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arXiv:1301.5236 · Physical Review A

BCS-BEC crossover in a quasi-two-dimensional Fermi gas

Andrea M. Fischer, Meera M. Parish

Published Aug 19, 2013• 19 citations
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Abstract

We consider a two-component gas of fermionic atoms confined to a quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in the transverse direction. We construct a mean-field theory of the BCS-BEC crossover at zero temperature that allows us to extrapolate to an infinite number of transverse harmonic oscillator levels. In the extreme BEC limit, where the confinement length exceeds the dimer size, we recover 3D dimers confined to two dimensions with weak repulsive interactions. However, even when the interactions are weak and the Fermi energy is less than the confinement frequency, we find that the higher transverse levels can substantially modify fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already observed the effects of higher transverse levels.

DOI
10.1103/physreva.88.023612

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This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.

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We consider a two-component gas of fermionic atoms confined to a quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in the transverse direction. We construct a mean-field theory of the BCS-BEC crossover at zero temperature that allows us to extrapolate to an infinite number of transverse harmonic oscillator levels. In the extreme BEC limit, where the confinement length exceeds the dimer size, we recover 3D dimers confined to two dimensions with weak repulsive interactions. However, even when the interactions are weak and the Fermi energy is less than the confinement frequency, we find that the higher transverse levels can substantially modify fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already observed the effects of higher transverse levels.
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We present a quasi-one-dimensional (Q1D) Bose–Fermi mixture model of strongly interacting Fermi gases through the confinement-induced resonance (CIR) to describe 3D fermions trapped in a Q1D geometry along the z axis. Based on the 1D Bethe ansatz method, we analyse the ground and excited states of the Q1D system and derive their integral equations in terms of the momentum distributions in the thermodynamic limit. By applying a Legendre expansion method, the crossover from the BCS superfluid of singlet pairs to the BEC of molecules is calculated in the ground and excited states. We then obtain the dependence of several physical quantities on the inverse of a dimensionless coupling parameter a ⊥ / a with a dimensionless density parameter na ⊥ of Q1D where is the transverse size and ω ⊥ is the 2D harmonic trap frequency in the xy plane. Our results can go back to the smooth 1D crossover when na ⊥ → 0. The theoretical results quantitatively show that the strongly coupling Fermi gas in the Q1D behaves as a Bose–Fermi mixture near the crossover.
We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radiofrequency spectrum, and the superfluid critical temperature Tc{T}_{c}Tc​ using a mean-field theory that accounts for all the energy levels of the harmonic confinement. Our calculation for Tc{T}_{c}Tc​ provides a natural generalization of the Thouless criterion to the quasi-2D geometry, and it correctly reduces to the 3D expression derived from the local density approximation in the limit where the confinement frequency ${\ensuremath{\omega}}_{z}\ensuremath{\rightarrow}0$. Furthermore, our results suggest that Tc{T}_{c}Tc​ can be enhanced by relaxing the confinement and perturbing away from the 2D limit.
We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using the fixed-node diffusion Monte Carlo method, we calculate the equation of state and density profiles for the full fermionic system, which allows us to address the importance of finite-range corrections arising from the internal fermionic structure of the dimers. We interpret the results in terms of a molecular Bose gas in quasi-two-dimensional confinement and compare them with theoretical predictions for a weakly interacting two-dimensional Bose gas, identifying the range of validity of mean-field and beyond-mean-field descriptions. We also develop an analytical theory for the transverse density profile, capturing its broadening with increasing interaction strength. This work provides a benchmark for an effective bosonic description of strongly bound fermionic dimers and offers insights into confinement-induced dimensional effects.
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.
This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.