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Chinese Physics Letters

Nonlocal Measure Synchronization in Coupled Bosonic Josephson Junctions

Tian Jing, Haibo Qiu, Chen Yong

Published Jul 1, 2010• 8 citations
Publisher

Abstract

We investigate the measure synchronization (MS) in two coupled bosonic Josephson junctions. By tuning up the coupling between the two dynamical systems, in addition to the normal MS, a nonlocal MS (NLMS) state is observed. Furthermore, with the dynamic stability analysis, we present the exact analytical solution of the transition point to NLMS.

DOI
10.1088/0256-307x/27/7/070501

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We investigate the measure synchronization (MS) in two coupled bosonic Josephson junctions. By tuning up the coupling between the two dynamical systems, in addition to the normal MS, a nonlocal MS (NLMS) state is observed. Furthermore, with the dynamic stability analysis, we present the exact analytical solution of the transition point to NLMS.
We present measure synchronization (MS) in a bosonic Josephson junction with spin-orbit coupling. The two atomic hyperfine states are coupled by a Raman dressing scheme, and they are regarded as two orientations of a pseudo-spin-1/21/21/2 system. A feature specific to a spin-orbit-coupled (SOC) bosonic Josephson junction is that the transition from non-MS to MS dynamics can be modulated by Raman laser intensity, even in the absence of interspin atomic interaction. A phase diagram of non-MS and MS dynamics as functions of Raman laser intensity and Josephson tunneling amplitude is presented. Taking into account interspin atomic interactions, the system exhibits MS breaking dynamics resulting from the competition between intraspin and interspin atomic interactions. When interspin atomic interactions dominate in the competition, the system always exhibits MS dynamics. For interspin interaction weaker than intraspin interaction, a window for non-MS dynamics is present. Since SOC Bose-Einstein condensates provide a powerful platform for studies on physical problems in various fields, the study of MS dynamics is valuable in researching the collective coherent dynamical behavior in a spin-orbit-coupled bosonic Josephson junction.
Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semiclassical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (the zero-phase mode) and four in the self-trapping regime (the π-phase mode), are clearly shown. Systematic investigations of the common features behind these different scenarios are performed. We show that the average energies of the two species merge at the MS transition point. The scaling of the power law near the MS transition is verified and the critical exponent is 1/2 for all of the different scenarios for MS. We also illustrate MS in a three-dimensional phase space; from this illustration, more detailed information on the dynamical process can be obtained. In particular, by analyzing the Poincaré sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at the MS transition point and such behavior depicts the general mechanism behind the different scenarios for the MS transitions. The new critical behavior found in a two-species BJJ is expected to be found in real systems of atomic Bose gases.
Abstract In this paper, by employing an occasionally coupling scheme in a two-species bosonic Josephson junction, it is found that for nonlocal measure synchronized states appearing in the two dynamic modes, known as 0-phase mode and π phase mode, their broken-symmetry can be restored. Nevertheless, there are dramatic differences for the results. For 0-phase mode, we can restore the broken symmetry by turning the nonlocal MS state into a conventional quasiperiodic MS state. However, for the π -phase mode, the broken symmetry is restored accompanied by the appearance of chaotic MS states.
In this paper, we investigate the dynamical synchronization of atomic populations in two Bosonic Josephson junctions(BJJs). The two BJJs are placed in two optical cavities, respectively. When there is no coupling between the two optical cavities, the dynamical evolution of the two BJJs is independent, and they can be in macroscopic quantum self-trapping regime or Josephson oscillation regime by controlling the strength of the interatomic interactions, respectively. However, when there is a coupling between the two optical cavities, we can adjust an external driving field to a specific value so that the two BJJs are dynamically synchronized even though the parameters of the two subsystems are different. We also found that it is possible to control the transition of the BJJ from the Josephson oscillation regime to the macroscopic quantum self-trapping regime by controlling the strength of the external driving field.
We study an atomic Josephson junction (AJJ) in the presence of two interacting Bose–Einstein condensates (BECs) confined in a double-well trap. We assume that bosons of different species interact with each other. The macroscopic wavefunctions of the two components obey a system of two 3D coupled Gross–Pitaevskii equations (GPEs). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODEs), for which the coupled pendula represent the mechanical analogues. These differential equations control the dynamical behaviour of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and nonzero—the macroscopic quantum self-trapping (MQST)—time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPEs and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signals the onset of MQST.
We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.