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arXiv:1604.06063 · Physical Review A

Fermi gases in the two-dimensional to quasi-two-dimensional crossover

Chingyun Cheng, Jayampathi Kangara, Ilya Arakelyan, John E. Thomas

Published Sep 30, 2016• 26 citations
arXivHTMLPDF

Abstract

We smoothly tune the dimensionality of pancake-shaped $^{6}\mathrm{Li}$ Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where ${E}_{F}/h{\ensuremath{\nu}}_{z}\ensuremath{\simeq}1$, with ${E}_{F}$ the Fermi energy and $h{\ensuremath{\nu}}_{z}$ the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree with 2D mean-field theory. Then we tune to the 2D regime, ${E}_{F}<<h{\ensuremath{\nu}}_{z}$, where the measured radio-frequency spectra are in very good agreement with 2D mean-field theory. Nevertheless, the measured cloud profiles strongly disagree, confirming predictions that a beyond mean-field approach is required throughout the 2D to quasi-2D crossover.

DOI
10.1103/physreva.94.031606

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This dissertation presents the first experiments on radio frequency (rf) spectroscopy of a quasi-two dimensional strongly interacting ultracold atomic Fermi gas. A 50-50 mixture of spin-up and spin-down atoms is confined in a series of pancake-shaped traps produced using an optical standing-wave. To make the system quasi-two dimensional, I adjust the Fermi energy in the weakly confined direction to be comparable to the harmonic oscillator energy level spacing in the tightly confined direction. For a perfectly two dimensional system, at low enough temperature, spin-up and spin-down atoms should form dimers in the ground state of the tightly confined direction. However, in our quasi-two dimensional system I find that the simple dimer theory does not agree with the measured radio-frequency spectra. Instead, the data can be explained by polaron to polaron transitions, which is a many-body effect. Here, a polaron is a spin-down impurity surrounded by a cloud of particle-hole pairs in a spin-up Fermi sea. With this unique strongly interacting quasi-two dimensional system, I am able to study the interplay between confinement induced two-body pairing and many-body physics in confined mesoscopic systems of several hundred atoms, which has not been previously explored and offers new challenges for predictions.
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We measure the density profiles for a Fermi gas of (6)Li containing N(1) spin-up atoms and N(2) spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N(2)/N(1) and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N(2)/N(1). Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.
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 follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.