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arXiv:1710.06581 · Europhysics Letters (EPL)

Studies of a single component Fermi gas near a p-wave resonance with the lowest order constrained variational method

Guangcun Liu, Yi-Cai Zhang

Published Jul 2, 2018• 5 citations
arXivHTMLPDF

Abstract

We study a single component Fermi gas near a p -wave resonance with the lowest order constrained variational (LOCV) method. We obtain the energy per particle for the ground state of the single component Fermi gas near a p -wave resonance with the LOCV method. We also calculate the compressibility of the single component Fermi gas near a p -wave resonance and it shows that in the strongly interacting BCS side, the system would lose its stability and collapse. The width of the unstable region is proportional to the Fermi energy which reflects the universality of the dilute Fermi gas. The two p -wave contacts are also obtained and their variation tendencies with the interaction strength are qualitatively in agreement with recent experimental results.

DOI
10.1209/0295-5075/122/40006

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We study a single component Fermi gas near a p -wave resonance with the lowest order constrained variational (LOCV) method. We obtain the energy per particle for the ground state of the single component Fermi gas near a p -wave resonance with the LOCV method. We also calculate the compressibility of the single component Fermi gas near a p -wave resonance and it shows that in the strongly interacting BCS side, the system would lose its stability and collapse. The width of the unstable region is proportional to the Fermi energy which reflects the universality of the dilute Fermi gas. The two p -wave contacts are also obtained and their variation tendencies with the interaction strength are qualitatively in agreement with recent experimental results.
We investigate the universalities of a single-component Fermi gas at a p -wave resonant point where the scattering volume is infinite with the lowest-order constrained variational (LOCV) method. We calculate the energy per particle for different effective ranges with different interaction configuration, our result confirms the universality assumption at the p -wave resonant point and we also find the universal parameter which is the counterpart of the Bertsch parameter for the p -wave case. We then examine the density dependence of the energy per particle at the p -wave resonant point and find n 2/3 density dependence which is the same as in the s -wave case.
In this thesis,we investigate the Unitary Fermi gas and its thermodynamic properties. We look into the problem using the Lowest Order Constrained Variational method,using the Jastrow correlation function and determine the thermodynamic quantities of interest around unitarity.From this variational calculation we calculate quantities like energy per particle and chemical potential and study their variation as a function of the s-wave scattering length. We find there are two energy branches which suggests that the way to approach unitarity is not unique.We compare our results with those found from toy model for unitary fermi gas,a single particle in a spherical box interacting with a fixed scatterer at the center of the cavity interactions being modelled by the fermi pseudo potential.We find a surprising qualitative agreement between the results obtained. We also study the BCS-BEC crossover in three dimension using mean field analysis, and evaluate quantities like gap parameter and chemical potential across the whole range of the crossover.
In this thesis, we investigate ultracold Bose-Fermi mixtures in both two and three dimensions using a non-perturbative approach based on the Lowest Order Constrained Variational (LOCV) method. This variational technique, originally developed in the context of nuclear matter, is applied here to dilute quantum gases at zero temperature, allowing for an accurate treatment of two-body correlations beyond perturbative limits. We begin by analysing Bose-Fermi mixtures near a broad Fano-Feshbach resonance, which enables precise tuning of the interspecies interaction strength. Particular attention is devoted to the low-dimensional case, where quantum fluctuations are enhanced and experimental realizations have become increasingly accessible. While the three-dimensional problem serves as a useful benchmark, the two-dimensional Bose-Fermi mixture presents unique challenges. Notably, no prior non-perturbative studies exist on its mechanical stability. A central goal of this work is to determine the conditions under which the 2D Bose-Fermi mixture remains mechanically stable as the boson-fermion attraction is increased. Our results demonstrate that the LOCV approach captures the relevant physics from weak to moderate coupling, offering a complementary perspective to perturbative methods or alternative non-perturbative approaches such as the T-matrix formalism. In this coupling range, we identify the critical strength of boson-boson repulsion necessary to prevent phase separation or collapse, thereby providing the first theoretical variational prediction of a stability phase diagram in this two dimensional regime. Overall, this work fills a gap in the literature and provides a useful reference point for future theoretical and experimental studies of strongly interacting Bose-Fermi systems in reduced dimensionality.
The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an effective contact interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multicomponent Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.
We investigate the problem of mechanical stability in two-dimensional Bose-Fermi mixtures at zero temperature, focusing on systems with a tunable Bose-Fermi (BF) interaction and a weak but finite boson-boson (BB) repulsion. The analysis is carried out within the framework of the lowest-order constrained variational (LOCV) approach, which allows for a nonperturbative treatment of strong interspecies correlations while retaining analytical transparency. The BF interaction is modeled by a properly regularized attractive contact potential, enabling the exploration of both the attractive and repulsive energy branches. We determine the minimal BB repulsion required to ensure mechanical stability of the mixture by evaluating the inverse compressibility matrix over the full range of BF coupling strengths, within the domain of validity of the LOCV approximation. The interaction contribution to the energy is benchmarked against available experimental data and quantum Monte Carlo results in the single-impurity limit, showing good agreement. Our analysis reveals how the critical BB coupling depends on interaction strength, density imbalance, and mass ratio. In particular, we find that mixtures with equal boson and fermion masses exhibit enhanced stability, requiring the smallest BB repulsion to prevent mechanical instability. In this case, a relatively small BB interaction is sufficient to stabilize attractive mixtures for all values of the BF interaction. These results provide a theoretical framework for assessing stability conditions in experimentally realizable two-dimensional Bose-Fermi mixtures with tunable interactions.
The influence of s- and p-wave interactions on trapped degenerate one- and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation, including the s- and p-wave terms of an effective contact interaction. On this basis the stability of the dilute gas against mean-field induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore, the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The findings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has a significant influence on the phase diagram of the degenerate Fermi gas and causes new phenomena such as absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases.