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arXiv:1101.3643 · Physical Review A

Sign reversal of the boson-boson interaction potential in planar Bose-Fermi mixtures under a synthetic magnetic field

T. P. Polak

Published Jan 18, 2011• 1 citation
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Abstract

We study the mutually coupled, strongly interacting bosonic and noninteracting fermionic, species of unequal masses in the regime were the retardation effects are an important part of the physics. A cloud of neutral atoms experiences a synthetic magnetic field because of a vector potential that imposes a phase shift on the constituents. The magnetic field causes the oscillations of the magnitude and sign of the effective interaction between bosons from repulsive to attractive in contrast to the static case. We show that the dynamics for the gaseous Bose-Fermi mixtures when reaching the quantum-Hall regime becomes highly nontrivial.

DOI
10.1103/physreva.83.011602

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We study the mutually coupled, strongly interacting bosonic and noninteracting fermionic, species of unequal masses in the regime were the retardation effects are an important part of the physics. A cloud of neutral atoms experiences a synthetic magnetic field because of a vector potential that imposes a phase shift on the constituents. The magnetic field causes the oscillations of the magnitude and sign of the effective interaction between bosons from repulsive to attractive in contrast to the static case. We show that the dynamics for the gaseous Bose-Fermi mixtures when reaching the quantum-Hall regime becomes highly nontrivial.
We have studied eects of inter-species interaction of the bosons in a BoseFermi mixture over a large regime of particle numbers under the synthetic magnetic eld.Analytically derived formulas for the density of states for several values of the magnetic elds f = 1/2, 1/3, 1/4, 1/6, 1/8 and 3/8 allows us to calculate, with a very good accuracy, the eective interaction between bosons.The presence of the Hofstadter buttery spectrum and fermionic species induces alternating sign potential between neutral bosonic atoms.Consequently bosons can attract or repulse each other whether sign of it strongly depends on the strength of the magnetic eld applied to the sample.
The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied.An articial magnetic eld is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents.A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations eects of the fermion mediated interaction between bosons.In consequence the eective interaction between bosons can change the magnitude and sign.This provides possible explanations of the bosonic coherence loss observed experimentally in the time of ight and peak width experiments.
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.
We investigate magnetic properties and statistical effects in one-dimensional (1D) strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization, and susceptibility in the presence of an external magnetic field HHH are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value ${H}_{c}^{F}\ensuremath{\approx}\frac{8}{\ensuremath{\gamma}}{E}_{F}$, where EF{E}_{F}EF​ is the Fermi energy and $\ensuremath{\gamma}$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0H=0H=0 and the critical value $H={H}_{c}^{M}\ensuremath{\approx}\frac{16}{\ensuremath{\gamma}}{E}_{F}$. We find that a pure boson phase occurs in the absence of the external field, fully polarized fermions and bosons coexist for 0<H<HcM0<H<{H}_{c}^{M}0<H<HcM​, and a fully polarized fermion phase occurs for $H\ensuremath{\geqslant}{H}_{c}^{M}$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.
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.
Recent experiments performed with fermionic /sup 6/Li and /sup 40/K atoms, which possess both Feshbach resonances at convenient magnetic fields are discussed. When /sup 40/K is mixed with a Bose-Einstein condensate of /sup 87/Rb, for sufficient atom numbers of both species, a collapse of the Fermi gas is observed. This is the result of the strong interspecies attractive interaction which overcomes the Fermi pressure in the quantum degenerate regime. As for the case of phonon-induced interaction between electrons in superconductors, it is predicted that the boson-fermion attractive interaction favors Cooper pairing of fermions when prepared in a mixture of two states.