Thermooptic two-mode interference device for reconfigurable quantum optic circuits

Abstract

Reconfigurable large-scale integrated quantum optic circuits require compact component having capability of accurate manipulation of quantum entanglement for quantum communication and information processing applications. Here, a thermooptic two-mode interference coupler has been introduced as a compact component for generation of reconfigurable complex multi-photons quantum interference. Both theoretical and experimental approaches are used for the demonstration of two-photon and four-photon quantum entanglement manipulated with thermooptic phase change in TMI region. Our results demonstrate complex multi-photon quantum interference with high fabrication tolerance and quantum fidelity in smaller dimension than previous thermooptic Mach–Zehnder implementations.

Appendix

1.1 Derivation of two-photon quantum states

Two-photon state $\left| {1,\,1} \right\rangle_{a2a1}$ is generated by launching one photon each into input $a_{1}$ and $a_{2}$ but there may be presence of $\left| {0,\,0} \right\rangle_{a2a1}$. The input power is fixed in such a way that the chances of getting $\left| {0,\,0} \right\rangle_{a2a1}$ are negligible. So the two-photon input state is written as $\left| \psi \right\rangle_{in\,2} = \,\left| {1,\,1} \right\rangle_{a2a1}$ and after getting phase ϕ via thermooptic heating in arm b₁c₁ of MZ interferometer having TMI half-couplers ($\Delta \theta = \pi /2$) in its both end the output two-photon state is written as

$$ \left| \psi \right\rangle_{{{\text{out}}_{2} }} = \left[ { - \cos (\varphi )\left| {1,1} \right\rangle_{b2b1} + \frac{1}{\sqrt 2 }\sin (\varphi )\left( {\left| {2,0} \right\rangle_{b2b1} - \left| {0,2} \right\rangle_{b2b1} } \right)} \right] $$

(7)

1.2 Derivation of four-photon quantum states

In generating four-photon quantum state $\left| {2,\,2} \right\rangle_{a2a1}$, there may be presence of $\left| {0,\,0} \right\rangle_{a2a1}$ and $\left| {1,\,1} \right\rangle_{a2a1}$ quantum states and the input state of four-photon input state is represented as $\left| \psi \right\rangle_{in\,4} = \sqrt {1 - \left| \gamma \right|^{2} } \left| {0,0} \right\rangle_{a2a1} + \gamma \left| {1,1} \right\rangle_{a2a1} + \gamma^{2} \left| {2,2} \right\rangle_{a2a1}$, where $\gamma$ is a constant (0 < $\gamma$ ≤ 1), which mainly depends nonlinearity and pump power. The pump power is raised to increase $\gamma$ for enhancing multi-photon contribution and is applied in controlled fashion to have more $\left| {2,\,2} \right\rangle_{a2a1}$ states in inputs of TMI coupler. As $\gamma$ cannot be neglected with respect to $\gamma^{2}$. So the output entanglement state is written as

$$ \begin{aligned} \left| \psi \right\rangle_{{{\text{out}}_{4} }} & = \gamma \left[ { - \cos (\varphi )\left| {1,1} \right\rangle_{b2b1} + \frac{1}{\sqrt 2 }\sin (\varphi )\left( {\left| {2,0} \right\rangle_{b2b1} - \left| {0,2} \right\rangle_{b2b1} } \right)} \right] \\ &\quad + \,\gamma^{2} \left[ {\sqrt {\frac{3}{4}} \sin^{2} (\varphi )[\left| {4,0} \right\rangle_{b2b1} + \left| {0,4} \right\rangle_{b2b1} ] + \sqrt {\frac{3}{2}} \cos (\varphi )\sin (\varphi )[\left| {3,1} \right\rangle_{b2b1} } \right. \\ &\quad \left. { - \,\left| {1,3} \right\rangle_{b2b1} ]\, + \left[1 - \frac{3}{2}\sin^{2} (\varphi )\right]\left| {2,2} \right\rangle_{b2b1} } \right] \\ \end{aligned} $$

(8)