08:59:54Z
date_updated: 2026-01-16T09:00:31Z
department:
- _id: '799'
external_id:
arxiv:
- '2511.13409'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: arXiv:2511.13409
status: public
title: On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks
type: preprint
user_id: '99427'
year: '2025'
...
---
_id: '61245'
article_number: '032404'
author:
- first_name: Franziska
full_name: Barkhausen, Franziska
id: '63631'
last_name: Barkhausen
- first_name: Laura
full_name: Ares Santos, Laura
last_name: Ares Santos
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: 'Barkhausen F, Ares Santos L, Schumacher S, Sperling J. Entanglement between
dependent degrees of freedom: Quasiparticle correlations. Physical Review A.
2025;111(3). doi:10.1103/physreva.111.032404'
apa: 'Barkhausen, F., Ares Santos, L., Schumacher, S., & Sperling, J. (2025).
Entanglement between dependent degrees of freedom: Quasiparticle correlations.
Physical Review A, 111(3), Article 032404. https://doi.org/10.1103/physreva.111.032404'
bibtex: '@article{Barkhausen_Ares Santos_Schumacher_Sperling_2025, title={Entanglement
between dependent degrees of freedom: Quasiparticle correlations}, volume={111},
DOI={10.1103/physreva.111.032404},
number={3032404}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Barkhausen, Franziska and Ares Santos, Laura and Schumacher, Stefan
and Sperling, Jan}, year={2025} }'
chicago: 'Barkhausen, Franziska, Laura Ares Santos, Stefan Schumacher, and Jan Sperling.
“Entanglement between Dependent Degrees of Freedom: Quasiparticle Correlations.”
Physical Review A 111, no. 3 (2025). https://doi.org/10.1103/physreva.111.032404.'
ieee: 'F. Barkhausen, L. Ares Santos, S. Schumacher, and J. Sperling, “Entanglement
between dependent degrees of freedom: Quasiparticle correlations,” Physical
Review A, vol. 111, no. 3, Art. no. 032404, 2025, doi: 10.1103/physreva.111.032404.'
mla: 'Barkhausen, Franziska, et al. “Entanglement between Dependent Degrees of Freedom:
Quasiparticle Correlations.” Physical Review A, vol. 111, no. 3, 032404,
American Physical Society (APS), 2025, doi:10.1103/physreva.111.032404.'
short: F. Barkhausen, L. Ares Santos, S. Schumacher, J. Sperling, Physical Review
A 111 (2025).
date_created: 2025-09-12T10:37:34Z
date_updated: 2025-09-12T10:42:16Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '706'
- _id: '35'
- _id: '230'
- _id: '623'
- _id: '429'
doi: 10.1103/physreva.111.032404
intvolume: ' 111'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '54'
name: TRR 142 - Project Area A
- _id: '56'
name: TRR 142 - Project Area C
- _id: '61'
name: 'TRR 142; TP A04: Nichtlineare Quantenprozesstomographie und Photonik mit
Polaritonen in Mikrokavitäten'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: 'Entanglement between dependent degrees of freedom: Quasiparticle correlations'
type: journal_article
user_id: '16199'
volume: 111
year: '2025'
...
---
_id: '58519'
abstract:
- lang: eng
text: A unified theoretical approach to describe the properties of multimode
squeezed light generated in a lossy medium is presented. This approach is valid
for Markovian environments and includes both a model of discrete losses based
on the beamsplitter approach and a generalized continuous loss model based on
the spatial Langevin equation. For an important class of Gaussian states, we derive
master equations for the second-order correlation functions and illustrate their
solution for both frequency-independent and frequency-dependent losses. Studying
the mode structure, we demonstrate that in a lossy environment no broadband basis
without quadrature correlations between the different broadband modes exists.
Therefore, various techniques and strategies to introduce broadband modes can
be considered. We show that the Mercer expansion and the Williamson-Euler decomposition
do not provide modes in which the maximal squeezing contained in the system can
be measured. In turn, we find a new broadband basis that maximizes squeezing in
the lossy system and present an algorithm to construct it.
article_number: '1621'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
last_name: Kopylov
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
citation:
ama: Kopylov DA, Meier T, Sharapova PR. Theory of Multimode Squeezed Light Generation
in Lossy Media. Quantum. 2025;9. doi:10.22331/q-2025-02-04-1621
apa: Kopylov, D. A., Meier, T., & Sharapova, P. R. (2025). Theory of Multimode
Squeezed Light Generation in Lossy Media. Quantum, 9, Article 1621.
https://doi.org/10.22331/q-2025-02-04-1621
bibtex: '@article{Kopylov_Meier_Sharapova_2025, title={Theory of Multimode Squeezed
Light Generation in Lossy Media}, volume={9}, DOI={10.22331/q-2025-02-04-1621},
number={1621}, journal={Quantum}, publisher={Verein zur Forderung des Open Access
Publizierens in den Quantenwissenschaften}, author={Kopylov, Denis A. and Meier,
Torsten and Sharapova, Polina R.}, year={2025} }'
chicago: Kopylov, Denis A., Torsten Meier, and Polina R. Sharapova. “Theory of Multimode
Squeezed Light Generation in Lossy Media.” Quantum 9 (2025). https://doi.org/10.22331/q-2025-02-04-1621.
