玻色-费米超流混合体系中的相互作用调制隧穿动力学

Interaction-modulated tunneling dynamics of a mixture of Bose-Fermi superfluid

研究了玻色-费米超流混合体系中的相互作用调制隧穿动力学特性,其中玻色子位于对称双势阱中,费米子位于对称双势阱中心的简谐势阱中.采用双模近似方法得到描述双势阱玻色-爱因斯坦凝聚的动力学特性方程组,并将其与简谐势阱中分子玻色-爱因斯坦凝聚的Gross-Pitaevskii方程进行耦合.通过对不同参数下玻色-费米混合体系中的隧穿现象进行数值研究,发现简谐势阱中费米子与双势阱中玻色子的相互作用使双势阱玻色-爱因斯坦凝聚的隧穿动力学特性更加丰富.不但驱使双势阱中玻色-爱因斯坦凝聚从类约瑟夫森振荡转变为宏观量子自囚禁,而且宏观量子自囚禁表现为三种不同的形式:相位与时间呈负相关并随时间单调减小的自囚禁、相位随时间演化有界的自囚禁以及相位与时间呈正相关并随时间单调增大的自囚禁.

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 twobody 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.