Spectral Response and Contact of the Unitary Fermi Gas

Abstract

We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.PACS numbers: 03.75. Ss, 05.30.Fk, 51.30.+i, 71.18.+y Understanding fermion pairing and pair correlations is of central relevance to strongly interacting Fermi systems such as nuclei [1,2], ultracold gases [3-6], liquid 3 He [7], high temperature superconductors [8], and neutron stars [9]. Strong interactions on the order of the Fermi energy challenge theoretical approaches, especially methods that predict dynamic properties such as transport or the spectral response at finite temperature [10]. Atomic Fermi gases at Feshbach resonances realize a paradigmatic system where the gas becomes as strongly interacting as allowed by unitarity [3][4][5][6]11]. Here, the system becomes universal, requiring only two energy scales: the Fermi energy E F and thermal energy k B T , where k B is the Boltzmann constant and T is the temperature. The corresponding length scales are the interparticle spacing λ F = n −1/3 and the thermal de Broglie wavelength λ T = h/ √ 2πmk B T , where m and n are the mass and number density of the atoms respectively. When the two energy scales are comparable, the system enters a quantum critical regime separating the high temperature Boltzmann gas from the fermionic superfluid [12]. Quantum criticality is often associated with the absence of quasiparticles [10,12,13], spurring a debate on the applicability of Fermi liquid theory to the degenerate normal fluid below the Fermi temperature [14][15][16]. It has been conjectured that preformed pairs exist above T c , up to a pairing temperature T * [3,5,11,[17][18][19][20][21].Radio frequency (rf) spectroscopy measures the momentum integrated, occupied spectral function, providing a powerful tool for studying interactions and correlations in Fermi gases [22][23][24][25][26][27]. Here, a particle is ejected from the interacting many-body state and transferred into a weakly interacting final state. Shifts in rf spectra indicate attractive or repulsive interactions in the gas. At high temperatures, the width of the rf spectrum reflects the scattering rate in the gas, while at low temperatures, the width has been used to infe...

Bose polarons near quantum criticality

“…Therefore C/k n decreases as T C /T in the non-degenerate regime [24,61]. The low-temperature value of the normalized contact is close to what one finds for the unitary Fermi polaron (C/k n = 4.3 [24]), the balanced unitary Fermi gas [65][66][67], and the near-unitary BEC [68]. Using the variational ansatz for the Bose polaron's energy (see Eq.…”

High-temperature expansion of the viscosity in interacting quantum gases

“…where a is the effective scattering length in d dimensions andĈ is the contact operator [21][22][23],Ĉ = m 2 g 2 4ψ † ↑ψ † ↓ψ↓ψ↑ in the zero-range model [43,44]. The contact parameterizes universal short-range correlations and thermodynamic properties and is thus a central experimental observable [45][46][47][48]. The expectation value of the contact sets the magnitude of the leading short-distance divergence of the pair correlations function, hence intuitively it describes the number of pairs with opposite spin in close proximity [49].…”

Graph-theory treatment of one-dimensional strongly repulsive fermions

“…The contact K can be determined from a range of experimental methods, including Bragg spectroscopy [73,74], RF spectroscopy [35,[75][76][77], RF Ramsey interferometry [78], and photoassociation experiments [79,80]. Of these, measuring the molecular fraction from photoassociation is likely to be one of the most sensitive methods [81] in the limit of one atom per spin component, where N = κ.…”