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Journal of Physics B Atomic Molecular and Optical Physics

Macroscopic quantum self-trapping of an ultracold Bose–Fermi mixture in a double-well potential

Santiago F. Caballero-Benítez, Elena A. Ostrovskaya, M. Gulácsi, Yuri S. Kivshar

Published Oct 26, 2009• 12 citations
Publisher

Abstract

We study the macroscopic quantum self-trapping effect in a mixture of Bose–Einstein condensate (BEC) and quantum degenerate fermions, confined in a double-well potential with a variable separation between the wells. The fermions form a finite-size cloud that affects the static and dynamical properties of the BEC. In particular, our quasi-analytical and numerical analysis based on a mean-field model shows that the main features of macroscopic quantum self-trapping in a pure bosonic system are modified by the influence of fermions. Both the onset of self-trapping and the properties of the self-trapped state depend on the amount of fermions in the system as well as on the type of inter-species interaction. The properties of the quantum degenerate mixture are explored using realistic parameters for a 40 K– 87 Rb system.

DOI
10.1088/0953-4075/42/21/215308

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We study the macroscopic quantum self-trapping effect in a mixture of Bose–Einstein condensate (BEC) and quantum degenerate fermions, confined in a double-well potential with a variable separation between the wells. The fermions form a finite-size cloud that affects the static and dynamical properties of the BEC. In particular, our quasi-analytical and numerical analysis based on a mean-field model shows that the main features of macroscopic quantum self-trapping in a pure bosonic system are modified by the influence of fermions. Both the onset of self-trapping and the properties of the self-trapped state depend on the amount of fermions in the system as well as on the type of inter-species interaction. The properties of the quantum degenerate mixture are explored using realistic parameters for a 40 K– 87 Rb system.
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.
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.
Abstract We investigate the macroscopic quantum self-trapping (MQST) phenomenon of a spin–orbit-coupled Bose–Einstein condensate (BEC) in a double-well potential, emphasizing the critical behavior at the transition to MQST. We show that as the nonlinear parameter characterizing the atomic interaction increases, the spin–orbit-coupled BEC appears as MQST, manifesting an asymmetric distribution of the atom in two wells. Then, the effect of the initial condition on the critical behavior at the transition to MQST is given. Analytic expressions for the dependence of the transition parameters on the system parameters and the initial condition are derived, which are in agreement with our numerical simulations.
The quantum self-trapping phenomenon of a Bose-Einstein condensate (BEC) represents a remarkable nonlinear effect of wide interest. By considering a purely dipolar BEC in a double-well potential, we study how the dipole orientation affects the ground-state structure and the transition between self-trapping and Josephson oscillations in dynamics. Three-dimensional numerical results and an effective two-mode model demonstrate that the onset of self-trapping of a dipolar BEC can be radically modified by the dipole orientation. We also analyze the failure of the two-mode model in predicting the rate of Josephson oscillations. We hope that our results can motivate experimental work as well as future studies of self-trapping of ultracold dipolar gases in optical lattices.
We theoretically study the static and dynamic behavior of a BEC immersed in a large Fermi sea of ultracold atoms under conditions of tunable interspecies interaction. The degenerate Bose-Fermi mixture is kept in an elongated trap, typical for a single-beam optical dipole trap. We focus on the case of repulsive Bose-Fermi interaction and develop mean-field models to simulate the system over a wide range of repulsion strength. We further get analytical solutions in the regimes of phase separation and weak interaction. We obtain static density profiles and the frequency of the radial breathing mode, which is an elementary dynamic phenomenon of the mixture. Our results unveil the structure of the Bose-Fermi interface and describe the origin of the frequency shift of the breathing mode when the components become phase-separated at strong repulsion. We show that the mediated interaction between bosons induced by the Fermi sea can be understood as an adiabatic second-order mean-field effect, which is valid also beyond the weak-interaction regime for relevant experimental conditions. These results are consistent with our recent observations [Lous et al., Phys. Rev. Lett. 120, 243403 (2018); Huang et al., Phys. Rev. A 99, 041602(R) (2019)] in a mixture of 41K^{41}\mathrm{K}41K and 6Li^{6}\mathrm{Li}6Li.