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International Journal of Modern Physics B

PERIODIC MODULATION ON THE BOSE–JOSEPHSON JUNCTION IN AN OPTICAL CAVITY

Bin Wang, Lei Tan

Published May 14, 2012• 0 citations
Publisher

Abstract

The periodic modulation on dynamic behavior of Bose–Josephson junction dispersively coupled to a single mode high-finesse optical cavity is investigated. The eigenenergies and the phase diagram of the system are obtained using the numerical methods under the mean field approximation. It is shown that the large atomic interaction strength will lead the eigenenergies to show a bistable and a loop structure. It is also found that the periodic modulation can change the period and frequency of the motion of the atoms and the intra cavity photons drastically. Furthermore, the strong condensate-field interplay will enhance the oscillation of the atoms and make some trapped atoms start oscillating. For certain parameters of the cavity field, the relative population oscillation exhibits a process from order to chaos.

DOI
10.1142/s021797921250083x

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The periodic modulation on dynamic behavior of Bose–Josephson junction dispersively coupled to a single mode high-finesse optical cavity is investigated. The eigenenergies and the phase diagram of the system are obtained using the numerical methods under the mean field approximation. It is shown that the large atomic interaction strength will lead the eigenenergies to show a bistable and a loop structure. It is also found that the periodic modulation can change the period and frequency of the motion of the atoms and the intra cavity photons drastically. Furthermore, the strong condensate-field interplay will enhance the oscillation of the atoms and make some trapped atoms start oscillating. For certain parameters of the cavity field, the relative population oscillation exhibits a process from order to chaos.
We study the mean-field dynamics of a Bose Josephson junction which is dispersively coupled to a single mode of a high-finesse optical cavity. An effective classical Hamiltonian for the Bose Josephson junction is derived, and its dynamics is studied from the perspective of a phase portrait. It is shown that the strong condensate-field interplay does alter the dynamics of the Bose Josephson junction drastically. The possibility of coherent manipulating and in situ observation of the dynamics of the Bose Josephson junction is discussed.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.
We use phase diagrams to study the mean-field dynamics of a spin–orbit coupled Bose–Josephson junction loaded in an optical cavity. We find that the spin Bose Josephson junction has four more combinations of 0- and π-phase motion modes than the bare junction. The spin–orbit coupling strength, the spin–weak atoms interaction energy, the cavity field drive and the cavity field detuning can increase the number of stable points of the Bose–Josephson junction energy. While the increase in cavity field dissipation would decrease the number of stable points of the energy. The increase in the number of 0- and π-phase motion modes will change the motion trajectory of atoms in the junction from a normal order to a disorder. This work indicates that quantum measurement and quantum simulation can be improved by controlling the dynamical quantities of spin atoms in a cavity.
We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.
Nonlinear systems, including atom–field interaction, are investigated due to their fundamental applications in quantum mechanics and rapidly growing fields of quantum communication, especially secure communication with chaotic dynamics. In this paper, we study the chaotic dynamics of a system consisting of an atomic Bose–Einstein condensate interacting with a quantized radiation field in a high-quality cavity with a periodically modulated length. The frequency modulation is adapted by a periodic time-dependent atom–field coupling strength. We use a semiclassical approach to decouple the atoms and field variables and then numerically solve the corresponding nonlinear dynamical equations of the system. Generally, the dynamics of the system sensitively depends on its initial conditions, thereby long-term prediction is impossible. We show that the system demonstrates the emergence of classical dynamical chaos from quantum electrodynamics. The chaotic behavior of energy transfer in the system can be enhanced by increasing the depth of frequency modulation. The strange attractor clearly illustrates that the system presents extremely exotic dynamics over a wide range of parameters. This implies that the dynamical quantities oscillate irregularly, never exactly repeating but always remaining in a bounded region of the phase space.