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arXiv:1003.2516 · Physical Review A

Radio-frequency spectroscopy of Li6 p -wave molecules: Towards photoemission spectroscopy of a p -wave superfluid

R. A. W. Maier, C. Marzok, Claus Zimmermann, Ph. W. Courteille

Published Jun 22, 2010• 28 citations
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Abstract

We study rf spectroscopy of a lithium gas with the goal to explore the possibilities for photoemission spectroscopy of a strongly interacting $p$-wave Fermi gas. Radio-frequency spectra of quasibound $p$-wave molecules and of free atoms in the vicinity of the $p$-wave Feshbach resonance located at $159.15$ G are presented. The spectra are free of detrimental final-state effects. The observed relative magnetic-field shifts of the molecular and atomic resonances confirm earlier measurements realized with direct rf association. Furthermore, evidence of molecule production by adiabatically ramping the magnetic field is observed. Finally, we propose the use of a one-dimensional optical lattice to study anisotropic superfluid gaps as most direct proof of $p$-wave superfluidity.

DOI
10.1103/physreva.81.064701

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We study rf spectroscopy of a lithium gas with the goal to explore the possibilities for photoemission spectroscopy of a strongly interacting ppp-wave Fermi gas. Radio-frequency spectra of quasibound ppp-wave molecules and of free atoms in the vicinity of the ppp-wave Feshbach resonance located at 159.15159.15159.15 G are presented. The spectra are free of detrimental final-state effects. The observed relative magnetic-field shifts of the molecular and atomic resonances confirm earlier measurements realized with direct rf association. Furthermore, evidence of molecule production by adiabatically ramping the magnetic field is observed. Finally, we propose the use of a one-dimensional optical lattice to study anisotropic superfluid gaps as most direct proof of ppp-wave superfluidity.
In this paper we present an overview of radio frequency (RF) spectroscopy in the atomic Fermi superfluids. An ultimate goal is to suggest new directions in the cold gas research agenda from the condensed matter perspective.Our focus is on the experimental and theoretical literature of cold gases and photoemission spectroscopy of the cuprates particularly as it pertains to areas of overlap. This paper contains a systematic overview of the theory of RF spectroscopy, both momentum integrated and momentum resolved. We discuss the effects of traps, population imbalance, final state interactions over the entire range of temperatures and compare theory and experiment. We show that this broad range of phenomena can be accomodated within the BCS-Leggett description of BCS-BEC crossover and that this scheme also captures some of the central observations in photoemission experiments in the cuprates. In this last context, we note that the key themes which have emerged in cuprate photoemission studies involve characterization of the fermionic self energy, of the pseudogap and of the effects of superconducting coherence (in passing from above to below the superfluid transition temperature, TcT_cTc​).These issues have a counterpart in the cold Fermi gases and it would be most useful in future to use these atomic systems to address these and the more sweeping question of how to describe that anomalous superfluid phase which forms in the presence of a normal state excitation gap.
We perform radio-frequency dissociation spectroscopy of weakly bound 6Li2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the 6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad 6Li Feshbach resonances with an accuracy better than 7×10(-4) of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.
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Using radio-frequency (rf) spectroscopy, we measure the ppp-wave contacts in a Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms near the ppp-wave Feshbach resonance. The rf spectrum exhibits clear asymptotic behavior, characterized by ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}1/2}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}3/2}$ dependencies. The magnetic-field dependence of the ppp-wave contacts agrees reasonably well with the virial expansion theory in a detuned magnetic-field range, validating the theory near half of the Fermi temperature. The ppp-wave contacts measured in this article constitute a second data set, complementing the data obtained from the 40K^{40}\mathrm{K}40K system and contributing valuable insights into ppp-wave interactions in ultracold Fermi gases.
We investigate experimentally and theoretically radio-frequency spectroscopy and pairing of a spin-orbit-coupled Fermi gas of 40{}^{40}40K atoms near a Feshbach resonance at B0=202.2{B}_{0}=202.2B0​=202.2 G. Experimentally, the integrated spectroscopy is measured, showing characteristic blue and red shifts in the atomic and molecular responses, respectively, with increasing spin-orbit coupling. Theoretically, 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 many-body prediction agrees qualitatively well with the observed spectroscopy near the Feshbach resonance.