Stability and anomalous compressibility of Bose gases near resonance: The scale-dependent interactions and thermal effects

Abstract

The stability of Bose gases near resonance has been a puzzling problem in recent years. In this Letter, we demonstrate that in addition to generating thermal pressure, thermal atoms enhance the repulsiveness of the scale-dependent interactions between condensed atoms due to renormalization effect and further stabilize the Bose gases. Consequently, we find that, as a precursor of instability, the compressibility develops an anomalous structure as a function of scattering length and is drastically reduced compared with the mean-field value. Furthermore, the density profile of a Bose gas in a harmonic trap is found to develop a flat top near the center. This is due to the anomalous behavior of compressibility and can be a potential smoking gun for probing such an effect. Recently, interest in interacting quantum gases has been revived due to the application of Feshbach resonance [1][2][3][4][5]. Feshbach resonance provides the tunability of the scattering length a, which uniquely characterizes the low-energy inter-particle interaction, from zero to infinity and also from negative to positive. It offers an easy experimental access to resonant quantum gases. Since the conventional perturbation theories are no longer valid for these strongly interacting systems, we are confronted with the theoretical challenge of unravelling the puzzle of large-scattering-length physics. Among the various applications of Feshbach resonance, what has attracted particular interest is the atomic Bose gas at large positive scattering lengths, known as the resonant Bose gas on the upper branch of a Feshbach resonance [6][7][8][9][10][11][12][13][14][15][16][17][18].For a dilute Bose gas where the scattering length is small and positive, the dominant contribution to its chemical potential is described by the Hartree-Fock mean-field value, µ HF = 4πan, with n the number density of the particles. The leading order correction to the mean-field result is proportional to a dimensionless parameter √ na 3 , and the dilute limit is hence defined as na 3 ≪ 1. Near resonance where na 3 ∼ 1 or ≫ 1, the dilute-gas theory [19][20][21][22][23][24][25][26][27] is not applicable and several nonperturbative approaches have been taken to understand resonant many-body physics. They all predict the fermionization of bosons near resonance, which denotes that the chemical potential of the Bose gas reaches nearly the Fermi energy of a Fermi gas with the same density [28][29][30]. In other words, the chemical potential of a Bose gas is predicted to increase linearly with a in the meanfield regime when na 3 ≪ 1 and saturate at an energy scale defined by n as resonance is approached. These theory predictions so far are consistent with experimental studies on chemical potentials [8].One of the major challenges of creating and probing unitary Bose gases experimentally comes from the short lifetime of the gases. Overcoming this difficulty has been one of the main focuses of a few recent experimental efforts [11,14,18]. Especially, a very interesting attempt was made a ...

Topological supersolidity of dipolar Fermi gases in a spin-dependent optical lattice

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