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arXiv:1312.2850 · Physical Review E

Measure synchronization in a two-species bosonic Josephson junction

Jing Tian, Haibo Qiu, Guanfang Wang, Yong Chen, Libin Fu

Published Sep 6, 2013• 32 citations
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Abstract

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.

DOI
10.1103/physreve.88.032906

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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.
We investigate dynamical phase transitions that are induced by interspecies interaction in a two-species bosonic Josephson junctions (BJJ), based on semi-classical theory. In zero-phase mode, similar to the case of a single-species BJJ, we observe the well-known dynamical phase transition from Josephson oscillation to self-trapping, which can be induced by both enhanced repulsive and attractive interspecies interactions. In π phase mode, dynamical phase transitions are even more interesting and counter-intuitive. We characterize a dynamical phase transition with the merging of two separate phase space domains into one, which is induced by increasing repulsive interspecies interaction. On the other hand, we find that by increasing attractive interspecies interaction, a phase separation of two formally overlapped phase space domains will occur. At last, we reveal that these intriguing dynamical phase transitions are caused by different kinds of bifurcations.
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.
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.
We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. 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 Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.