Collective Excitations of a Dipolar Bose—Einstein Condensate in an Anharmonic Trap

Abstract

The collective excitations of a one-dimensional dipolar Bose-Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.

Anharmonicity-induced phase transition of spin–orbit coupled Bose–Einstein condensates

“…Before the realization of the SO coupled BECs, the influence of weakly deviated pure harmonic potential (hereafter called anharmonicity) on the properties of condensates (both the ground state [13,[23][24][25][26][27][28][29][30][31][32] and the dynamic properties [22,[33][34][35][36][37][38][39][40][41][42][43]) has been extensively studied, and it is found that the anharmonicity of trapping potential affects one-component condensates [26-29, 33-37, 39, 40], dipolar condensates [38] and rotating condensates [23,24,30]. For one-component condensates, the anharmonicity not only makes condensates with a positive scattering length become metastable condensates [44], but also modifies the frequency of collective oscillations such as dipole and breathing modes [33-35, 37, 39, 40, 45].…”

“…For rotating condensates, the anharmonicity allows one to increase the rotation frequency of the condensates above the trap frequency [23], and the resulting change in the ground state phase diagram of the rotating condensates is obtained [24]. For dipolar condensates, the collapse and revival of the collective excitation of condensates can be affected by dipole-dipole interactions and anharmonic distortion [38]. For the thermodynamic properties of condensates, the specific heat, transition temperature and condensation fraction of interacting Bose gases are also modified by anharmonic potential [27].…”

Dynamics of Bose-Einstein condensates under anharmonic trap

“…Within the precise underlying Gross-Pitaevskii (GP) framework, the dynamics of a BEC in an anharmonic potential was studied explicitly in [29,30]. Indeed, the oscillation modes of a 1D BEC trapped in anharmonic potential were discussed with a system of twobody interaction [31,32], two-body and three-body interaction at a low temperature [33,34], as well as for finite temperature [35], and dipolar Bose gas in [36][37][38][39]. The oscillation modes of a 3D BEC in an anharmonic trap were studied in [40].…”