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arXiv:1204.5896 · Physical Review A

Dynamical effects of exchange symmetry breaking in mixtures of interacting bosons

Malte C. Tichy, Jacob Friis Sherson, Klaus Mølmer

Published Dec 26, 2012• 6 citations
arXivHTMLPDF

Abstract

In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of interparticle interaction to interwell tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, that is, which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.

DOI
10.1103/physreva.86.063630

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In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of interparticle interaction to interwell tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, that is, which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.
We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.
In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a Bose-Einstein condensate (BEC) with weak repulsive interaction is confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically is positioned in the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theory to describe the evolution of the BEC in the double-well potential through the time-dependent Gross-Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, and hence can be simulated as well by a Gross-Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which results in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction among fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be expressed in three forms: the phase tends to be negative and monotonically decreases with time, the phase evolves with time, and the phase tends to be positive and increases monotonically with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in a Bose-Fermi superfluid mixture by varying different interaction parameters via Feshbach resonance and confinement-induced resonance.
We study the macroscopic quantum self-trapping effect in a mixture of Bose-Einstein condensate and a large number of quantum degenerate fermions, trapped in a double-well potential with a variable separation between the wells. The large number of fermions localized in each well form quasi-static impurities that affect the dynamics of the bosonic cloud. Our semi-analytical analysis based on a mean-field model shows that main features of macroscopic quantum self trapping in a pure bosonic system are radically modified by the influence of fermions, with both the onset of self-trapping and properties of the self-trapped state depending on the fermion concentration as well as on the type of inter-species interaction. Remarkably, repulsive inter-species interaction leads to population inversion of the bosonic energy levels in the trapping potential and hence to the inversion of symmetry of the macroscopic wavefunction. Realistic physical estimates are given based on experimental parameters for a 40^{40}40K-87^{87}87Rb system.
We consider an ultracold bosonic binary mixture confined in a quasi-one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled to each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the interwell population imbalance of each component and of the polarization, which is the imbalance of the total populations of the two species. From this set of equations we disentangle the different macroscopic quantum tunneling and self-trapping scenarios occurring for both population imbalances and the polarization in terms of the interplay between the interatomic interactions and the other relevant energies in the problem, like the spin-orbit coupling or the conventional tunneling term. We find a rich dynamics in all three variables and discuss the experimental feasibility of such a system.
This work contains a detailed analysis of the properties of the ground state of a two-component two-site Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters, while the hopping terms are kept fixed. To characterize the ground state, we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites, and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy, or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g., Schr\"odinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.
We study the dynamics of Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double well potential. Two interesting mixture genuine effects are identified. First, we find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. Secondly, in the balanced population case, the Josephson oscillations behave as if the interatomic interactions have been partially cancelled. This effect could be used as a new procedure to measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are physically interpreted in terms of an analytical description of the binary mixture using a two-mode model.