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arXiv:0704.0650 · Physical Review A

Coherent mesoscopic quantum tunneling in boson-fermion mixtures

Dmitry Mozyrsky, Ivar Martin, Eddy Timmermans

Published Nov 1, 2007• 7 citations
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Abstract

We show that cold atom systems of simultaneously trapped Bose-Einstein condensates (BECs) and quantum degenerate fermionic atoms provide promising laboratories for the study of macroscopic quantum tunneling. Our theoretical studies reveal that the spatial extent of a small trapped BEC immersed in a Fermi sea can tunnel and coherently oscillate between the values of the separated and mixed configurations (the phases of the phase separation transition of BEC-fermion systems). We evaluate the period, amplitude, and dissipation rate for $^{23}\mathrm{Na}$ and $^{40}\mathrm{K}$ atoms, and we discuss the experimental prospects for observing this phenomenon.

DOI
10.1103/physreva.76.051601

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Journal of Atomic and Molecular Physics•Jan 1, 2006•0 citations
We show that cold atom systems of simultaneously trapped Bose-Einstein condensates (BECs) and quantum degenerate fermionic atoms provide promising laboratories for the study of macroscopic quantum tunneling. Our theoretical studies reveal that the spatial extent of a small trapped BEC immersed in a Fermi sea can tunnel and coherently oscillate between the values of the separated and mixed configurations (the phases of the phase separation transition of BEC-fermion systems). We evaluate the period, amplitude, and dissipation rate for 23Na^{23}\mathrm{Na}23Na and 40K^{40}\mathrm{K}40K atoms, and we discuss the experimental prospects for observing this phenomenon.
The kinetics of the phase separation transition in boson-fermion cold-atom mixtures is investigated. We identify the parameters at which the transition is governed by a quantum nucleation mechanism, responsible for the formation of critical nuclei of a stable phase. We demonstrate that for low fermion-boson mass ratio the density dependence of the quantum nucleation transition rate is experimentally observable. The crossover to the macroscopic quantum tunneling regime is analyzed. Based on a microscopic description of interacting cold-atom boson-fermion mixtures, we derive an effective action for the critical droplet and obtain an asymptotic expression for the nucleation rate in the vicinity of the phase transition and near the spinodal instability of the mixed phase. We show that dissipation due to excitations in the fermion subsystem play a dominant role close to the transition point.
The experimental study of condensate mixtures is a particularly exciting application of the recently developed atomic-trap Bose-Einstein condensate (BEC) technology: such multiple condensates represent the first laboratory systems of distinguishable boson superfluid mixtures. In addition, as the authors point out in this paper, the possibility of inter-condensate tunneling greatly enhances the richness of the condensate mixture physics. Not only does tunneling give rise to the oscillating particle currents between condensates of different chemical potentials, such as those studied extensively in the condensed matter Josephson junction experiments, it also affects the near-equilibrium dynamics and stability of the condensate mixtures. In particular, the stabilizing influence of tunneling with respect to spatial separation (phase separation) could be of considerable practical importance to the atomic trap systems. Furthermore, the creation of mixtures of atomic and molecular condensates could introduce a novel type of tunneling process, involving the conversion of a pair of atomic condensate bosons into a single molecular condensate boson. The static description of condensate mixtures with such type of pair tunneling suggests the possibility of observing dilute condensates with the liquid-like property of a self-determined density.
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.
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 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.