Temperature Dependence of the Universal Contact Parameter in a Unitary Fermi Gas

Abstract

The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(kF a), where kF is the Fermi wave-vector and a is the s-wave scattering length, and the temperature T /TF , where TF is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature. [1][2][3]. Universal systems should satisfy two requirements: firstly, the gas must be dilute enough that the mean interparticle spacing n −1/3 greatly exceeds the range of the interaction potential r 0 , and, secondly, the interactions, characterized by the s-wave scattering length, a, should be sufficiently strong that a greatly exceeds n −1/3 . All Fermi systems that satisfy these requirements will behave identically on a scale given by the average particle separation, independent of the details of the interaction potential. Recent theoretical work by Tan [4][5][6] and others [7][8][9][10][11] has identified several exact relations applicable to Fermi systems in the universal regime. The central parameter in these relations is a quantity called the contact I, which forms a link between microscopic and macroscopic system properties.Contact quantifies the likelihood of finding two interacting fermions with very small separation and is closely linked to the pair-correlation function [4]. In strong analogy with the phase diagram of the Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid crossover of two-component Fermi gases [12], I depends upon two parameters: the dimensionless interaction strength 1/(k F a), where k F is the Fermi wavevector, and the relative temperature T /T F , where T F is the Fermi temperature. Previous theoretical [7,13] and experimental [14][15][16] work has investigated the interaction dependence of the contact, and a number of recent studies have calculated the temperature dependence of the contact [13,[17][18][19]. To date however, there have been no measurements of this latter dependence.In this letter, we report the first measurements of the temperature dependence of the contact using Bragg spectroscopy of a 6 Li Fermi gas at unitarity. Bragg spectroscopy allows for quantitative measurements of the static structure factor S(k) which is directly proportional to the contact at high momenta. We extract the first and second moments from our Bragg spectra and use these to obtain the dynamic structure factor S(k, ω) and from this S(k) and the contact. Our results are in good agreement with theoretical predictions and indicate that pair-correlations at high momenta persist well above the critical temperature for superfluidity.Tan's exact relations for Fermi gases near the ...

Universal contact and collective excitations of a strongly interacting Fermi gas

“…In order to appreciate the sensitivity of the slope to the choice of the values of ξ and ζ, in Fig.2, we also show the predictions [green (light gray) line] for the frequency shifts using the values ξ = 0.41 and ζ = 0.74, yielding the smaller value I/N k 0 F ≃ 2.7 for the contact. This value is closer to the measurement of the contact carried out in [5] and [9] at slightly higher values of temperature. The resulting slope δω/ω ∼ 0.09/(k 0 F a) provides a worse description of the experimental data for the collective frequencies.…”

“…where with the index ± referring to the higher (+) and lower (−) frequencies of (9). In the second equality of (15), we have used relation (7) for the contact parameter calculated for an harmonically trapped atomic cloud and we have expressed the Fermi momentum k F in terms of the ideal Fermi gas wave vector k…”

Transverse Demagnetization Dynamics of a Unitary Fermi Gas

“…As is clear from its definition, C is also proportional to the local interaction energy. Although contact has been shown to relate various thermodynamic and many-body properties of a short-range interacting gas, it has so far been studied only in equilibrium and only with an unmagnetized gas [25,[30][31][32][33]. Figure 3A shows that after a short hold time the spectrum exhibits only the single-particle peak, whereas after a longer hold time, the spectrum develops a high-frequency tail.…”

Nonequilibrium and local detection of the normal fraction of a trapped two-dimensional Bose gas

“…Some of the complications that naturally occur in experiments are then numerically investigated: a Bogoliubov theory is used to assess the conditions to be imposed to the geometry and the temporal duration of the pulse; a classical field model is used to assess the conditions on the amplitude of the gauge field for the linear response theory to be valid. A main difficulty appears to be the relatively small amount of energy that can be deposited in the gas before nonlinear couplings become difficult to extrapolate out: the resulting figure is on the order of 1% of the total energy of the gas, which is however not far from the sensitivity of state-of-the-art thermodynamic measurements of the energy [21][22][23][24][25].…”

“…Our scheme however requires a measurement of an energy change, not an absolute measurement of the energy, giving hope for a better precision. Recent experiments have actually measured the change of the momentum [24] and of the energy [25] of a gas to determine its structure factor with good precision, not for a gauge field excitation as proposed here, but for a…”