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Observation of the density effect on the closed-channel fraction in a $^6$Li superfluid

Xiangpei Liu, Xing-Can Yao, Hao-Ze Chen, Xiaoqiong Wang, Yu‐Xuan Wang, Yu-Ao Chen, Qijin Chen, Kathryn Levin, Jian-Wei Pan

Published Mar 29, 2019• 1 citation
OpenAlex

Abstract

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 $Z$ 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 $Z$ as a function of interaction strength and the Fermi temperature $T_F$ in a trapped $^6$Li superfluid throughout the entire BCS--BEC crossover. Away from the deep BEC regime, the fraction $Z$ is sensitive to $T_F$. In particular, our data show $Z \propto T_F^{\alpha}$ with $\alpha=1/2$ 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.

Related papers

Observation of the density dependence of the closed-channel fraction of a 6Li superfluid

Xiangpei Liu, Xing-Can Yao, Hao-Ze Chen +6 more

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 ${Z_{{\rm{cc}}}}$ 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 ${Z_{{\rm{cc}}}}$ as a function of interaction strength and the Fermi temperature ${T_{\rm{F}}}$ 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 ${Z_{\rm cc}}$ is sensitive to ${{{T}}_F}$. In particular, our data show ${Z_{{\rm{cc}}}} \propto T_{\rm{F}}^\alpha $ with $\alpha = {\rm{1/2}}$ 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.

arXiv:1903.12321•National Science Review•Dec 21, 2021•8 citations

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

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

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.

arXiv:2007.10901•Jul 21, 2020•0 citations

A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC–BCS crossover

Eloisa Cuestas, A. P. Majtey

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.

Journal of Physics Condensed Matter•Apr 14, 2021•1 citation

Population of Closed-Channel Molecules in Trapped Fermi Gases with Broad Feshbach Resonances

Qijin Chen, Kathryn Levin

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.

arXiv:cond-mat/0505689•Physical Review Letters•Dec 28, 2005•26 citations

Pairing of fermionic lithium-6 throughout the BEC-BCS crossover

Guthrie B. Partridge

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.

•Jan 1, 2007•0 citations

Superfluid properties of an ultracold Fermi gas with an orbital Feshbach resonance in the BCS-BEC crossover region

Taro Kamihori, Daichi Kagamihara, Yoji Ohashi

We theoretically investigate the superfluid properties of a two-band gas of $^{173}\mathrm{Yb}$ Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by interband and intraband pairing interactions associated with OFR by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, the effects of an experimentally inaccessible deep bound state are removed to model a real $^{173}\mathrm{Yb}$ Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced interband interaction. In addition to these superfluid quantities, we also examine collective modes, such as the Goldstone mode, the Schmid (Higgs) mode, and Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multiband superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.

arXiv:2103.16933•Physical Review A•May 24, 2021•1 citation
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.
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.
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 theoretically investigate the superfluid properties of a two-band gas of 173Yb^{173}\mathrm{Yb}173Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by interband and intraband pairing interactions associated with OFR by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, the effects of an experimentally inaccessible deep bound state are removed to model a real 173Yb^{173}\mathrm{Yb}173Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced interband interaction. In addition to these superfluid quantities, we also examine collective modes, such as the Goldstone mode, the Schmid (Higgs) mode, and Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multiband superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.