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ACTA PHOTONICA SINICA

Generation of Two-Mode Squeezing and Continuous Variable Entanglement in a Nonlinear Coupler Inside a Optical Cavity

Hua Tan

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The generation of two-mode squeezed and entangled light in a nonlinear coupler inside an optical cavity was studied.The master equation of the two-mode field was solved by the method of characteristic function.It shows that the state of the two-mode field is a two-mode Gaussian one,and under some conditions,the two-mode cavity field exhibits stable two-mode squeezing and continuous variable entanglement.The degree of the squeezing and entanglement is dependent on the damping rate of the cavity field and the coupling constants between the two modes.

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The generation of two-mode squeezed and entangled light in a nonlinear coupler inside an optical cavity was studied.The master equation of the two-mode field was solved by the method of characteristic function.It shows that the state of the two-mode field is a two-mode Gaussian one,and under some conditions,the two-mode cavity field exhibits stable two-mode squeezing and continuous variable entanglement.The degree of the squeezing and entanglement is dependent on the damping rate of the cavity field and the coupling constants between the two modes.
We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
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 down conversion, inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modeled using the Lindblad master equation, and we show that the 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 minimum correlation variance inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our analytic 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.
The generation of macroscopic and spatially separated three-mode entangled light for triply coupled ${\ensuremath{\chi}}^{(3)}$ Kerr coupler inside a pumped optical cavity is investigated. With the linearized analysis for small perturbation around the steady state of the pumped cavity modes, the linearized Hamiltonian and the corresponding master equation are obtained. It is found that the bright three-mode squeezing and full inseparable entanglement can be achieved both inside and outside the cavity.
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.