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Register a new userFermion pairing in mixed-dimensional atomic mixtures
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We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s$-wave, $p$-wave, $d_{x^2-y^2}$-wave, and $g_{xy(x^2-y^2)}$-wave pairing symmetries. Other instabilities such as a charge-density wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d$-wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d$-wave pairing), an even higher critical temperature may be achieved.
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Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments.
We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with $SU(2)times SU(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional ($s$-wave) number density waves are formed with a $pi$-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with $d_{xy}$-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the $d_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for $d_{xy}$-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to phase-space discrepancy for different inter-species Umklapp couplings. Using a phase space argument for leading corrections in the one-loop renormalization group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intra-species Umklapp couplings and that this triggers the $d_{xy}$-density-wave instability.
We use Quantum Monte Carlo (QMC) simulations to study the pairing mechanism in a one-dimensional fermionic system governed by the Hubbard model with attractive contact interaction and with imbalance between the two spin populations. This is done for the uniform system and also for the system confined in a harmonic trap to compare with experiments on confined ultra-cold atoms. In the uniform case we determine the phase diagram in the polarization-temperature plane and find that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is robust and persists to higher temperature for higher polarization. In the confined case, we also find that the FFLO phase is stabilized by higher polarization and that it is within the range of detection of experiments currently underway.
Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of $p$-wave pairing between spin polarised fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency/momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical temperature. Focusing on experimentally relevant systems, we perform a systematic analysis varying the boson-boson and boson-fermion interaction strength as well as their masses, and identify the most suitable system for realising a $p$-wave superfluid. Our results show that such a superfluid indeed is experimentally within reach using light bosons mixed with heavy fermions.
We theoretically investigate quantum-mechanical dynamics of quasi-one-dimensional boson-fermion mixtures of atomic gases trapped in a toroidal potential, where effective inter-atomic interactions are tunable and affect the dynamics. We especially focus on effects of quantum statistics and many-body correlations beyond the Hartree-Fock (HF) mean-field approximation on the dynamics. In order to predict the dynamics, we utilize the numerical exact diagonalization method and also reproduce the calculation in the HF approximation for comparison. The toroidal gases originally have a rotational symmetry in the toroidal direction. We firstly prepare a deformed ground state as an initial state by adding a weak potential deformed in the toroidal direction, and then remove the potential to start the dynamics. In the dynamics, number densities of the deformed gases exhibit oscillations as demonstrated in the present paper. As a result, we find out that the bosons and fermions show quite different behaviors owing to quantum statistics. In particular, the bosons exhibit a low-frequency oscillation in the strong boson-boson attraction regime owing to the many-body correlations, and it can not be reproduced in the HF approximation. The oscillation of the fermions is strongly influenced by that of the bosons through the boson-fermion interaction as a forced oscillator. In addition, we also discuss a relationship between the low-frequency oscillation and restoration of the broken symmetry.
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