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arXiv:2007.10901

Capturing the Feshbach-induced Pairing Physics in the BEC-BCS Crossover

Eloisa Cuestas, José Ignacio Robledo, A. P. Majtey

Published Jul 21, 2020• 0 citations
arXivHTMLPDF

Abstract

By including the effect of a trap with characteristic energy given by the Fermi temperature $T_F$ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.

DOI
10.48550/arxiv.2007.10901

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By including the effect of a trap with characteristic energy given by the Fermi temperature TFT_FTF​ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction ZZZ across the BEC-BCS crossover and into the BCS regime of a 6^66Li atomic Fermi gas. We obtain the expected behavior Z∝TFZ \propto \sqrt{T_F}Z∝TF​​ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the ZZZ dependency on TFT_FTF​ on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.
Abstract By including the effect of a trap with characteristic energy given by the Fermi temperature T F in a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a 40 K atomic Fermi gas. We also reproduce the experimental closed-channel fraction Z across the BEC–BCS crossover and into the BCS regime of a 6 Li atomic Fermi gas. We obtain the expected behavior Z ∝ T F at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on T F on the BCS side, where a significant quantitative discrepancy between experimental data and theory’s predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity between Z and T F predicted by our model for a 40 K atomic Fermi gas.
Observation of the density effect on the closed-channel fraction in a 6^66Li superfluid
Atomic Fermi gases provide an ideal platform for studying the pairing and superfluid physics, using a Feshbach resonance between closed channel molecular states and open channel scattering states. Of particular interest is the strongly interacting regime. We show that the closed-channel fraction ZZZ provides an effective probe for the important many-body interacting effects, especially through its density dependence, which is absent from two-body theoretical predictions. Here we measure ZZZ as a function of interaction strength and the Fermi temperature TFT_FTF​ in a trapped 6^66Li superfluid throughout the entire BCS--BEC crossover. Away from the deep BEC regime, the fraction ZZZ is sensitive to TFT_FTF​. In particular, our data show Z∝TFαZ \propto T_F^{\alpha}Z∝TFα​ with α=1/2\alpha=1/2α=1/2 at unitarity, in quantitative agreement with calculations of a two-channel pairing fluctuation theory, and α\alphaα increases rapidly into the BCS regime, reflecting many-body interaction effects as predicted.
Abstract Atomic Fermi gases provide an ideal platform for studying pairing and superfluid physics, using a Feshbach resonance between closed-channel molecular states and open-channel scattering states. Of particular interest is the strongly interacting regime. We show that the closed-channel fraction Zcc{Z_{{\rm{cc}}}}Zcc​ provides an effective probe for important many-body interacting effects, especially through its density dependence, which is absent from two-body theoretical predictions. Here we measure Zcc{Z_{{\rm{cc}}}}Zcc​ as a function of interaction strength and the Fermi temperature TF{T_{\rm{F}}}TF​ in a trapped 6Li superfluid throughout the entire Bardeen-Cooper-Schrieffer–Bose-Einstein-condensate crossover, in quantitative agreement with theory when important thermal contributions outside the superfluid core are taken into account. Away from the deep-BEC regime, the fraction Zcc{Z_{\rm cc}}Zcc​ is sensitive to TF{{{T}}_F}TF​. In particular, our data show ${Z_{{\rm{cc}}}} \propto T_{\rm{F}}^\alpha $ with α=1/2\alpha = {\rm{1/2}}α=1/2 at unitarity, in quantitative agreement with calculations of a two-channel pairing fluctuation theory, and $\alpha $ increases rapidly into the BCS regime, reflecting many-body interaction effects as predicted.
We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation crossover theory at general temperature , and show that this fraction provides a measure of the T-dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low- measurements in (6)Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.
The pairing of fermionic particles is an essential ingredient of superconductivity and of the superfluidity of 3He. While such phenomena are accurately described by BCS theory in the limit of weak pairing strength, a complete understanding remains elusive when pairing strength is increased, such as in high temperature superconductors. We create ultracold gases of trapped fermionic 6Li atoms, through which we directly observe fermionic pairing. In our system, there are no impurities whatsoever, and parameters such as the number and temperature of the trapped atoms are precisely and independently controlled. In addition, a Feshbach resonance enables the continuous tuning of interaction strength and sign between the paired atoms. This control allows us to observe the smooth crossover of a molecular Bose Einstein condensate (MBEC) to a superfluid of weakly interacting Cooper pairs. With these tools, we have performed several fundamental measurements of pairing in fermionic systems.\nWe use optical molecular spectroscopy to precisely measure the closed-channel contribution to the many body state of paired 6Li atoms within a broad Feshbach resonance. The magnitude of this contribution is small, and supports the concept of universality for the description of broad Feshbach resonances. Moreover, the dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover, and for the first time, into the weakly interacting BCS regime.\nWe also prepare a polarized Fermi gas with unequal numbers of two spin states of 6Li atoms. The real-space densities of the polarized, strongly-interacting, two-component Fermi gas reveal two low temperature regimes. At the lowest temperatures, the gas separates into a phase with a uniformly paired superfluid core surrounded by a shell of normal, unpaired atoms. This phase separation is accompanied by a spatial deformation of the core. At higher temperatures, the uniformly paired core persists, though it does not deform. This temperature dependence is consistent with a tri-critical point in the phase diagram. These measurements of pairing in a polarized Fermi gas are relevant to predictions of exotic phases of quark matter and magnetized superconductors.
We investigate strong-coupling effects on the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance describes a composite quasiboson that can give rise to an additional pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance two-particle bound state is lowered. In a recent paper, we showed that in the uniform Fermi gas, this tunable pairing interaction naturally leads to a crossover from a BCS state to a Bose-Einstein condensate (BEC) of the Nozi\`eres and Schmitt-Rink kind, in which the BCS-type superfluid phase transition continuously changes into the BEC type as the threshold energy is decreased. In this paper, we extend our previous work by including the effect of a harmonic trap potential, treated within the local-density approximation. We also give results for both weak and strong coupling to the Feshbach resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the shape of the atomic density profile at the superfluid phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above Tc.{T}_{\mathrm{c}}.Tc​. We also discuss the ``phase diagram'' above Tc{T}_{\mathrm{c}}Tc​ as a function of the tunable threshold energy $2\ensuremath{\nu}.$ We introduce a characteristic temperature ${T}^{*}(2\ensuremath{\nu})$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.