Boiling a Unitary Fermi Liquid

Abstract

We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T . In this regime, we observe a characteristic T 2 dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T , the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝ T −1/2 . In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.Landau's Fermi liquid theory provides a quasiparticle description of the low-temperature behavior for a large class of unordered fermionic states of matter, including most normal metals, atomic nuclei, and liquid helium-3 [1]. Strongly interacting Fermi gases with highly imbalanced spin populations have been identified as belonging to the same class [2][3][4][5][6][7][8][9][10][11][12][13][14]. The quasiparticles in spin-imbalanced Fermi gases are Fermi polarons: spin impurities dressed by an excess cloud of majority fermions. The stability of quasiparticles in a Fermi liquid is a consequence of the restricted phase space for collisions due to Pauli blocking. With increasing temperature T , the accessible phase space increases, and the lifetime of quasiparticles shortens, leading to the breakdown of Fermi liquid theory. In this intermediate temperature regime the gas is neither a Fermi liquid nor a classical Boltzmann gas. For strong interactions, this regime is void of well-defined quasiparticles and controlled by the quantum critical point of the unitary, spin-balanced gas at zero chemical potential and temperature [15][16][17].Ultracold Fermi gases offer a unique opportunity to study the crossover from a low-temperature Fermi liquid to a classical Boltzmann gas, due to the large accessible temperature range. In spin-imbalanced Fermi gases, the two inequivalent Fermi surfaces provide additional richness. As the temperature is lowered from the classical regime, the Fermi surface of the majority forms first, giving minority spins the quasiparticle character of polarons. At even lower temperatures, the polarons themselves become quantum degenerate and form a Fermi surface.In this work, we access the entire crossover from degenerate polarons to the classical Boltzmann gas through the quantum critical region. The internal properties of the polaronic quasiparticles are measured via radio-frequency (rf) spectroscopy [10,[18][19][20] on a homogeneous Fermi gas [21,22]. At low temperatures, the...

High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series

“…The ∼ 1% difference with the one particle-hole variational ansatz [15,16] is much larger than our error bar, and the agreement with the two particle-hole variational ansatz [84] is remarkable. On the experimental side, we agree with the latest value obtained via radio frequency spectroscopy measurements of a strongly spin-balanced Fermi gas in a spatially uniform box potential [9], as well as with the earlier determinations of Refs. [2,93].…”

“…The polaron energy E p is determined from the pole of the propagator G, which gives the implicit equation in terms of the self-energy [32] E p = Σ(p = 0, ω = 0, µ = E p ). (9) lattice quantum Monte Carlo [92] -0.60 (5) experiment [9] TABLE II. Polaron energy Ep/εF at the unitary limit.…”

Fate of the Bose polaron at finite temperature

“…Here, the impurity-medium interactions can be varied from weak to strong coupling via Feshbach resonances [4], allowing one to investigate the manner in which the impurity becomes "dressed" by excitations of the medium. Cold-atom experiments have already greatly improved our understanding of the impurity in a degenerate Fermi gas -otherwise known as the Fermi polaron [5][6][7][8][9][10][11][12][13][14]. However, attention is now focusing more on the Bose polaron, corresponding to the case of a mobile impurity in a Bose-Einstein condensate (BEC).…”

Bose polarons near quantum criticality

“…In addition, the impurities can serve as a sensor of quantum and classical critical behavior of the host gas itself [17]. The dressing of resonant impurities into quasiparticles in a cold atom environment was first observed in the case of the Fermi polaron [18][19][20][21][22][23][24] -an atomic impurity embedded in a Fermi sea [25][26][27][28]. Impurities immersed in a Bose-Einstein condensate (BEC) have been posited to form the paradigmatic Bose polarons originally considered by Pekar [29][30][31].…”

“…These correlations are quantified by the contact [50][51][52][53][54][55], which also captures the change in the polaron energy with interaction strength. For near-resonant interactions, we find the spectral width Γ -a measure of the quasiparticle decay rate [18,24,50,56] -to grow linearly with temperature at the Planckian scale k B T / , and Γ to exceed the impurity's energy close to the onset of quantum degeneracy for the bosonic bath. These properties of the spectral width are direct signatures of quantum critical behavior.…”