We investigate the quantum fluctuation characteristic for time dependent regular loss modulated optical parametric amplifier for below and above threshold regions. It is found that a high squeezing and entanglement can be achieved.
Abstract We propose a method to generate an entangled squeezed state using an optical parametric amplifier (OPA) and a beam splitter (BS). This device can manipulate the output quantum light field by modulating two parameters: the intensity of the OPA and the transmittance of the optical BS. For the output quantum state associated with a symmetric BS, there is no quadrature squeezing. Moreover, neither photon correlation nor entanglement are observed. However, in terms of sum squeezing, the quantum state corresponding to the symmetric BS is the strongest. Therefore, an asymmetric BS and a highly squeezing OPA are the best choices for generating the quantum entangled squeezed states.
Cavity optomechanical systems involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling us to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the detuning of the laser pumping around the mechanical frequency, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regular periodic oscillation to a period-doubling motion, in which case the light-mechanical entanglement can be well studied by the logarithmic negativity and can manifest the dynamical transition the classical nonlinear dynamics. In addition, the optomechanical entanglement shows a second-order transition characteristic at the critical parametric gain. For the laser detuning being about twice the mechanical frequency, the kind of normal mode splitting comes up in the laser detuning dependence of optomechanical entanglement, which is induced by the squeezing of the optical and mechanical hybrid modes and finds no classical correspondence. The OPA-assisted optomechanical systems therefore offer a simple way to study and exploit quantum manifestations of classical nonlinear dynamics.
The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein–Podolsky–Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.
We consider specific signatures of squeezing for time-modulated light fields and propose the scheme of an optical parametric oscillator driven by a continuously modulated pump field. The application of a periodically modulated driving field instead of a continuous wave field drastically improves the degree of quadrature integral squeezing. This quantity goes below the standard limit of 50% relative to the level of vacuum fluctuations. We develop semiclassical and quantum theories of an optical parametric oscillator under the influence of a pump field with harmonically modulated amplitude for all operational regimes, including numerical simulations at the threshold point. The results can be directly applied in time-resolved quantum communication protocols.
We present a new analytical solution for Fokker–Planck equation of phase-mismatched frequency non-degenerate optical parametric amplifier (FNOPA). We investigate the squeezing and continuous variable (CV) entanglement characteristic of a FNOPA working at phase-mismatched condition. We numerically calculate the dependence of the CV entanglement on the relative loss parameter ξ and the phase-mismatched parameter η~. The smaller η~ can bring a long-time entanglement. This method can also be applied to multipartite entanglement situation.