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arXiv:2404.03230

Quantum Phases of a Dipolar Fermi Gas with Laser-assisted Interwire Tunneling

Jinxin Li, Xue-Jing Feng, Zhang, Ying-Ying, Jingxue Liu, Lu Qin, Zunlue Zhu, Xing-Dong Zhao, Liang‐Liang Wang

Published Apr 4, 2024• 0 citations
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Abstract

We systematically investigate unconventional superfluid phases of fermionic dipolar particles lying in a double-wire setup with laser-assisted interwire tunneling. Our numerical simulations, based on the nonlocal Kohn-Sham Bogoliubov-de Gennes equation, reveal the existence of a large Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) region with a stripe phase under an imbalance of particle densities between two wires. When the laser-assisted interwire tunneling is present, it induces a transition from the FFLO phase to the topological superfluid phase and the associated Majorana zero modes exhibit an oscillation structure, which is significantly enhanced by the long-range nature of the interwire dipolar interaction. This distinguishes itself from the results obtained with usual contact interaction and offers new opportunities for manipulating and reshaping Majorana zero modes by adjusting the degree of the nonlocality and the interwire separation.

DOI
10.48550/arxiv.2404.03230

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We systematically investigate unconventional superfluid phases of fermionic dipolar particles lying in a double-wire setup with laser-assisted interwire tunneling. Our numerical simulations, based on the nonlocal Kohn-Sham Bogoliubov-de Gennes equation, reveal the existence of a large Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) region with a stripe phase under an imbalance of particle densities between two wires. When the laser-assisted interwire tunneling is present, it induces a transition from the FFLO phase to the topological superfluid phase and the associated Majorana zero modes exhibit an oscillation structure, which is significantly enhanced by the long-range nature of the interwire dipolar interaction. This distinguishes itself from the results obtained with usual contact interaction and offers new opportunities for manipulating and reshaping Majorana zero modes by adjusting the degree of the nonlocality and the interwire separation.
Spin-orbit coupling (SOC) changes the Fermi surface and creates topological states with non-Abelian Majorana zero modes. However, it also drastically suppresses the Cooper pairing with finite momentum and thus the coexistence of Majorana zero modes and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is still challenging to be observed. In this work we introduce more complex interactions to the platform and investigate the unconventional superfluidity of a dipolar fermionic gas in a biwire configuration with the SOC induced by laser-assisted interwire tunneling. Employing a nonlocal self-consistent Bogoliubov--de Gennes formalism, we reveal a complex phase diagram featuring various topological-superfluid phases. In particular, due to the peculiar competition between the long-range dipolar interaction and the SOC, a phase separation structure emerges, exhibiting a stripe FFLO phase core encompassed by the topological-superfluid states. Moreover, the long-range dipolar interaction induces a remarkable oscillatory structure in the resultant Majorana zero modes at the FFLO phase boundary and enables direct manipulation of these zero modes. Finally, we provide an experimental proposal to realize our system and give the method to detect the novel quantum phase. The discovery of the Majorana zero modes at the interface between the FFLO state and the topological phase, along with their unique properties, deepens our understanding of Majorana fermions and enriches the zoo of Majorana quasiparticles.
We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value, the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with mostly a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the sss-wave and ppp-wave pairing in the order parameter.
We investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.
Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.
Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.
The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue for exploring new quantum matters. In experiments, the SO coupling is implemented simultaneously with a Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with nonzero center-of-mass momentum Cooper pairings, in contrast to the zero center-of-mass momentum pairings in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in SO-coupled Fermi gases in the presence of a large out-of-plane Zeeman field. In this paper, we address this question by studying the mean-field quantum phases of 1D (quasi-1D) SO-coupled fermionic cold-atom optical lattices.