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arXiv:1210.2160 · Physical Review A

Momentum-resolved radio-frequency spectroscopy of a spin-orbit-coupled atomic Fermi gas near a Feshbach resonance in harmonic traps

Shi-Guo Peng, Xia-Ji Liu, Hui Hu, Kaijun Jiang

Published Dec 10, 2012• 15 citations
arXivHTMLPDF

Abstract

We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of ${}^{40}$K atoms at Shanxi University and ${}^{6}$Li atoms at the Massachusetts Institute of Technology.

DOI
10.1103/physreva.86.063610

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We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of 40{}^{40}40K atoms at Shanxi University and 6{}^{6}6Li atoms at the Massachusetts Institute of Technology.
Interacting Fermi gases with spin-orbit coupling are responsible for many intriguing phenomena such as topological superfluids and Majorana fermions. Here we characterize theoretically fermionic pairing in a strongly interacting spin-orbit coupled Fermi gas, by using momentum-resolved radio-frequency spectroscopy. We develop a strong-coupling TTT-matrix theory and present a phase diagram near the unitary resonance limit. A smooth transition from atomic to molecular responses in the momentum-resolved spectroscopy is predicted, with a clear signature of anisotropic pairing at and below resonance. Our prediction with many-body pairing can be directly tested in a spin-orbit coupled Fermi gas of 40^{40}40K or 6^{6}6Li atoms near broad Feshbach resonances.
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We theoretically investigate a Rashba spin-orbit-coupled Fermi gas near Feshbach resonances, by using mean-field theory and a two-channel model that takes into account explicitly Feshbach molecules in the closed channel. In the absence of spin-orbit coupling, when the channel coupling ggg between the closed and the open channels is strong, it is widely accepted that the two-channel model is equivalent to a single-channel model that excludes Feshbach molecules. This is the so-called broad resonance limit, which is well satisfied by ultracold atomic Fermi gases of 6{}^{6}6Li atoms and 40{}^{40}40K atoms in current experiments. Here, with Rashba spin-orbit coupling we find that the condition for equivalence becomes much more stringent. As a result, the single-channel model may already be insufficient to describe properly an atomic Fermi gas of 40{}^{40}40K atoms at a moderate spin-orbit coupling. We determine a characteristic channel coupling strength gc{g}_{c}gc​ as a function of the spin-orbit-coupling strength, above which the single-channel and two-channel models are approximately equivalent. We also find that for narrow resonance with small-channel coupling, the pairing gap and molecular fraction are strongly suppressed by SO coupling. Our results can be readily tested in 40{}^{40}40K atoms by using optical molecular spectroscopy.
The binding energy of Feshbach molecules from a two-component Fermi gas of 40{}^{40}40K atoms has been experimentally measured with the momentum-resolved Raman spectroscopy. Comparing with the radio-frequency spectroscopy, in the present experiment the signal of unpaired (free atoms) and the bound molecules can be directly observed and the binding energy can be simultaneously determined in a single running experiment. The energy-momentum dispersion spectra of the ultracold Fermi gas in the BEC side are also measured and reconstructed. The present experimental technology of the momentum-resolved Raman spectroscopy can be easily extended to perform spatially momentum-resolved Raman spectroscopy and to obtain the response spectra of a homogeneous system in the local density approximation.