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Acta Physica Sinica

Nonlinear Ramsey interference of Fermi superfluid gases in unitarity regime

Hongjuan Meng, Gou Xue-Qiang, Wen-Yuan Wang, Yang Yang, Ying Ma, Ma Yun-Yun, Duan Wen-Shan

Published Jan 1, 2012• 1 citation
Publisher

Abstract

We investigate the relationships between the nonlinear Ramsey interference pattern of the angular frequency and system parameters of fermi superfluid gase in unitarity regime in three limited cases. We find that the interaction between fermions and the difference in energy between double-well potentials have a significant influence on the angular frequency of the interference pattern. Through numerical simulation and theoretical analysis, the relationship between angular frequency of the interference pattern and the system parameters is given, and the numerical simulations and theoretical analyses are in good agreement.

DOI
10.7498/aps.61.197301

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We investigate the relationships between the nonlinear Ramsey interference pattern of the angular frequency and system parameters of fermi superfluid gase in unitarity regime in three limited cases. We find that the interaction between fermions and the difference in energy between double-well potentials have a significant influence on the angular frequency of the interference pattern. Through numerical simulation and theoretical analysis, the relationship between angular frequency of the interference pattern and the system parameters is given, and the numerical simulations and theoretical analyses are in good agreement.
The nonlinear Ramsey interferometry of Fermi superfluid gases in a double-well potential is investigated in this paper. We found that the frequency of the Ramsey fringes exactly reflects the strength of nonlinearity, or the scattering length of the Fermi superfluid gases. The cases of sudden limit, the adiabatic limit and the general case are studied. The analytical result is in good agreement with the numerical ones. The adiabatic condition is proposed. In general situation, the zero-frequency point emerge. Finally the possible applications of the theory are discussed.
We investigate the interference of the superfluid Fermi gases released from a double-well potential in the crossover from the unitarity limit to the Bose–Einstein condensate (BEC) limit. For two initially coupled Fermi superfluids, we show the formation of the clear and nonuniform interference fringes, in which the fringe spacing grows linearly in the evolution time, and the expansion velocity of the fringes increases significantly from the BEC limit to the unitarity limit. For two spatially separated Fermi superfluids, however, we show that in the strongly interacting regime, the interference patterns are characterized by the complicated spatial structures. By studying the interferences in the unitarity limit under different values of the strength of the double-well potential, we find that these complicated structures actually originate from the formations of spontaneous vortex rings, due to the transverse instability.
According to the theory of nonlinear Rosen-Zener tunneling, we investigate the nonlinear Ramsey interference of Bose-Einstein condensate in a double-well potential with Gaussian pulse. Rich Ramsey fringes are shown by the numerical simulations. The influences on the fringes of the atom-atom interaction and the period of Gaussian pulse are discussed. We obtain the analytical expression for the fundamental frequency of Ramsey fringes by using Hamilton equation. The relation of the frequency to the interaction strength and the Gaussian-pulse period is found by analyzing the fringes through Fourier transformation. The numerical simulations are consistent with our theoretical predictions.
We study the evolution of the interference patterns of strongly interacting Fermi gases in a harmonic trap after removal of the optical lattice, by numerically solving the superfluid order-parameter equation. We find that for the strongly interacting Fermi gas elastic collisions during the expansion blur the interference peaks. In order to obtain a nearly ballistic expansion, the fast magnetic field ramp technique is applied in experiment. We simulate the fast magnetic field ramp process before expansions of strongly interacting Fermi gases. We find that clear interference patterns are formed, and oscillate for a long time in the harmonic trap. We also calculate the interference patterns in different superfluid regimes, which accord with the experimental observations.
In the mean-field theory and two-mode approximation, we study the self-trapping of superfluid Fermi gases in the BEC regime and in unitarity by observing the evolution of the population imbalance with time and the variation of the average of population imbalance with several non-linear interaction parameters. The high-frequency modulations of both the symmetric double-well potential and the potential well are studied. The boundary conditions of the self-trapping and non-self-trapping are given. We find that high-frequency modulation in a certain range of modulation can make the self-trapping phenomenon easier to achieve. Finally, we study the influence of the initial value on self-trapping, and find that the increase of the absolute of the initial value can make the self-trapping more conducive to the realization.
We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.