Continuous-variable entanglement in a two-mode lossy cavity: an exact solution

Abstract

Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric downconversion (SPDC), inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modelled using the Lindblad master equation, and we show that the exact solution to this model is the density operator for a two-mode squeezed thermal state, with a time-dependent squeezing amplitude and average thermal photon number for each mode. We derive an expression for the maximum entanglement inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our exact solution to the important example of a microring resonator that is pumped with a Gaussian pulse. The expressions that we derive will help researchers optimize CV entanglement in lossy cavities.

12 pages, 6 figures

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• A simple way to incorporate loss when modelling multimode entangled state generation
• Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
• Non-Gaussian two mode squeezed thermal states in continuous variable quantum teleportation
• Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator
• Measurement-based quantum computation utilizing the graph states of Bose-Einstein condensates and continuous variables