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arXiv:1201.3560 · Physical Review Letters

Polaron-to-Polaron Transitions in the Radio-Frequency Spectrum of a Quasi-Two-Dimensional Fermi Gas

Y. Zhang, Willie Ong, Ilya Arakelyan, John E. Thomas

Published Jun 8, 2012• 156 citations
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Abstract

We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.

DOI
10.1103/physrevlett.108.235302

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We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.
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.
We theoretically study the normal phase properties of strongly interacting two-component Fermi gases in two spatial dimensions. In the limit of weak attraction, we find that the gas can be described in terms of effective polarons. As the attraction between fermions increases, we find a crossover from a gas of noninteracting polarons to a pseudogap regime. We investigate how this crossover is manifested in the radio-frequency (rf) spectroscopy. Our findings qualitatively explain the differences in the recent rf spectroscopy measurements of two-dimensional Fermi gases [Sommer et al., Phys. Rev. Lett. 108, 045302 (2012) and Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)].
We smoothly tune the dimensionality of pancake-shaped 6Li^{6}\mathrm{Li}6Li 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 EF{E}_{F}EF​ 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.
Abstract We study the polaron problem of an impurity immersed in the background of a Fermi sea confined in one-dimensional or two-dimensional isotropic traps. By changing the trapping potential from loose to tight, a dimensional crossover from anisotropically trapped three-dimensional to quasi-two-dimensional (quasi-2D) or quasi-one-dimensional (quasi-1D) configurations is investigated by calculating the ground-state energy in a wide range of interaction strength. We adopt a low-dimensional effective Hamiltonian in the form of a two-channel model, where the excited levels in the confined directions are described phenomenologically by a dressed molecule, and use the variational approach up to one pair of particle-hole fluctuations to calculate the energies of polaron and molecule states. We map out the phase diagrams for both quasi-1D and quasi-2D configurations and different mass ratios, and conclude that the polaron phase is preferable with tighter confinement and lighter impurity mass in lower dimensions. We also find that owing to the significant population of excited levels by strong interaction, a strictly low-dimensional system with all particles residing in the ground state of the trap can never work when study polaron-molecule transition, even in the tightly confined limit. This discrepancy has been observed in an experiment of quasi-2D gases of 40 K atoms and is well explained by our calculation.
We investigate the thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using self-consistent frameworks of strong-coupling diagrammatic approaches, both the ejection and the reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to the Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 093401 (2019)] and suggests the importance of beyond-two-body correlations in the high-temperature regime due to the absence of Pauli-blocking effects.