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Physical Review A

Effects of nonlinear dispersion on squeezed states in two-photon devices

P. Garca-Fernández, Francisco Javier Bermejo

Published Feb 1, 1989• 4 citations
Publisher

Abstract

The deleterious effects of nonlinear dispersion on squeezed light in two-photon devices when absorption losses are included have been analyzed making use of the variables called two-mode quadrature-phase amplitudes. The uncertainties in the quadrature amplitudes have been computed from a generalized Fokker-Planck equation. The dependence of squeezing on the nonlinear coupling, the modulation (including the case of high modulations), the pumping phase (where nonlinear dispersion causes an intensity-dependent shift in the minimum squeezing), and the absorption losses have been studied.

DOI
10.1103/physreva.39.1869

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The deleterious effects of nonlinear dispersion on squeezed light in two-photon devices when absorption losses are included have been analyzed making use of the variables called two-mode quadrature-phase amplitudes. The uncertainties in the quadrature amplitudes have been computed from a generalized Fokker-Planck equation. The dependence of squeezing on the nonlinear coupling, the modulation (including the case of high modulations), the pumping phase (where nonlinear dispersion causes an intensity-dependent shift in the minimum squeezing), and the absorption losses have been studied.
This paper introduces a new formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes are created or destroyed two at a time. The key property of a two-photon device is that it excites pairs of output modes independently. Thus our new formalism deals with two modes at a time; a continuum multimode description can be built by integrating over independently excited pairs of modes. For a pair of modes at frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\epsilon}, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency \ensuremath{\epsilon} of waves ``cos[\ensuremath{\Omega}(t-x/c)]'' and ``sin[\ensuremath{\Omega}(t-x/c)]'' and (ii) two-mode squeezed states, which are the output states of an ideal two-photon device. The quadrature-phase amplitudes and the two-mode squeezed states serve as the building blocks for our formalism; their properties and their physical interpretation are extensively investigated.
Squeezed states of light are theoretically investigated in a system with a locally placed two-photon absorption medium. We assume that the two-photon absorption process is caused by elementary excitations in the medium (such as biexcitons). Many eigenmodes of photons and those of the elementary excitations are taken into account because of the locality of the absorber. Multi-mode Wigner functions are defined and used for representation of the density operator of the electromagnetic field. The Wigner functions exhibit multi-variable Gaussian distribution and the quantum states of photons are multi-mode quadrature squeezed states. We also discuss effects on squeezing due to detuning of the incident light, the size of the medium, the position of a photo-detector, and damping rates of photons and the elementary excitations.
A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
Squeezing in both intracavity and travelling-wave multiphoton absorption is investigated theoretically for incident intense nearly coherent light. It is shown that after sufficiently strong travelling-wave k-photon absorption (k=2,3...) a squeezed state of the radiation field is reached that is not a minimum uncertainty state. In this state the inphase and quadrature variances of the normalized electric field strength approach the asymptotic values k/(4(2k-1)) and k/4, respectively. With the help of an approximate Heisenberg picture treatment of a continuous mode field travelling through a broad-band k-photon absorber an analytical expression is obtained for the evolution of the squeezing spectrum in dependence on the degree of absorption. For intracavity multiphoton absorption the spectrum of output squeezing is investigated with the help of the usual Langevin equation approach. It turns out that the squeezing bandwidth in intracavity and travelling-wave multiphoton absorption is determined by the cavity bandwidth and the absorber linewidth, respectively.
Quantum statistical properties of interacting optical fields in Kerr nonlinear couplers may be regarded as one of the most fundamental problems yet to be solved in quantum optics. As an analytical solution to this system is not always possible, a semi-analytic or direct numerical solution must be employed in order to obtain a more complete description of their evolution. This study investigates the quantum properties of four-mode couplers composed of two and four Kerr nonlinear waveguides, both with and without cavity set up via phase space representation. In these systems, the electromagnetic fields are described by their Hamiltonians, while the time-evolution of the systems are described by the Von-Neumann equation. Following standard techniques, the master equations for the density matrices of the systems are obtained and further converted to the corresponding classical Fokker- Planck equations using both positive P and Wigner representations. The corresponding set of Langevin Stochastic equations is then obtained from the Fokker-Planck equations by means of Ito rules. Finally, the systems are integrated numerically and averaged over many trajectories to get the relevant information. The effects of self-action nonlinearity, cross-action coupling and the initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Furthermore, the influences of multimode interaction on the dynamics of the squeezed states are discussed. In this research, we show that the system may produce squeezed states in both quadrature variances for all calculated parameters. The multimode two channel model can provide better squeezing in contrast to the conventional device. The amplitude oscillation of maximal squeezing may be amplified by manipulation of the initial state of the coherent light in the first mode, and the range may be extended through multimode interaction. When the model is contained in a cavity, the system is able to generate better amplitude oscillations and squeezing range with leaf-revival-collapse-like behaviour; with the whole oscillation able to evolute below the standard quantum limit Regular photon transition and self trapping effects of the interacting modes in the four channels model are simulated, and squeezing is predicted for various initial intensities of the coherent field and nonlinear coupling parameter g. The cavity setup caused the system to undergo fluctuation amplification and the potential for different types of squeezing to be generated is observed. Depending on how we choose the interaction parameter values, the system may generate better squeezing in comparison to the cavity-less model.