It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: ω0 → ω1 + ω2, ω2 → ω1 + ω1 under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.
We demonstrate a quantum regime of dissipative nonlinear oscillators where the creation of Fock states as well as the superpositions of Fock states are realized for time-intervals exceeding the characteristic decoherence time. The preparation of quantum states is conditioned by strong Kerr nonlinearity as well as by excitation of resolved lower oscillatory energy levels with a specific train of Gaussian pulses. This provides practical signatures to look for in experiments with cooled nonlinear oscillators.
We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with time-dependent parameters and take place for the regimes of long time intervals exceeding dissipation time and for macroscopic levels of oscillatory excitation numbers. Two schemas of time modulation: (i) periodic variation of the strength of the χ(3) nonlinearity; (ii) periodic modulation of the amplitude of the driving force, are considered. These effects are obtained within the framework of phase-space quantum distributions. It is demonstrated that the Wigner functions of oscillatory mode in both bistable and chaotic regimes acquire negative values and interference patterns in parts of phase-space due to appropriately time-modulation of the oscillatory nonlinear dynamics. It is also shown that the time-modulation of the oscillatory parameters essentially improves the degree of sub-Poissonian statistics of excitation numbers.
We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.
We consider quantum dynamics of a parametrically driven anharmonic oscillator (PDAO) at a few-photon level. In this scheme the oscillatory mode is excited through the degenerate down-conversion process. This scheme could be experimentally realized in superconducting solid-state devices based on the nonlinearity of the Josephson junction or in cooled nano-mechanical oscillators. We investigate PDAO in the strong quantum regime that means strong Kerr-nonlinearity of the mode with respect to the mode's dissipation for two cases of excitations: by a monochromatic driving field or by a train of Gaussian pulses. We demonstrate production of the nonclassical oscillatory states with two-fold symmetry in phase-space which are approximately close to the lower pure Fock states. Production of the superposition of the Fock states for time-intervals exceeding the characteristic time of decoherence and dissipation is also shown.
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