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arXiv:2210.10407 · Physical Review A

Dynamic structure factor of one-dimensional Fermi superfluid with spin-orbit coupling

Zheng Gao, Lianyi He, Huaisong Zhao, Shi-Guo Peng, Peng Zou

Published Jan 12, 2023• 8 citations
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Abstract

We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Our theoretical results display four kinds of single-particle excitations induced by the two-branch structure of the single-particle spectrum, and the cross single-particle excitation is much easier to see in the spin dynamic structure factor at a small transferred momentum. Also we find a new rotonlike collective mode emerges at a fixed transferred momentum $q\ensuremath{\simeq}2{k}_{F}$, and it only appears once the system enters the topological superfluid state. The occurrence of this rotonlike excitation is related to the switch of the global minimum in the single-particle spectrum from $k=0$ to $k\ensuremath{\simeq}2{k}_{F}$.

DOI
10.1103/physreva.107.013304

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We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Our theoretical results display four kinds of single-particle excitations induced by the two-branch structure of the single-particle spectrum, and the cross single-particle excitation is much easier to see in the spin dynamic structure factor at a small transferred momentum. Also we find a new rotonlike collective mode emerges at a fixed transferred momentum q\ensuremath≃2kFq\ensuremath{\simeq}2{k}_{F}q\ensuremath≃2kF​, and it only appears once the system enters the topological superfluid state. The occurrence of this rotonlike excitation is related to the switch of the global minimum in the single-particle spectrum from k=0k=0k=0 to k\ensuremath≃2kFk\ensuremath{\simeq}2{k}_{F}k\ensuremath≃2kF​.
We theoretically calculate the dynamic structure factor of a two-dimensional Rashba-type spin-orbit-coupled (SOC) Fermi superfluid with the random phase approximation and analyze the main characters of dynamical excitation shown by both density and spin dynamic structure factors during a continuous phase transition between a Bardeen-Cooper-Schrieffer superfluid and a topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to the two-branch structure of the quasiparticle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless DDDDDD-type pair-breaking excitation at the critical Zeeman field hc{h}_{c}hc​ and is imparted a finite width to phonon peak when the transferred momentum q\mathit{q}q is around the Fermi vector kF{k}_{F}kF​. At a much larger transferred momentum (q=4kF)(\mathit{q}=4{k}_{F})(q=4kF​), the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.
Abstract Exploring anisotropic dynamics in exotic superconductors or superfluids with spin–orbit coupling (SOC) is essential for understanding the role of SOC in these systems. We theoretically calculate the density dynamical structure factor of a two-dimensional Fermi superfluid with Raman-type SOC and investigate its primary anisotropic dynamical characteristics under varying SOC strengths during the Lifshitz phase transition. Owing to the recoil momentum of the SOC laser beam, both the collective phonon mode and the single-particle excitations exhibit distinct anisotropic behavior. In contrast to superfluids without SOC, the phonon mode under SOC not only has a shorter lifetime due to stronger competition with single-particle excitations but also exhibits an anisotropic sound velocity. The sound velocity initially decreases and then increases as the SOC strength increases. Moreover, three types of threshold energies for single-particle excitations to break Cooper pairs are identified, which elucidate the complex edge curves of the dynamical structure factor.
We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation approach at zero temperature, and find their dynamical characters across the phase transition from a balanced conventional Bardeen-Cooper-Schrieffer (BCS) superfluid to a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a Bose-Einstein-condensate-like regime of the Fermi superfluid, dynamic structure factors can help distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition from BCS to Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum where the collective phonon excitation acquires a finite width, and also a relatively strong atomic excitation at a large transferred momentum, because of the existence of unpaired Fermi atoms. Our results can be used to differentiate Sarma superfluid from BCS superfluid.
We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum ppp, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum ppp, and separates two kinds of single-particle excitations in the positive ppp direction. However, this higher mode disappears in the opposite direction of ppp, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment.
We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh and study all of the dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of center-of-mass momentum ppp, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum ppp and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation in the positive ppp direction. However, this higher mode disappears in the opposite direction of ppp, where two single-particle excitations overlap with each other. These signals of dynamical excitations could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.
We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6 Li or 40 K atoms using Bragg spectroscopy.