Cryogenic electro-optic modulation in titanium in-diffused lithium niobate waveguides

<jats:title>Abstract</jats:title> <jats:p>Lithium niobate is a promising platform for integrated quantum optics. In this platform, we aim to efficiently manipulate and detect quantum states by combining superconducting single photon detectors and modulators. The cryogenic operation of a superconducting single photon detector dictates the optimisation of the electro-optic modulators under the same operating conditions. To that end, we characterise a phase modulator, directional coupler, and polarisation converter at both ambient and cryogenic temperatures. The operation voltage <jats:inline-formula> <jats:tex-math><?CDATA $V_{\pi/2}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> of these modulators increases, due to the decrease in the electro-optic effect, by 74% for the phase modulator, 84% for the directional coupler and 35% for the polarisation converter below 8.5<jats:inline-formula> <jats:tex-math><?CDATA $\,\mathrm{K}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. The phase modulator preserves its broadband nature and modulates light in the characterised wavelength range. The unbiased bar state of the directional coupler changed by a wavelength shift of 85<jats:inline-formula> <jats:tex-math><?CDATA $\,\mathrm{nm}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> while cooling the device down to 5<jats:inline-formula> <jats:tex-math><?CDATA $\,\mathrm{K}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>. The polarisation converter uses periodic poling to phasematch the two orthogonal polarisations. The phasematched wavelength of the utilised poling changes by 112<jats:inline-formula> <jats:tex-math><?CDATA $\,\mathrm{nm}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> when cooling to 5<jats:inline-formula> <jats:tex-math><?CDATA $\,\mathrm{K}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="jpphotonac6c63ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>.</jats:p>