ieee: 'D. A. Kopylov, T. Meier, and P. R. Sharapova, “Theory of Multimode Squeezed
Light Generation in Lossy Media,” Quantum, vol. 9, Art. no. 1621, 2025,
doi: 10.22331/q-2025-02-04-1621.'
mla: Kopylov, Denis A., et al. “Theory of Multimode Squeezed Light Generation in
Lossy Media.” Quantum, vol. 9, 1621, Verein zur Forderung des Open Access
Publizierens in den Quantenwissenschaften, 2025, doi:10.22331/q-2025-02-04-1621.
short: D.A. Kopylov, T. Meier, P.R. Sharapova, Quantum 9 (2025).
date_created: 2025-02-05T12:57:37Z
date_updated: 2025-09-18T13:22:26Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '35'
- _id: '230'
- _id: '623'
- _id: '27'
doi: 10.22331/q-2025-02-04-1621
intvolume: ' 9'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Quantum
publication_identifier:
issn:
- 2521-327X
publication_status: published
publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
status: public
title: Theory of Multimode Squeezed Light Generation in Lossy Media
type: journal_article
user_id: '16199'
volume: 9
year: '2025'
...
---
_id: '62911'
abstract:
- lang: eng
text: In this paper, we theoretically study the spectral and temporal properties
of pulsed spontaneous parametric down-conversion (SPDC) generated in lossy waveguides.
Our theoretical approach is based on the formalism of Gaussian states and the
Langevin equation, which is elaborated for weak parametric down-conversion and
photon-number-unresolved click detection. Using the example of frequency-degenerate
type-II SPDC generated under the pump-idler group-velocity-matching condition,
we show how the joint-spectral intensity, mode structure, normalized second-order
correlation function, and Hong-Ou-Mandel interference pattern depend on internal
losses of the SPDC process. We found that the joint-spectral intensity is almost
insensitive to internal losses, while the second-order correlation function shows
a strong dependence on them, being different for the signal and idler beams in
the presence of internal losses. Based on the sensitivity of the normalized second-order
correlation function, we show how its measurement can be used to experimentally
determine internal losses.
article_number: '033122'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
last_name: Kopylov
- first_name: Michael
full_name: Stefszky, Michael
id: '42777'
last_name: Stefszky
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Christine
full_name: Silberhorn, Christine
id: '26263'
last_name: Silberhorn
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
citation:
ama: 'Kopylov DA, Stefszky M, Meier T, Silberhorn C, Sharapova PR. Spectral and
temporal properties of type-II parametric down-conversion: The impact of losses
during state generation. Physical Review Research. 2025;7(3). doi:10.1103/zp72-7qwl'
apa: 'Kopylov, D. A., Stefszky, M., Meier, T., Silberhorn, C., & Sharapova,
P. R. (2025). Spectral and temporal properties of type-II parametric down-conversion:
The impact of losses during state generation. Physical Review Research,
7(3), Article 033122. https://doi.org/10.1103/zp72-7qwl'
bibtex: '@article{Kopylov_Stefszky_Meier_Silberhorn_Sharapova_2025, title={Spectral
and temporal properties of type-II parametric down-conversion: The impact of losses
during state generation}, volume={7}, DOI={10.1103/zp72-7qwl},
number={3033122}, journal={Physical Review Research}, publisher={American Physical
Society (APS)}, author={Kopylov, Denis A. and Stefszky, Michael and Meier, Torsten
and Silberhorn, Christine and Sharapova, Polina R.}, year={2025} }'
chicago: 'Kopylov, Denis A., Michael Stefszky, Torsten Meier, Christine Silberhorn,
and Polina R. Sharapova. “Spectral and Temporal Properties of Type-II Parametric
down-Conversion: The Impact of Losses during State Generation.” Physical Review
Research 7, no. 3 (2025). https://doi.org/10.1103/zp72-7qwl.'
ieee: 'D. A. Kopylov, M. Stefszky, T. Meier, C. Silberhorn, and P. R. Sharapova,
“Spectral and temporal properties of type-II parametric down-conversion: The impact
of losses during state generation,” Physical Review Research, vol. 7, no.
