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arXiv:1205.1110 · Physical Review A

Momentum-resolved Raman spectroscopy of a noninteracting ultracold Fermi gas

Pengjun Wang, Zhengkun Fu, Lianghui Huang, Jing Zhang

Published May 18, 2012• 8 citations
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Abstract

We report the experiment on probing the one-body spectral function in a trapped noninteracting ${}^{40}$K Fermi gas by means of the momentum-resolved Raman spectroscopy. The experimental result is in good agreement with the expected quadratic dispersion in the noninteracting regime. Through the comparison with the radio-frequency spectrum, we found that the Raman spectrum shows some new characteristics.

DOI
10.1103/physreva.85.053626

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We report the experiment on probing the one-body spectral function in a trapped noninteracting 40{}^{40}40K Fermi gas by means of the momentum-resolved Raman spectroscopy. The experimental result is in good agreement with the expected quadratic dispersion in the noninteracting regime. Through the comparison with the radio-frequency spectrum, we found that the Raman spectrum shows some new characteristics.
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.
We address recent momentum-resolved radio frequency (rf) spectroscopy experiments, showing how they yield more stringent tests than other comparisons with theory, associated with the ultracold Fermi gases. We demonstrate that, by providing a clear dispersion signature of pairing, they remove the ambiguity plaguing the interpretation of previous rf experiments. Our calculated spectral intensities are in semiquantitative agreement with the data. Even in the presence of a trap, the spectra are predicted to exhibit two BCS-like branches.
We investigate theoretically momentum-resolved radio-frequency (rf) spectroscopy of a noninteracting atomic Fermi gas in a spin-orbit coupled lattice. This lattice configuration has been recently created at MIT [Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)] for 6{}^{6}6Li atoms, by coupling the two hyperfine spin states with a pair of Raman laser beams and additional rf coupling. Here, we show that momentum-resolved rf spectroscopy can measure single-particle energies and eigenstates and therefore resolve the band structure of the spin-orbit coupled lattice. In our calculations, we take into account the effects of temperatures and harmonic traps. Our predictions are to be confronted with future experiments on spin-orbit coupled Fermi gases of 40{}^{40}40K atoms in a lattice potential.
We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasiparticle states of a gas of strongly interacting ultracold atoms. This technique is inspired by angle-resolved photoemission spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to rf spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.
It is of central importance to probe the local spectral function $A(\mathbf{k},\ensuremath{\omega})$ of a strongly interacting Fermi gas in a trap. Momentum-resolved rf spectroscopy has been demonstrated to be able to probe the trap-averaged $A(\mathbf{k},\ensuremath{\omega})$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum-resolved rf spectra of the minority fermions of a phase-separated, population-imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},\ensuremath{\omega})$ of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through Bose-Einstein condensation regimes using different theories.
By using a non-self-consistent many-body TTT-matrix theory, we calculate the finite-temperature Raman spectroscopy of a mobile impurity immersed in a Fermi bath in three dimensions. The dependencies of the Raman spectrum on the transferred momentum, temperature, and impurity-bath interaction are discussed in detail. We confirm that the peak in the Raman spectrum shows a weaker dependence on the impurity concentration than that in the radio-frequency spectroscopy due to the nonzero transferred momentum, as anticipated. We compare our theoretical prediction with the recent measurement by Gal Ness et al. [G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Phys. Rev. X 10, 041019 (2020)] without any adjustable parameters. At weak coupling, we find a good quantitative agreement. However, close to the Feshbach resonance the agreement becomes worse. At strong coupling, we find that an unrealistic Fermi bath temperature might be needed to account for the experimental data.