Single-Particle Excitations and Effects of Hetero-Pairing Fluctuations in a Bose–Fermi Mixture with a Feshbach Resonance

Abstract

JapanWe theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong heteropairing 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 T BEC . In the unitary regime at T BEC , 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 strongcoupling 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.

Single-particle properties of a strongly interacting Bose-Fermi mixture with mass and population imbalance

“…We evaluate Σ s (p, iω s ) within the framework of the T -matrix-type approximation developed in Ref. [46], which is diagrammatically described in Fig.1. This diagrammatic structure is formally the same as that in the ordinary (non-selfconsistent) T -matrix approximation (TMA); however, the crucial difference is that the bare Bose Green's function,…”

“…In this paper, we investigate single-particle properties of a Bose-Fermi mixture with a hetero-nuclear Feshbach resonance. Extending the previous work [46] to include mass and population imbalances, we examine how these affect strong-coupling corrections to SW.…”

“…In a mass-and population-balanced Bose-Fermi mixture, two of the authors have recently shown that a strong Bose-Fermi pairing interaction causes couplings between Fermi atomic excitations and Bose atomic excitations, as well as atomic excitations and molecular excitations [46]. As an interesting phenomenon associated with these couplings, the Fermi component of the single-particle spectral weight (SW) has been shown to exhibit a threepeak structure, consisting of two sharp peaks along the free fermion dispersion and composite molecular dispersion, and a broad downward peak being related to Bose single-particle excitations.…”

Normal-State Properties of a Unitary Bose–Fermi Mixture: A Combined Strong-Coupling Approach with Universal Thermodynamics

“…Indeed, this approach has been started by several groups. [34][35][36][37][38][39][40][41][42] In this paper, we theoretically investigate normal-state properties of a unitary gas mixture of single-component Bose and Fermi atoms, as a typical strongly interacting Bose-Fermi mixture. Including Bose-Fermi hetero-pairing fluctuations associated with a tunable interspecies interaction, we examine strong-coupling corrections to thermodynamic quantities in the unitarity limit.…”

“…First, regarding how to treat hetero-pairing fluctuations, Refs. 41,42) have pointed out that the ordinary non selfconsistent T -matrix approximation (TMA), 9,43,44) which has frequently been used for the study of ultracold Fermi gases in the BCS-BEC crossover region, has room for improvement,…”