3, Art. no. 033122, 2025, doi: 10.1103/zp72-7qwl.'
mla: 'Kopylov, Denis A., et al. “Spectral and Temporal Properties of Type-II Parametric
down-Conversion: The Impact of Losses during State Generation.” Physical Review
Research, vol. 7, no. 3, 033122, American Physical Society (APS), 2025, doi:10.1103/zp72-7qwl.'
short: D.A. Kopylov, M. Stefszky, T. Meier, C. Silberhorn, P.R. Sharapova, Physical
Review Research 7 (2025).
date_created: 2025-12-05T09:33:36Z
date_updated: 2025-12-05T09:55:22Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '288'
- _id: '230'
- _id: '623'
- _id: '429'
- _id: '35'
doi: 10.1103/zp72-7qwl
intvolume: ' 7'
issue: '3'
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: 'Spectral and temporal properties of type-II parametric down-conversion: The
impact of losses during state generation'
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '62913'
author:
- first_name: Anna
full_name: Hunstig, Anna
id: '73659'
last_name: Hunstig
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Hendrik
full_name: Rose, Hendrik
id: '55958'
last_name: Rose
orcid: 0000-0002-3079-5428
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: 'Hunstig A, Peitz S, Rose H, Meier T. Accelerating the analysis of optical
quantum systems using the Koopman operator. In: 2024 IEEE 63rd Conference on
Decision and Control (CDC). IEEE; 2025. doi:10.1109/cdc56724.2024.10886589'
apa: Hunstig, A., Peitz, S., Rose, H., & Meier, T. (2025). Accelerating the
analysis of optical quantum systems using the Koopman operator. 2024 IEEE 63rd
Conference on Decision and Control (CDC). https://doi.org/10.1109/cdc56724.2024.10886589
bibtex: '@inproceedings{Hunstig_Peitz_Rose_Meier_2025, title={Accelerating the analysis
of optical quantum systems using the Koopman operator}, DOI={10.1109/cdc56724.2024.10886589},
booktitle={2024 IEEE 63rd Conference on Decision and Control (CDC)}, publisher={IEEE},
author={Hunstig, Anna and Peitz, Sebastian and Rose, Hendrik and Meier, Torsten},
year={2025} }'
chicago: Hunstig, Anna, Sebastian Peitz, Hendrik Rose, and Torsten Meier. “Accelerating
the Analysis of Optical Quantum Systems Using the Koopman Operator.” In 2024
IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2025. https://doi.org/10.1109/cdc56724.2024.10886589.
ieee: 'A. Hunstig, S. Peitz, H. Rose, and T. Meier, “Accelerating the analysis of
optical quantum systems using the Koopman operator,” 2025, doi: 10.1109/cdc56724.2024.10886589.'
mla: Hunstig, Anna, et al. “Accelerating the Analysis of Optical Quantum Systems
Using the Koopman Operator.” 2024 IEEE 63rd Conference on Decision and Control
(CDC), IEEE, 2025, doi:10.1109/cdc56724.2024.10886589.
short: 'A. Hunstig, S. Peitz, H. Rose, T. Meier, in: 2024 IEEE 63rd Conference on
Decision and Control (CDC), IEEE, 2025.'
date_created: 2025-12-05T09:37:58Z
date_updated: 2025-12-05T09:40:24Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '230'
- _id: '623'
- _id: '35'
doi: 10.1109/cdc56724.2024.10886589
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: 2024 IEEE 63rd Conference on Decision and Control (CDC)
publication_status: published
publisher: IEEE
status: public
title: Accelerating the analysis of optical quantum systems using the Koopman operator
type: conference
user_id: '16199'
year: '2025'
...
---
_id: '62980'
abstract:
- lang: eng
text: We introduce a new classification of multimode states with a fixed
number of photons. This classification is based on the factorizability of homogeneous
multivariate polynomials and is invariant under unitary transformations. The classes
physically correspond to field excitations in terms of single and multiple photons,
each of which is in an arbitrary irreducible superposition of quantized modes.
We further show how the transitions between classes are rendered possible by photon
addition, photon subtraction, and photon-projection nonlinearities. We explicitly
put forward a design for a multilayer interferometer in which the states for different
classes can be generated with state-of-the-art experimental techniques. Limitations
of the proposed designs are analyzed using the introduced classification, providing
a benchmark for the robustness of certain states and classes.
article_number: '033062'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification
for nonlinear optical circuits. Physical Review Research. 2025;7(3). doi:10.1103/sv6z-v1gk
apa: Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S.,
Meier, T., Sharapova, P. R., & Sperling, J. (2025). Multiphoton, multimode
state classification for nonlinear optical circuits. Physical Review Research,
7(3), Article 033062. https://doi.org/10.1103/sv6z-v1gk
bibtex: '@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025,
title={Multiphoton, multimode state classification for nonlinear optical circuits},
volume={7}, DOI={10.1103/sv6z-v1gk},
number={3033062}, journal={Physical Review Research}, publisher={American Physical
Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura
and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova,
Polina R. and Sperling, Jan}, year={2025} }'
chicago: Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo,
Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton,
Multimode State Classification for Nonlinear Optical Circuits.” Physical Review
Research 7, no. 3 (2025). https://doi.org/10.1103/sv6z-v1gk.
ieee: 'D. A. Kopylov et al., “Multiphoton, multimode state classification
for nonlinear optical circuits,” Physical Review Research, vol. 7, no.
