Bistability and chaos at low levels of quanta

Abstract

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.

Multiphoton blockades in pulsed regimes beyond stationary limits

“…In this spirit, we emphasize the idea of improving the degree of quantum effects in open systems, as well as obtaining qualitatively new quantum effects by applying of the sequence of tailored pulses. This approach was recently exploited for formation of high degree continuous-variable entanglement in the nondegenerate optical parametric oscillator [27,28], and for investigation of quantum interference in mesoscopic domain [29][30][31]. Recently, generation of nonclassical states in cavity QED with pulsed input has been investigated in [26] and production of a superposition states in the periodically pulsed nonlinear resonator has been demonstrated in [30], [32].…”

Kicked nonlinear quantum scissors and entanglement generation

“…For instance, they were concerning generation of various quantum states of the field [1][2][3][4], quantum-optical properties of nonlinear structures [5][6][7] Moreover, nonlinear oscillator models were considered in a context of Einstein-Podolsky-Rosen paradox [8], construction various models of quantum nonlinear scissors (QNS) [9][10][11][12][13][14][15][16] or photon (phonon) blockade [17,18]. In this paper we shall concentrate on a new model involving two quantum nonlinear oscillators that behaves as qubit-qubit system and allow for generation of Bell states.…”

Excitations of photon-number states in Kerr nonlinear resonator at finite temperatures

“…(3) numerically based on quantum state diffusion method. The applications of this method for studies of driven anharmonic oscillator can be found in [6,8,9,29]. In the calculations, a finite basis of number states |n is kept large enough (where n max is typically 50) so that the highest energy states are never populated appreciably.…”

“…For this goal we investigate selective excitation in the pulsed regime, considering KNR driven by a sequence of classical Gaussian pulses separated by time intervals. This system has been used in the field of PB and generation of Fock states [6,8,9] as well as for production of superpositions states in a mesoscopic range [28] and for demonstration of chaos at a low level of quanta [29,30].…”