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arXiv:2312.01181 · Communications in Theoretical Physics

Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase

Zeqing Wang, Ran Qi

Published Mar 19, 2024• 1 citation
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Abstract

Abstract Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.

DOI
10.1088/1572-9494/ad3543

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Abstract Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.
Motivated by recent experimental progress, we make an investigation of ppp- and ddd-wave resonant Bose gas. An explanation of the Nozi\`eres and Schmitt-Rink (NSR) scheme in terms of two-channel model is provided. Different from the sss-wave case, high-partial-wave interaction supports a quasibound state in the weak-coupling regime. Within the NSR approximation, we study the equation of state, critical temperature, and particle population distributions. We clarify the effect of the quasibound state on the phase diagram and the dimer production. A multicritical point where normal phase, atomic superfluid phase, and molecular superfluid phase meet is predicted within the phase diagram. We also show the occurrence of a resonant conversion between solitary atoms and dimers when temperature kBT{k}_{B}TkB​T approximates the quasibound energy.
The low-energy modes of a superfluid atomic Fermi gas at zero temperature are investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase is studied in detail. The atoms are assumed to be in only one internal state, so that for a sufficiently diluted gas the pairing of fermions can be considered effective in the l=1 channel only. In agreement with previous works on p-wave superfluidity in Fermi systems, it is found that the px+ipyp_x+ip_ypx​+ipy​ phase represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS) and BEC sides. Our calculations show that at low energy three branches of collective modes can emerge, with different species of dispersion relations: a phonon-like mode, a single-particle-like mode and a gapped mode. A comparison with the Bogoliubov excitations of the corresponding spinor Bose condensate is made. They reproduce the dispersion relations of the excitation modes of the p-wave superfluid Fermi gas to a high accuracy.
We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green's function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature TBECT_{\rm BEC}TBEC​. In the unitary regime at TBECT_{\rm BEC}TBEC​, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight.We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas.
The use of Feshbach resonances in the field of ultracold gases has received a lot of attention recently. In first instance it was realized that these resonances can be used to alter the interaction strength in an atomic gas, by means of tuning an external magnetic field. Furthermore, by sweeping the magnetic field from one side of the resonance to the other, a degenerate gas of bosonic molecules can be created, a significant accomplishment. By making the interactions between fermionic atoms strongly attractive, a fermionic superfluid was recently made, a feat that has drawn a lot of attention in the physics community and from the media. We present work that describes these many-particle systems near a Feshbach resonance in a comprehensive way by using the concept of dressed molecules. These dressed molecules are essentially two-particle states that are a superposition of a tightly bound bare molecule, and two unbound bare atoms. This description reduces to the correct paired wave-function in the two-body limit. Moreover it gives a physically correct description of all the phenomena mentioned above: the Bose-condensation of a gas near a Feshbach resonance, that contains molecules, is more correctly interpreted as a Bose-condensation of dressed molecules. The fermionic superfluid contains a condensate of bosonic pairs, normally called Cooper pairs, that can be understood as the dressed molecules. For the latter case, the dressed-molecule picture also gives an elegant characterization of the crossover between a Bose condensate of pure molecules on one side of the resonance, to a fermionic Bardeen-Cooper-Schrieffer superfluid on the other side. Then, the dressed molecules change continuously from being mostly a bare molecule, to being mostly a loose pair of two atoms. It is clear that the nature of the dressed molecules is much determined by the probability for it to be in the bare-molecular state. This probability we denote with a single parameter Z. We present various ways of calculating it, and study how it affects the macroscopic physics.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
We provide a comprehensive theoretical study of the radio-frequency (rf) spectra of a two-component Fermi gas with balanced populations in the normal region of the temperature-vs-coupling phase diagram. In particular, rf spectra are analyzed in terms of two characteristic peaks, which can be either distinct or overlapping. On the BEC side of the crossover, these two contributions are associated with a fermionic quasi-particle peak and a bosonic-like contribution due to pairing. On the BCS side of the crossover, the two peaks are instead associated with interactions between particles occurring, respectively, at high or low relative momenta. Through this two-peak analysis, we show how and to what extent the correlation between the widths of the rf spectra and the pair size, previously identified in the superfluid phase at low temperature, can be extended to the normal phase, as well as how the temperature-vs-coupling phase diagram of the BCS-BEC crossover can be partitioned in a number of distinct physical sectors. Several analytic results for the shape and widths of the rf spectra are also derived in appropriate temperature and coupling limits.