3, Art. no. 033062, 2025, doi: 10.1103/sv6z-v1gk.'
mla: Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for
Nonlinear Optical Circuits.” Physical Review Research, vol. 7, no. 3, 033062,
American Physical Society (APS), 2025, doi:10.1103/sv6z-v1gk.
short: D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).
date_created: 2025-12-09T09:08:39Z
date_updated: 2025-12-09T09:10:01Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
doi: 10.1103/sv6z-v1gk
intvolume: ' 7'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '62979'
abstract:
- lang: eng
text: We introduce a new classification of multimode states with a fixed number
of photons. This classification is based on the factorizability of homogeneous
multivariate polynomials and is invariant under unitary transformations. The classes
physically correspond to field excitations in terms of single and multiple photons,
each of which being in an arbitrary irreducible superposition of quantized modes.
We further show how the transitions between classes are rendered possible by photon
addition, photon subtraction, and photon-projection nonlinearities. We explicitly
put forward a design for a multilayer interferometer in which the states for different
classes can be generated with state-of-the-art experimental techniques. Limitations
of the proposed designs are analyzed using the introduced classification, providing
a benchmark for the robustness of certain states and classes.
author:
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Meier T, Sharapova PR, Sperling J, Ober-Blöbaum S, Wembe Moafo BE, Offen C.
Multiphoton, multimode state classification for nonlinear optical circuits. Published
online 2025.
apa: Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B.
E., & Offen, C. (2025). Multiphoton, multimode state classification for
nonlinear optical circuits.
bibtex: '@article{Meier_Sharapova_Sperling_Ober-Blöbaum_Wembe Moafo_Offen_2025,
title={Multiphoton, multimode state classification for nonlinear optical circuits},
author={Meier, Torsten and Sharapova, Polina R. and Sperling, Jan and Ober-Blöbaum,
Sina and Wembe Moafo, Boris Edgar and Offen, Christian}, year={2025} }'
chicago: Meier, Torsten, Polina R. Sharapova, Jan Sperling, Sina Ober-Blöbaum, Boris
Edgar Wembe Moafo, and Christian Offen. “Multiphoton, Multimode State Classification
for Nonlinear Optical Circuits,” 2025.
ieee: T. Meier, P. R. Sharapova, J. Sperling, S. Ober-Blöbaum, B. E. Wembe Moafo,
and C. Offen, “Multiphoton, multimode state classification for nonlinear optical
circuits.” 2025.
mla: Meier, Torsten, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits. 2025.
short: T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo,
C. Offen, (2025).
date_created: 2025-12-09T08:59:27Z
date_updated: 2025-12-09T09:10:23Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '230'
- _id: '623'
- _id: '429'
- _id: '35'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: preprint
user_id: '16199'
year: '2025'
...
---
_id: '63160'
article_number: '245304'
author:
- first_name: Hendrik
full_name: Rose, Hendrik
id: '55958'
last_name: Rose
orcid: 0000-0002-3079-5428
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: 'Rose H, Schumacher S, Meier T. Microscopic approach to the quantized light-matter
interaction in semiconductor nanostructures: Complex coupled dynamics of excitons,
biexcitons, and photons. Physical Review B. 2025;112(24). doi:10.1103/528f-7smh'
apa: 'Rose, H., Schumacher, S., & Meier, T. (2025). Microscopic approach to
the quantized light-matter interaction in semiconductor nanostructures: Complex
coupled dynamics of excitons, biexcitons, and photons. Physical Review B,
112(24), Article 245304. https://doi.org/10.1103/528f-7smh'
bibtex: '@article{Rose_Schumacher_Meier_2025, title={Microscopic approach to the
quantized light-matter interaction in semiconductor nanostructures: Complex coupled
dynamics of excitons, biexcitons, and photons}, volume={112}, DOI={10.1103/528f-7smh},
number={24245304}, journal={Physical Review B}, publisher={American Physical Society
(APS)}, author={Rose, Hendrik and Schumacher, Stefan and Meier, Torsten}, year={2025}
}'
chicago: 'Rose, Hendrik, Stefan Schumacher, and Torsten Meier. “Microscopic Approach
to the Quantized Light-Matter Interaction in Semiconductor Nanostructures: Complex
Coupled Dynamics of Excitons, Biexcitons, and Photons.” Physical Review B
112, no. 24 (2025). https://doi.org/10.1103/528f-7smh.'
ieee: 'H. Rose, S. Schumacher, and T. Meier, “Microscopic approach to the quantized
light-matter interaction in semiconductor nanostructures: Complex coupled dynamics
of excitons, biexcitons, and photons,” Physical Review B, vol. 112, no.
24, Art. no. 245304, 2025, doi: 10.1103/528f-7smh.'
mla: 'Rose, Hendrik, et al. “Microscopic Approach to the Quantized Light-Matter
Interaction in Semiconductor Nanostructures: Complex Coupled Dynamics of Excitons,
Biexcitons, and Photons.” Physical Review B, vol. 112, no. 24, 245304,
American Physical Society (APS), 2025, doi:10.1103/528f-7smh.'
short: H. Rose, S. Schumacher, T. Meier, Physical Review B 112 (2025).
date_created: 2025-12-16T15:50:42Z
date_updated: 2025-12-16T15:52:55Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '297'
- _id: '623'
- _id: '429'
- _id: '230'
- _id: '35'
- _id: '27'
doi: 10.1103/528f-7smh
intvolume: ' 112'
issue: '24'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '54'
name: TRR 142 - Project Area A
- _id: '59'
name: 'TRR 142; TP A02: Nichtlineare Spektroskopie von Halbleiter-Nanostrukturen
mit Quantenlicht'
- _id: '445'
name: Hochleistungsrechner Noctua in Paderborn
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review B
publication_identifier:
issn:
- 2469-9950
- 2469-9969
publication_status: published
publisher: American Physical Society (APS)
status: public
title: 'Microscopic approach to the quantized light-matter interaction in semiconductor
nanostructures: Complex coupled dynamics of excitons, biexcitons, and photons'
type: journal_article
user_id: '16199'
volume: 112
year: '2025'
...
