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arXiv:1002.0557 · Europhysics Letters (EPL)

Phase transition, entanglement and squeezing in a triple-well condensate

Thiago F. Viscondi, K. Furuya, M. C. de Oliveira

Published Apr 1, 2010• 23 citations
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Abstract

We provide an in-depth characterization of a three-mode Bose-Einstein condensate trapped in a symmetric circular triple-well potential. We show how the purity related to the su (3) algebra scales for increasing number of atoms and signals the quantum phase transition between two dynamical regimes in a specific configuration. This measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state. Unlike the well-known double-well model, the triple-well model exhibits a first-order quantum phase transition, which could be investigated with the current trapping technology.

DOI
10.1209/0295-5075/90/10014

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We provide an in-depth characterization of a three-mode Bose-Einstein condensate trapped in a symmetric circular triple-well potential. We show how the purity related to the su (3) algebra scales for increasing number of atoms and signals the quantum phase transition between two dynamical regimes in a specific configuration. This measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state. Unlike the well-known double-well model, the triple-well model exhibits a first-order quantum phase transition, which could be investigated with the current trapping technology.
We present a complete analysis of the dynamics of a Bose–Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes the parameter dependence analysis of the equilibrium points and their local stability, which is closely related to the condensate collective behaviour. We also consider the effects of off-site interactions, and how these 'cross-collisions' may become relevant for a large number of trapped bosons. Even in the presence of cross-collisional terms, the model still features an integrable sub-regime, known as the twin-condensate dynamics, which corresponds to invariant surfaces in the classical phase space. However, the quantum dynamics preserves the twin-condensate defining characteristics only partially, thus breaking the invariance of the associated quantum subspace. Moreover, the periodic geometry of the trapping potential allowed us to investigate the dynamics of finite angular momentum collective excitations, which can be suppressed by the emergence of chaos. Finally, using the generalized purity associated with the su(3) algebra, we were able to quantify the dynamical classicality of a quantum evolved system, as compared to the corresponding classical trajectory.
We consider the ground-state structure of two-component Bose–Einstein condensates trapped in a triple-well potential. We observe three structural phases of self-trapping, phase separation and symmetry state phase, which reflect the interplay of the intraspecies and interspecies interactions. We also show that the transitions from the self-trapping phase to the symmetry phase and from the phase separation to the symmetry phase are first-order phase transitions, while the transition from the self-trapping phase to the phase separation phase is a continuous one.
We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
The generalized purity is employed for investigating the process of coherence loss and delocalization of the QQQ function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles (N)(N)(N). A power-law dependence of the critical parameter with NNN is derived.
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.
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an sss-wave scattering length a<0a<0a<0 and a three-body scattering hypervolume D>0D>0D>0. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.