Radio-frequency response and contact of impurities in a quantum gas

Abstract

We investigate the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermi's golden rule that introducing (or injecting) an impurity into the medium is equivalent to ejecting an impurity that is initially interacting with the medium, since the "injection" and "ejection" spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using a range of theoretical methods, including variational approaches. We use this property to compute the finite-temperature equation of state and Tan contact of the Fermi polaron. Our results for the contact of a mobile impurity are in excellent agreement with recent experiments and we find that the finite-temperature behavior is qualitatively different compared to the case of infinite impurity mass.

4 pages, 2 figures

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

Cited by in corpus (16)

• In situ thermometry of a cold Fermi gas via dephasing impurities
• Observation of a smooth polaron-molecule transition in a degenerate Fermi gas
• Quasiparticle lifetime of the repulsive Fermi polaron
• Universal aspects of a strongly interacting impurity in a dilute Bose condensate
• Theory of radio-frequency spectroscopy of impurities in quantum gases
• Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium
• Thermodynamic signatures of the polaron-molecule transition in a Fermi gas
• Crossover from exciton polarons to trions in doped two-dimensional semiconductors at finite temperature
• Rabi oscillations and magnetization of a mobile spin-1/2 impurity in a Fermi sea
• Mobile impurity in a one-dimensional gas at finite temperatures
• Universal properties of dipolar Bose polarons in two dimensions
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• Polaritons for testing the universality of an impurity in a Bose-Einstein condensate
• Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas
• Repulsive Fermi and Bose Polarons in Quantum Gases
• Single Particle Spectroscopies of $p$-wave and $d$-wave Interacting Bose Gases in Normal Phase