---
_id: '63562'
abstract:
- lang: eng
text: 'Entangled two-mode Gaussian states constitute an important building
block for continuous variable quantum computing and communication protocols. In
this work, we theoretically study two-mode bipartite states, which are extracted
from multimode light generated via type-II parametric downconversion (PDC) in
lossy waveguides. For these states, we demonstrate that the squeezing quantifies
entanglement and we construct a measurement basis, which results in the maximal
bipartite entanglement. We illustrate our findings by numerically solving the
spatial master equation for PDC in a Markovian environment. The optimal measurement
modes are compared with two widely used broadband bases: the Mercer–Wolf basis
(the first-order coherence basis) and the Williamson–Euler basis.'
article_number: '046116'
author:
- first_name: Denis
full_name: Kopylov, Denis
id: '98502'
last_name: Kopylov
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
citation:
ama: Kopylov D, Meier T, Sharapova PR. Bipartite entanglement extracted from multimode
squeezed light generated in lossy waveguides. APL Quantum. 2025;2(4). doi:10.1063/5.0293116
apa: Kopylov, D., Meier, T., & Sharapova, P. R. (2025). Bipartite entanglement
extracted from multimode squeezed light generated in lossy waveguides. APL
Quantum, 2(4), Article 046116. https://doi.org/10.1063/5.0293116
bibtex: '@article{Kopylov_Meier_Sharapova_2025, title={Bipartite entanglement extracted
from multimode squeezed light generated in lossy waveguides}, volume={2}, DOI={10.1063/5.0293116}, number={4046116},
journal={APL Quantum}, publisher={AIP Publishing}, author={Kopylov, Denis and
Meier, Torsten and Sharapova, Polina R.}, year={2025} }'
chicago: Kopylov, Denis, Torsten Meier, and Polina R. Sharapova. “Bipartite Entanglement
Extracted from Multimode Squeezed Light Generated in Lossy Waveguides.” APL
Quantum 2, no. 4 (2025). https://doi.org/10.1063/5.0293116.
ieee: 'D. Kopylov, T. Meier, and P. R. Sharapova, “Bipartite entanglement extracted
from multimode squeezed light generated in lossy waveguides,” APL Quantum,
vol. 2, no. 4, Art. no. 046116, 2025, doi: 10.1063/5.0293116.'
mla: Kopylov, Denis, et al. “Bipartite Entanglement Extracted from Multimode Squeezed
Light Generated in Lossy Waveguides.” APL Quantum, vol. 2, no. 4, 046116,
AIP Publishing, 2025, doi:10.1063/5.0293116.
short: D. Kopylov, T. Meier, P.R. Sharapova, APL Quantum 2 (2025).
date_created: 2026-01-12T13:18:51Z
date_updated: 2026-01-12T13:23:36Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '429'
- _id: '230'
- _id: '623'
- _id: '35'
doi: 10.1063/5.0293116
intvolume: ' 2'
issue: '4'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: APL Quantum
publication_identifier:
issn:
- 2835-0103
publication_status: published
publisher: AIP Publishing
status: public
title: Bipartite entanglement extracted from multimode squeezed light generated in
lossy waveguides
type: journal_article
user_id: '16199'
volume: 2
year: '2025'
...
---
_id: '51339'
author:
- first_name: Jonas
full_name: Babai-Hemati, Jonas
last_name: Babai-Hemati
- first_name: Felix
full_name: vom Bruch, Felix
id: '71245'
last_name: vom Bruch
- first_name: Harald
full_name: Herrmann, Harald
id: '216'
last_name: Herrmann
- first_name: Christine
full_name: Silberhorn, Christine
id: '26263'
last_name: Silberhorn
citation:
ama: Babai-Hemati J, vom Bruch F, Herrmann H, Silberhorn C. Tailored second harmonic
generation inTi-diffused PPLN waveguides usingmicro-heaters. Optics Express.
Published online 2024. doi:10.1364/oe.510319
apa: Babai-Hemati, J., vom Bruch, F., Herrmann, H., & Silberhorn, C. (2024).
Tailored second harmonic generation inTi-diffused PPLN waveguides usingmicro-heaters.
