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Register a new userA dipolar self-induced bosonic Josephson junction
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We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping phenomena in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions.
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We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACS) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find $1/N$ corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we find that also for a few atoms the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also the numerical results of SSB are better reproduced by the ACS approach with respect to the MF one. Instead the onset of MQST is correctly reproduced by ACS theory only in the large $N$ regime and, for this phenomenon, the $1/N$ correction to the MF formula is not reliable.
Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semi-classical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (0 phase mode) and four in the self-trapping regime ($pi$ phase mode), have been clearly shown. Systematic investigations of the common features behind these different scenarios have been 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 has been 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. Particularly, by analyzing the Poincare sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at 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 revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.
We study a model describing $N$ identical bosonic atoms trapped in a double-well potential together with a single impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the critical value of the coupling strength has the same dependence on the parameters as the critical coupling value in the Dicke model. We also show that, like the Dicke model, the mean-field dynamics go from being regular to chaotic above the bifurcation and macroscopic excitations of the bosons are observed. Overall, the boson-impurity system behaves like a poor mans version of the Dicke model.
The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a 1D asymmetric double-well potential is studied by solving the many-body Schrodinger equation numerically accurately. We examine how the loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric DW, the two wells are not equivalent anymore -the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right well. We examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-body position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well. However, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Overall, the many-body position and momentum variances bear the prominent signatures of the density oscillations of the system in the asymmetric double well as well as a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-body position variance.
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