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arXiv:2306.15904 · Physical Review Letters

Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules

Xin-Yuan Gao, D. Blume, Yangqian Yan

Published Jul 25, 2023• 7 citations
arXivHTMLPDF

Abstract

Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco et al., A degenerate Fermi gas of polar molecules, Science 363, 853 (2019).SCIEAS0036-807510.1126/science.aau7230], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the p-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using p-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally-in agreement with the Bethe-Wigner threshold law-linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular p-wave gases but also to atomic single-component Fermi gases, such as ^{40}K and ^{6}Li.

DOI
10.1103/physrevlett.131.043401

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Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco et al., A degenerate Fermi gas of polar molecules, Science 363, 853 (2019).SCIEAS0036-807510.1126/science.aau7230], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the p-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using p-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally-in agreement with the Bethe-Wigner threshold law-linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular p-wave gases but also to atomic single-component Fermi gases, such as ^{40}K and ^{6}Li.
The recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T ≳ T F , we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T ≪ T c ∼0.2 T F . We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.
Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the NNN-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.
We study the dependence of the p-wave contact on the Fermi temperature T_{F} and reduced temperature T/T_{F} based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow m=0 and m=±1 dipolar splitting of the p-wave Feshbach resonance in ^{6}Li, enabling the independent determination of the contact for all three m components. For each component, we identify a near-resonant scaling with sqrt[T_{F}], indicating the contribution of the normalized effective range k_{F}R_{e}. In addition, we show that the peak contacts observed near resonance increase as T/T_{F} is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the p-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced p-wave Fermi gases.
The aim of this thesis was to measure the three-body contact in the unitary Fermi gas for the first time. The three-body contact is a physical observable that quantifies the three-body short-range correlations. Our probe, sensitive to three fermions with spins ↑↑↓ or ↓↓↑ at short distances, is three-body loss from the optical trap, caused by recombination into a deeply bound molecule and a free atom. In our system, the two spins signify two different hyperfine states of 6Li. We calibrate that recombination process by measuring three-body loss in the motional ground state of three fermions in an optical tweezer at unitarity. The numerically determined three-body contact C_3 (3) 3 of the three fermion system and the experimentally obtained loss rate allow us to extract Im[a_3], which quantifies the coupling to the deeply bound molecular state. Depending on the initial spin configuration ↑↑↓ or ↓↓↑, we find two different values, differing by almost a factor of two. This difference can only be explained by microscopic details of the interatomic coupling. In the many-body unitary Fermi gas, we use the coupling parameter Im[a_3] to extract the zero-temperature dimensionless three-body contact density ζ3\zeta_3ζ3​ from three-body loss measurements. We obtain a value of ζ3\zeta_3ζ3​ = 0.22(4) and observe that the loss rate scales with a characteristic three-body constant s = 1.77, which stems from an underlying SO(2,1) symmetry. We heat the gas and determine ζ3\zeta_3ζ3​ in the thermal regime, observing agreement with the theoretical prediction based on the virial expansion. The extracted value of ζ3\zeta_3ζ3​ > 0, which eludes theory, indicates three-body correlations. At the same time, the experimentally confirmed constant s proves the existence of irreducible three-body correlations that cannot be explained by two-body correlations alone.
A recent experiment [L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules, Science 363, 853 (2019)] reported for the first time the preparation of a Fermi degenerate gas of polar molecules and observed a suppression of their chemical reaction rate compared to the one expected from a treatment assuming classical Maxwell-Boltzmann statistics. While it was hypothesized that the suppression in the ultracold regime had its roots in the Fermi statistics of the molecules, this argument is inconsistent with the fact that the Fermi pressure should set a lower bound for the chemical reaction rate. Here we develop a simple model of chemical reactions that occur via the formation and decay of molecular complexes. We indeed find that pure two-body molecule losses are unable to explain the observed suppression. Instead we extend our description beyond two-body physics by including multibody complex-molecule interactions. Although our model is able to quantitatively reproduce recent experimental observations, it requires parameters physically unlikely for direct microscopic interactions. The underlying processes, however, might emerge effectively from many-body or medium effects. A detailed understanding of the direct microscopic mechanisms responsible for these higher-order interaction processes is therefore still pending.
We experimentally investigate the unitarity-limited behavior of the three-body loss near a ppp-wave Feshbach resonance in a single-component Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms. At the unitarity limit, the three-body loss coefficient L3{L}_{3}L3​ exhibits universality in the sense that it is independent of the interaction strength and follows the predicted temperature scaling law of ${L}_{3}\ensuremath{\propto}{T}^{\ensuremath{-}2}$. When decreasing the interaction strength from the unitarity regime, the three-body loss coefficient as a function of the interaction strength and temperature can be described by the theory based on the association of an excited resonant quasibound state and its relaxation into a deep stable dimer by collision with a third atom in the framework of the standard Breit-Wigner theoretical approach. The results reported here are important to understand the properties of a resonant ppp-wave Fermi gas in the prospect of quantum few- and many-body physics.