Optics Express. https://doi.org/10.1364/oe.510319
bibtex: '@article{Babai-Hemati_vom Bruch_Herrmann_Silberhorn_2024, title={Tailored
second harmonic generation inTi-diffused PPLN waveguides usingmicro-heaters},
DOI={10.1364/oe.510319}, journal={Optics
Express}, publisher={Optica Publishing Group}, author={Babai-Hemati, Jonas and
vom Bruch, Felix and Herrmann, Harald and Silberhorn, Christine}, year={2024}
}'
chicago: Babai-Hemati, Jonas, Felix vom Bruch, Harald Herrmann, and Christine Silberhorn.
“Tailored Second Harmonic Generation InTi-Diffused PPLN Waveguides Usingmicro-Heaters.”
Optics Express, 2024. https://doi.org/10.1364/oe.510319.
ieee: 'J. Babai-Hemati, F. vom Bruch, H. Herrmann, and C. Silberhorn, “Tailored
second harmonic generation inTi-diffused PPLN waveguides usingmicro-heaters,”
Optics Express, 2024, doi: 10.1364/oe.510319.'
mla: Babai-Hemati, Jonas, et al. “Tailored Second Harmonic Generation InTi-Diffused
PPLN Waveguides Usingmicro-Heaters.” Optics Express, Optica Publishing
Group, 2024, doi:10.1364/oe.510319.
short: J. Babai-Hemati, F. vom Bruch, H. Herrmann, C. Silberhorn, Optics Express
(2024).
date_created: 2024-02-13T13:03:01Z
date_updated: 2024-02-13T13:09:51Z
department:
- _id: '15'
- _id: '623'
- _id: '288'
doi: 10.1364/oe.510319
keyword:
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
project:
- _id: '266'
grant_number: PROFILNRW-2020-067
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
publication: Optics Express
publication_identifier:
issn:
- 1094-4087
publication_status: published
publisher: Optica Publishing Group
status: public
title: Tailored second harmonic generation inTi-diffused PPLN waveguides usingmicro-heaters
type: journal_article
user_id: '216'
year: '2024'
...
---
_id: '55173'
article_number: '013705'
author:
- first_name: Christian
full_name: Di Fidio, Christian
last_name: Di Fidio
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Di Fidio C, Ares L, Sperling J. Quantum walks and entanglement in cavity networks.
Physical Review A. 2024;110(1). doi:10.1103/physreva.110.013705
apa: Di Fidio, C., Ares, L., & Sperling, J. (2024). Quantum walks and entanglement
in cavity networks. Physical Review A, 110(1), Article 013705. https://doi.org/10.1103/physreva.110.013705
bibtex: '@article{Di Fidio_Ares_Sperling_2024, title={Quantum walks and entanglement
in cavity networks}, volume={110}, DOI={10.1103/physreva.110.013705},
number={1013705}, journal={Physical Review A}, publisher={American Physical Society
(APS)}, author={Di Fidio, Christian and Ares, Laura and Sperling, Jan}, year={2024}
}'
chicago: Di Fidio, Christian, Laura Ares, and Jan Sperling. “Quantum Walks and Entanglement
in Cavity Networks.” Physical Review A 110, no. 1 (2024). https://doi.org/10.1103/physreva.110.013705.
ieee: 'C. Di Fidio, L. Ares, and J. Sperling, “Quantum walks and entanglement in
cavity networks,” Physical Review A, vol. 110, no. 1, Art. no. 013705,
2024, doi: 10.1103/physreva.110.013705.'
mla: Di Fidio, Christian, et al. “Quantum Walks and Entanglement in Cavity Networks.”
Physical Review A, vol. 110, no. 1, 013705, American Physical Society (APS),
2024, doi:10.1103/physreva.110.013705.
short: C. Di Fidio, L. Ares, J. Sperling, Physical Review A 110 (2024).
date_created: 2024-07-11T07:20:08Z
date_updated: 2024-07-11T07:21:12Z
department:
- _id: '623'
- _id: '15'
- _id: '170'
- _id: '706'
- _id: '429'
doi: 10.1103/physreva.110.013705
intvolume: ' 110'
issue: '1'
language:
- iso: eng
project:
- _id: '266'
grant_number: PROFILNRW-2020-067
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
publication: Physical Review A
publication_identifier:
issn:
- 2469-9926
- 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Quantum walks and entanglement in cavity networks
type: journal_article
user_id: '75127'
volume: 110
year: '2024'
...
---
_id: '54668'
abstract:
- lang: eng
text: Samples of dielectric optical waveguides of rib or strip type in thin-film
lithium niobate (TFLN) technology are characterized with respect to their optical
loss using the Fabry-Pérot method. Attributing the losses mainly to sidewall roughness,
we employ a simple perturbational procedure, based on rigorously computed mode
profiles of idealized channels, to estimate the attenuation for waveguides with
different cross sections. A single fit parameter suffices for an adequate modelling
of the effect of the waveguide geometry on the loss levels.
