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Journal of the Physical Society of Japan

Interaction Effects on Phase Stiffness in Bose–Fermi Mixture Systems

Somei Suga, Kenta Shiina, 弘之 森

Published Apr 26, 2017• 0 citations
Publisher

Abstract

Bose–Fermi atom mixture systems confined in a ring geometry threaded by a synthesized magnetic field were theoretically investigated in numerical and analytical approaches. Numerical simulations were performed to study effects of the boson–boson interactions and boson–fermion interactions on phase stiffness. In the simulations, the phase stiffness was measured for repulsive and attractive boson–fermion interactions and found to increase with the repulsive interactions and decrease with the attractive ones. There was also a characteristic behavior found in the phase stiffness with the attractive interactions under a certain condition of the particle number. We confirmed these effects by renormalization group calculations including higher-order fluctuations.

DOI
10.7566/jpsj.86.054002

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Bose–Fermi atom mixture systems confined in a ring geometry threaded by a synthesized magnetic field were theoretically investigated in numerical and analytical approaches. Numerical simulations were performed to study effects of the boson–boson interactions and boson–fermion interactions on phase stiffness. In the simulations, the phase stiffness was measured for repulsive and attractive boson–fermion interactions and found to increase with the repulsive interactions and decrease with the attractive ones. There was also a characteristic behavior found in the phase stiffness with the attractive interactions under a certain condition of the particle number. We confirmed these effects by renormalization group calculations including higher-order fluctuations.
Persistent current of a Bose–Fermi mixture confined in a ring geometry threaded by a synthesized magnetic field is theoretically investigated. Numerical simulations are performed to study the role of boson–boson interactions and that of boson–fermion interactions on the transport property. The result shows that the boson–fermion interactions enhance the phase stiffness, which is a measure of the magnitude of the persistent current, more for the bosons than for the fermions. The same behavior is verified by a renormalization group calculation. The difference in the stiffness enhancement can be attributed to the difference in the localization property of the bosons and the fermions in one dimension.
We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.
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We investigate the problem of mechanical stability in two-dimensional Bose-Fermi mixtures at zero temperature, focusing on systems with a tunable Bose-Fermi (BF) interaction and a weak but finite boson-boson (BB) repulsion. The analysis is carried out within the framework of the lowest-order constrained variational (LOCV) approach, which allows for a nonperturbative treatment of strong interspecies correlations while retaining analytical transparency. The BF interaction is modeled by a properly regularized attractive contact potential, enabling the exploration of both the attractive and repulsive energy branches. We determine the minimal BB repulsion required to ensure mechanical stability of the mixture by evaluating the inverse compressibility matrix over the full range of BF coupling strengths, within the domain of validity of the LOCV approximation. The interaction contribution to the energy is benchmarked against available experimental data and quantum Monte Carlo results in the single-impurity limit, showing good agreement. Our analysis reveals how the critical BB coupling depends on interaction strength, density imbalance, and mass ratio. In particular, we find that mixtures with equal boson and fermion masses exhibit enhanced stability, requiring the smallest BB repulsion to prevent mechanical instability. In this case, a relatively small BB interaction is sufficient to stabilize attractive mixtures for all values of the BF interaction. These results provide a theoretical framework for assessing stability conditions in experimentally realizable two-dimensional Bose-Fermi mixtures with tunable interactions.