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Physical Review A

Dressed-molecule theory for the quasi-two-dimensional quantum anomaly

Fan Wu, Jianshen Hu, Lianyi He

Published Dec 28, 2023• 0 citations
Publisher

Abstract

In this work the dressed-molecule theory is used to describe the two-dimensional quantum anomaly of breathing mode in a recent experimental system [M. Holten et al., Phys. Rev. Lett. 121, 120401 (2018); T. Peppler et al., Phys. Rev. Lett. 121, 120402 (2018)]. With the aid of a beyond-mean-field Gaussian pair fluctuation theory, we employ the dressed-molecule states to characterize the axial excited states and the Feshbach molecular states and propose a low-energy effective theory. We show that, in the whole crossover from a BCS superfluid to a Bose-Einstein condensate, our theory can describe the two-dimensional experimental systems precisely in the low-energy region. We explain the puzzling experimental observations of the smaller than expected breathing-mode frequency. Our establishment of the dressed-molecule theory for two-dimensional fermions can help in the understanding of the conformal anomaly in quasi-low-dimensional quantum systems.

DOI
10.1103/physreva.108.063318

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•Feb 7, 2007•1 citation
In this work the dressed-molecule theory is used to describe the two-dimensional quantum anomaly of breathing mode in a recent experimental system [M. Holten et al., Phys. Rev. Lett. 121, 120401 (2018); T. Peppler et al., Phys. Rev. Lett. 121, 120402 (2018)]. With the aid of a beyond-mean-field Gaussian pair fluctuation theory, we employ the dressed-molecule states to characterize the axial excited states and the Feshbach molecular states and propose a low-energy effective theory. We show that, in the whole crossover from a BCS superfluid to a Bose-Einstein condensate, our theory can describe the two-dimensional experimental systems precisely in the low-energy region. We explain the puzzling experimental observations of the smaller than expected breathing-mode frequency. Our establishment of the dressed-molecule theory for two-dimensional fermions can help in the understanding of the conformal anomaly in quasi-low-dimensional quantum systems.
In this work, the dressed molecules theory is used to describe the two-dimensional quantum anomaly of breathing mode in the recent experimental system\cite{Holten2018,Peppler2018}. With the aid of a beyond mean-field, Gaussian pair fluctuation theory, we employ the dressed molecules states to characterize the axial excited states and the Feshbach molecular states, and propose a complete low energy effective theory. We show that, in the whole crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), our theory can describe the two-dimensional experimental systems precisely in low energe region. We explain the the puzzling experimental observations of the smaller than expected breathing mode frequency perfectly. Our establishment of the dressed molecules theory for 2D fermions is crucial to understand the conformal anomaly in the quasi low-dimensional quantum systems.
A harmonically trapped strongly interacting Fermi gas in two dimensions is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale invariant value ωB=2ω⊥\omega_{B}=2\omega_{\perp}ωB​=2ω⊥​, where ω⊥\omega_{\perp}ω⊥​ is the frequency of the trapping potential. This quantum anomaly, however, has never been conclusively confirmed in current experiments {[}E. Vogt \textit{et al.}, Phys. Rev. Lett. \textbf{108}, 070404 (2012); Holten \textit{et al.}, arXiv:1803.08879; Peppler \textit{et al.}, arXiv:1804.05102{]}. Here, we theoretically investigate the universal density equation of state and the breathing mode frequency of a unitary Fermi gas at the dimensional crossover from three to two dimensions. We find that the simple model of a two-dimensional strongly interacting Fermi gas with a single sss-wave scattering length is not adequate to describe the experiments, as commonly believed. A more complete description of quasi-two-dimensions leads to a much weaker quantum anomaly in the breathing mode frequency, consistent with the experimental observations.
Abstract We study the crossover from the Bardeen–Cooper–Shrieffer regime to the Bose–Einstein-condensation regime in an anisotropic trapped quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules, we extend the Gaussian pair fluctuation theory to quasi-two-dimensional systems. The equation of state, pair size and sound velocity as well as the convexity parameters of the Goldstone mode are investigated to show how Fermi superfluidity is affected by reduced dimensionality and Gaussian fluctuations at zero temperature in a wide range of crossover. We compare our results with the recent experiment of 6 L i atomic gases and find good agreements.
We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance.
We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable sss-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.
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.