author:
- first_name: Manfred
full_name: Hammer, Manfred
id: '48077'
last_name: Hammer
orcid: 0000-0002-6331-9348
- first_name: Silia
full_name: Babel, Silia
id: '63231'
last_name: Babel
orcid: https://orcid.org/0000-0002-1568-2580
- first_name: Henna
full_name: Farheen, Henna
id: '53444'
last_name: Farheen
orcid: 0000-0001-7730-3489
- first_name: Laura
full_name: Padberg, Laura
id: '40300'
last_name: Padberg
- first_name: J. Christoph
full_name: Scheytt, J. Christoph
id: '37144'
last_name: Scheytt
orcid: '0000-0002-5950-6618 '
- first_name: Christine
full_name: Silberhorn, Christine
id: '26263'
last_name: Silberhorn
- first_name: Jens
full_name: Förstner, Jens
id: '158'
last_name: Förstner
orcid: 0000-0001-7059-9862
citation:
ama: Hammer M, Babel S, Farheen H, et al. Estimation of losses caused by sidewall
roughness in thin-film lithium niobate rib and strip waveguides. Optics Express.
2024;32(13):22878. doi:10.1364/oe.521766
apa: Hammer, M., Babel, S., Farheen, H., Padberg, L., Scheytt, J. C., Silberhorn,
C., & Förstner, J. (2024). Estimation of losses caused by sidewall roughness
in thin-film lithium niobate rib and strip waveguides. Optics Express,
32(13), 22878. https://doi.org/10.1364/oe.521766
bibtex: '@article{Hammer_Babel_Farheen_Padberg_Scheytt_Silberhorn_Förstner_2024,
title={Estimation of losses caused by sidewall roughness in thin-film lithium
niobate rib and strip waveguides}, volume={32}, DOI={10.1364/oe.521766},
number={13}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Hammer,
Manfred and Babel, Silia and Farheen, Henna and Padberg, Laura and Scheytt, J.
Christoph and Silberhorn, Christine and Förstner, Jens}, year={2024}, pages={22878}
}'
chicago: 'Hammer, Manfred, Silia Babel, Henna Farheen, Laura Padberg, J. Christoph
Scheytt, Christine Silberhorn, and Jens Förstner. “Estimation of Losses Caused
by Sidewall Roughness in Thin-Film Lithium Niobate Rib and Strip Waveguides.”
Optics Express 32, no. 13 (2024): 22878. https://doi.org/10.1364/oe.521766.'
ieee: 'M. Hammer et al., “Estimation of losses caused by sidewall roughness
in thin-film lithium niobate rib and strip waveguides,” Optics Express,
vol. 32, no. 13, p. 22878, 2024, doi: 10.1364/oe.521766.'
mla: Hammer, Manfred, et al. “Estimation of Losses Caused by Sidewall Roughness
in Thin-Film Lithium Niobate Rib and Strip Waveguides.” Optics Express,
vol. 32, no. 13, Optica Publishing Group, 2024, p. 22878, doi:10.1364/oe.521766.
short: M. Hammer, S. Babel, H. Farheen, L. Padberg, J.C. Scheytt, C. Silberhorn,
J. Förstner, Optics Express 32 (2024) 22878.
date_created: 2024-06-10T11:18:06Z
date_updated: 2024-07-22T07:43:02Z
ddc:
- '530'
department:
- _id: '61'
- _id: '429'
- _id: '623'
- _id: '263'
- _id: '288'
doi: 10.1364/oe.521766
file:
- access_level: open_access
content_type: application/pdf
creator: fossie
date_created: 2024-06-10T11:25:00Z
date_updated: 2024-06-10T11:25:00Z
file_id: '54669'
file_name: 2024-06 Hammer - Optics Express - Estimation of losses caused by sidewall
roughness in thin-film lithium niobate rib and strip waveguides.pdf
file_size: 4004782
relation: main_file
file_date_updated: 2024-06-10T11:25:00Z
has_accepted_license: '1'
intvolume: ' 32'
issue: '13'
keyword:
- tet_topic_waveguide
language:
- iso: eng
oa: '1'
page: '22878'
project:
- _id: '53'
grant_number: '231447078'
name: 'TRR 142: TRR 142 - Maßgeschneiderte nichtlineare Photonik: Von grundlegenden
Konzepten zu funktionellen Strukturen'
- _id: '175'
grant_number: '231447078'
name: 'TRR 142 - C11: TRR 142 - Kompakte Photonenpaar-Quelle mit ultraschnellen
Modulatoren auf Basis von CMOS und LNOI (C11*)'
- _id: '167'
grant_number: '231447078'
name: 'TRR 142 - B06: TRR 142 - Ultraschnelle kohärente opto-elektronische Kontrolle
eines photonischen Quantensystems (B06*)'
- _id: '266'
grant_number: PROFILNRW-2020-067
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
publication: Optics Express
publication_identifier:
issn:
- 1094-4087
publication_status: published
publisher: Optica Publishing Group
status: public
title: Estimation of losses caused by sidewall roughness in thin-film lithium niobate
rib and strip waveguides
type: journal_article
user_id: '158'
volume: 32
year: '2024'
...
