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arXiv:2402.06977

Superfluid transition of disordered dipolar Fermi gases in a 2D lattice

Viktoriia Pinchenkova, Sergey I. Matveenko, Georgy V. Shlyapnikov

Published Feb 10, 2024• 0 citations
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Abstract

We consider a superfluid transition in two-component dipolar Fermi gases in a two-dimensional lattice with a weak on-site disorder. The momentum dependent dipole-dipole interaction amplitude violates the Anderson theorem and in the weakly interacting regime this leads to an increase of the superfluid transition temperature. We find that in a sufficiently deep lattice (tight-binding regime) and in the low momentum limit superfluid properties can be considered in the same way as in free space replacing the mass of atoms by an effective mass in the lattice. The disorder-induced increase of the critical temperature can be significantly more pronounced than in free space.

DOI
10.48550/arxiv.2402.06977

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We consider a superfluid transition in two-component dipolar Fermi gases in a two-dimensional lattice with a weak on-site disorder. The momentum dependent dipole-dipole interaction amplitude violates the Anderson theorem and in the weakly interacting regime this leads to an increase of the superfluid transition temperature. We find that in a sufficiently deep lattice (tight-binding regime) and in the low momentum limit superfluid properties can be considered in the same way as in free space replacing the mass of atoms by an effective mass in the lattice. The disorder-induced increase of the critical temperature can be significantly more pronounced than in free space.
We investigate the effect of weak disorder on the superfluid properties of two-component quasi-two-dimensional dipolar Fermi gases. The dipole-dipole interaction amplitude is momentum dependent, which violates the Anderson theorem claiming that the weak disorder has practically no influence on the superfluid transition temperature in the weakly interacting regime. We find that for dipolar fermions the transition temperature in this regime can be strongly increased by the disorder like in the purely two-dimensional case. However, the effect becomes smaller with increasing the intercomponent fermion-fermion interaction, and in the strongly interacting regime the superfluid transition temperature in the weak disorder becomes very close to that in the absence of disorder.
We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem that claims the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10nK10\phantom{\rule{0.16em}{0ex}}\mathrm{nK}10nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which has not been observed so far.
In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.
Many-body effects on superfluidity and transition temperatures are calculated for optical lattices and uniform systems with ultracold multi-component Fermi gases. The induced interactions depend sensitively on the interactions between the multi-components and their densities. The s- and d-wave pairing gaps and critical temperatures are calculated for optical lattices at low (dilute) filling as well as near half filling to leading orders in the interaction strength with and without induced interactions. They can deviate strongly from dilute two-component systems and affect the phase diagram. In two dimensional optical lattices the induced interactions are singular at half filling and strongly affect s- and d-wave superfluidity.
We show that atomic Fermi gases in quasi-two-dimensional (2D) geometries are promising for achieving superfluidity. In the regime of BCS pairing for weak attraction, we calculate the critical temperature Tc{T}_{c}Tc​ and analyze possibilities of increasing the ratio of Tc{T}_{c}Tc​ to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi-2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale.
We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn{n}_{n}nn​ and quantum depletion nd{n}_{d}nd​ both exhibit a characteristic 1/ln(1/n2Da2D2)1/\mathrm{ln}(1/{n}_{2\mathrm{D}}{a}_{2\mathrm{D}}^{2})1/ln(1/n2D​a2D2​) dependence. Their ratio nn/nd{n}_{n}/{n}_{d}nn​/nd​ increases to 222 compared to the familiar 4/34/34/3 in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.