Universal relations for a strongly interacting Fermi gas near a Feshbach resonance

Braaten, Eric; Kang, Daekyoung; Platter, Lucas

doi:10.1103/physreva.78.053606

Cited by 108 publications

(139 citation statements)

References 24 publications

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“…(b) Recently, the localization of minority atoms by an optical lattice was demonstrated with an imbalanced Bose-Bose mixture of 87 Rb and 41 K atoms [95]. The localization of the impurity atoms at length scales of roughly 10% of the Fermi wavelength has been achieved at typical densities; thus, the impurity can be treated as pointlike, and one can neglect its excitations to the excited states of the trapping potentials, as in our analysis above.…”

Section: Discussionmentioning

confidence: 96%

“…This phenomenon, as well as the full structure of Að!Þ at k F jaj ) 1, can be understood as the result of a nontrivial interplay between two-body physics that involves the impurity and the hole near the bottom of the band, and the dynamics of multiple particle-hole excitations created at the Fermi surface. The possibility of a nontrivial interplay between many-body and few-body physics is a unique feature of ultracold-atom physics, and has attracted significant theoretical [86,87] and experimental [88] interest recently.…”

Section: Universal Radio-frequency Spectramentioning

confidence: 99%

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Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

et al. 2012

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The recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. In this paper, we discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid-state systems. Specifically, we consider a system of impurity atoms, localized by a strong optical-lattice potential, immersed in a sea of itinerant Fermi atoms. We point out that the Ramsey-interference-type experiments with the impurity atoms allow one to study the OC in the time domain, while radio-frequency (RF) spectroscopy probes the OC in the frequency domain. The OC in such systems is universal, not only in the long-time limit, but also for all times and is determined fully by the impurity-scattering length and the Fermi wave vector of the itinerant fermions. We calculate the universal Ramsey response and RF-absorption spectra. In addition to the standard power-law contributions, which correspond to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel, important contribution to the OC that comes from exciting one extra particle from the bottom of the itinerant band. This contribution gives rise to a nonanalytic feature in the RF-absorption spectra, which shows a nontrivial dependence on the scattering length, and evolves into a true power-law singularity with the universal exponent 1=4 at the unitarity. We extend our discussion to spin-echo-type experiments, and show that they probe more complicated nonequilibirum dynamics of the Fermi gas in processes in which an impurity switches between states with different interaction strength several times; such processes play an important role in the Kondo problem, but remained out of reach in the solid-state systems. We show that, alternatively, the OC can be seen in the energy-counting statistics of the Fermi gas following a sudden quench of the impurity state. The energy distribution function, which can be measured in time-of-flight experiments, exhibits characteristic power-law singularities at low energies. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying nonequilibrium impurity physics, allowing one to explore the nonequilibrium OC and even to simulate quantum transport through nanostructures. This provides a previously missing connection between cold atomic systems and mesoscopic quantum transport.

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Section: Discussionmentioning

confidence: 96%

Section: Universal Radio-frequency Spectramentioning

confidence: 99%

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

et al. 2012

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“…The coefficient of the leading operator is a Dirac delta function of r ′ − r. It can be derived simply by using the (anti)commutation relations for the field operators. The coefficients of higher dimension operators can be calculated using diagrammatic methods [6,13]. Upon inserting the OPE in Eq.…”

Section: Operator Product Expansionmentioning

confidence: 99%

Universal relation for the inelastic two-body loss rate

Braaten

Hammer

2013

J. Phys. B: At. Mol. Opt. Phys.

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Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.

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“…In particular, the HFT has recently been used to derive a number of exact relations for strongly-correlated systems with short-range interations, in the context of ultra-cold quantum gases [5,6,26]. Since this theorem applies only for pure states, these exact relations strictly hold at zero temperature for any change or equivalently at finite temperatures for an adiabatic change.…”

Section: A Hft For Pure Statesmentioning

confidence: 99%

“…It has been found that the contact parameter also appears in many other short-range (highmomentum) or short-time (high-frequency) properties of the system [11][12][13][14][15][16]. This parameter has recently been measured in an ultracold 40 K gas via the measurements of the highmomentum tail of the momentum distribution and of the highfrequency tail of the radio-frequency signal [17], and also measured in an ultracold 6 Li gas via the measurements of the static structure factor [18]. The measured temperature and scattering length dependence of the contact parameter compare well with the theoretical predictions [19,20].…”

Section: Introductionmentioning

confidence: 99%

Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble

Iskin

2011

Phys. Rev. A

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After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average and trapping energies, and for the entropy, specific heat, pressure and atomic compressibility of stronglycorrelated ultra-cold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly-interacting BCS and BEC limits, showing that the temperature dependence of the contact parameter can be determined by the variation of either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the Virial theorem in a canonical ensemble, and discuss its implications for quantum gases.

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Universal relations for a strongly interacting Fermi gas near a Feshbach resonance

Cited by 108 publications

References 24 publications

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Universal relation for the inelastic two-body loss rate

Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble

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