---
_id: '55751'
abstract:
- lang: eng
text: Lateral leakage of TM modes in dielectric optical waveguides of rib/ridge
or strip-loaded types can be fully suppressed, if the waveguide core is formed
not through a strip that protrudes at one side (up) from the remaining lateral
guiding slab, but through parallel strips on both sides (up and down), such that
the resulting cross section becomes vertically symmetric. The fairly general arguments
underlying the leakage suppression apply to TM modes of all orders simultaneously,
and are independent of wavelength. These plus-shaped waveguides support strictly
guided, non-leaky TM modes for, in principle, arbitrarily shallow etching.
article_type: original
author:
- first_name: Necati
full_name: Üstün, Necati
last_name: Üstün
- first_name: Henna
full_name: Farheen, Henna
id: '53444'
last_name: Farheen
orcid: 0000-0001-7730-3489
- first_name: Manfred
full_name: Hammer, Manfred
id: '48077'
last_name: Hammer
orcid: 0000-0002-6331-9348
- first_name: Jens
full_name: Förstner, Jens
id: '158'
last_name: Förstner
orcid: 0000-0001-7059-9862
citation:
ama: Üstün N, Farheen H, Hammer M, Förstner J. Symmetry-protected TM modes in rib-like,
plus-shaped optical waveguides with shallow etching. Journal of the Optical
Society of America B. 2024;41(9):2077. doi:10.1364/josab.528729
apa: Üstün, N., Farheen, H., Hammer, M., & Förstner, J. (2024). Symmetry-protected
TM modes in rib-like, plus-shaped optical waveguides with shallow etching. Journal
of the Optical Society of America B, 41(9), 2077. https://doi.org/10.1364/josab.528729
bibtex: '@article{Üstün_Farheen_Hammer_Förstner_2024, title={Symmetry-protected
TM modes in rib-like, plus-shaped optical waveguides with shallow etching}, volume={41},
DOI={10.1364/josab.528729},
number={9}, journal={Journal of the Optical Society of America B}, publisher={Optica
Publishing Group}, author={Üstün, Necati and Farheen, Henna and Hammer, Manfred
and Förstner, Jens}, year={2024}, pages={2077} }'
chicago: 'Üstün, Necati, Henna Farheen, Manfred Hammer, and Jens Förstner. “Symmetry-Protected
TM Modes in Rib-like, plus-Shaped Optical Waveguides with Shallow Etching.” Journal
of the Optical Society of America B 41, no. 9 (2024): 2077. https://doi.org/10.1364/josab.528729.'
ieee: 'N. Üstün, H. Farheen, M. Hammer, and J. Förstner, “Symmetry-protected TM
modes in rib-like, plus-shaped optical waveguides with shallow etching,” Journal
of the Optical Society of America B, vol. 41, no. 9, p. 2077, 2024, doi: 10.1364/josab.528729.'
mla: Üstün, Necati, et al. “Symmetry-Protected TM Modes in Rib-like, plus-Shaped
Optical Waveguides with Shallow Etching.” Journal of the Optical Society of
America B, vol. 41, no. 9, Optica Publishing Group, 2024, p. 2077, doi:10.1364/josab.528729.
short: N. Üstün, H. Farheen, M. Hammer, J. Förstner, Journal of the Optical Society
of America B 41 (2024) 2077.
date_created: 2024-08-25T10:24:58Z
date_updated: 2024-08-25T10:48:42Z
ddc:
- '530'
department:
- _id: '61'
- _id: '429'
doi: 10.1364/josab.528729
file:
- access_level: local
content_type: application/pdf
creator: fossie
date_created: 2024-08-25T10:30:28Z
date_updated: 2024-08-25T10:30:28Z
file_id: '55752'
file_name: 2024-08 Farheen - JOSA B - Symmetry-protected TM modes in rib-like, plus-shaped
optical waveguides with shallow etching.pdf
file_size: 920206
relation: main_file
- access_level: open_access
content_type: application/pdf
creator: fossie
date_created: 2024-08-25T10:48:05Z
date_updated: 2024-08-25T10:48:05Z
file_id: '55753'
file_name: 2024-08 Farheen - JOSA B - Symmetry-protected TM modes in rib-like, plus-shaped
optical waveguides with shallow etching (preprint).pdf
file_size: 931810
relation: main_file
title: (preprint)
file_date_updated: 2024-08-25T10:48:05Z
has_accepted_license: '1'
intvolume: ' 41'
issue: '9'
keyword:
- tet_topic_waveguide
language:
- iso: eng
oa: '1'
page: '2077'
project:
- _id: '266'
grant_number: PROFILNRW-2020-067
name: 'PhoQC: PhoQC: Photonisches Quantencomputing'
- _id: '167'
grant_number: '231447078'
name: 'TRR 142 - B06: TRR 142 - Ultraschnelle kohärente opto-elektronische Kontrolle
eines photonischen Quantensystems (B06*)'
publication: Journal of the Optical Society of America B
publication_identifier:
issn:
- 0740-3224
- 1520-8540
publication_status: published
publisher: Optica Publishing Group
status: public
title: Symmetry-protected TM modes in rib-like, plus-shaped optical waveguides with
shallow etching
type: journal_article
user_id: '158'
volume: 41
year: '2024'
...