Theory of radio-frequency spectroscopy of impurities in quantum gases

Liu, Weizhe Edward; Shi, Zhe; Parish, Meera M.; Levinsen, Jesper

doi:10.1103/physreva.102.023304

Cited by 36 publications

(41 citation statements)

References 86 publications

(172 reference statements)

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“…Note that AðωÞ is equivalent to the probability distribution of work performed by suddenly switching on the impurity potential V imp ðrÞ [59,77,78]. Since the properties of vðtÞ and AðωÞ have been extensively discussed in the literature [24,56,62,63,[79][80][81], here we simply summarize the notable features. Scattering from the impurity generates particle-hole excitations in the gas.…”

mentioning

confidence: 99%

In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities

et al. 2020

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The precise measurement of low temperatures is a challenging, important, and fundamental task for quantum science. In particular, in situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here, we demonstrate that the temperature of a noninteracting Fermi gas can be accurately inferred from the nonequilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity.

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confidence: 99%

In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities

et al. 2020

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“…We therefore need to take Cauchy principle value of the integral. This numerical difficulty does not arise in the finite-temperature variational approach [41,43,45],…”

Section: A Numerical Calculationsmentioning

confidence: 99%

“…In more detail, in the ejection rf-spectrosocpy scheme, a system of strongly interacting Fermi polarons is initially prepared and then a rf pulse transfers impurities to a third, unoccupied hyperfine state. In the absence of the final-state effect (i.e., the transferred impurity atom does not interact with the Fermi sea) and in the linear response regime, the transfer rate as a function of the energy ω, defined as the ejection rf spectrum, is given by [38,43,[50][51][52],…”

Section: Ejection Rf-spectroscopy In the Unitary Limitmentioning

confidence: 99%

“…In the single impurity limit, n imp → 0 and µ I → −∞ at finite temperature. In this idealized case, we may replace the Fermi-Dirac distribution function by a classical Boltzmann distribution [43], f (ω − µ I ) ≃ e −βω e βµI . Therefore, we obtain,…”

Section: Ejection Rf-spectroscopy In the Unitary Limitmentioning

confidence: 99%

“…The latter may suffer from some uncontrollable errors, since, strictly speaking, the numerical analytic continuation is not a well-defined procedure [35,48]. Alternatively, an interesting finitetemperature variational approach has recently been proposed by Meera Parish and her collaborators [41,43,45]. By solving the Chevy ansatz (extended to finite temperature) at the level of one-particle-hole excitation and keeping a sufficiently large number of discrete eigenstates [41], both short-time dynamics and rf-spectroscopy of Fermi polarons at finite temperature have been investigated in detail.…”

Section: Introductionmentioning

confidence: 99%

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Fermi polarons at finite temperature: Spectral function and rf-spectroscopy

Hu,

Liu

2022

Preprint

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We present a systematic study of a mobile impurity immersed in a three-dimensional Fermi sea of fermions at finite temperature, by using the standard non-self-consistent many-body T -matrix theory that is equivalent to a finite-temperature variational approach with the inclusion of one-particlehole excitation. The impurity spectral function is determined in the real-frequency domain, avoiding any potential errors due to the numerical analytic continuation in previous T -matrix calculations and the small spectral broadening parameter used in variational calculations. In the weak-coupling limit, we find that the quasiparticle decay rate of both attractive and repulsive polarons does not increase significantly with increasing temperature, and therefore Fermi polarons may remain welldefined far above Fermi degeneracy. In contrast, near the unitary limit with strong coupling, the decay rate of Fermi polarons rapidly increase and the quasiparticle picture breaks down close to the Fermi temperature. We analyze in detail the recent ejection and injection radio-frequency (rf) spectroscopy measurements, performed at Massachusetts Institute of Technology (MIT) and at European Laboratory for Non-Linear Spectroscopy (LENS), respectively. We show that the momentum average of the spectral function, which is necessary to account for the observed rfspectroscopy, has a sizable contribution to the width of the quasiparticle peak in spectroscopy. As a result, the measured decay rate of Fermi polarons could be significantly larger than the calculated quasiparticle decay rate at zero momentum. By take this crucial contribution into account, we find that there is a reasonable agreement between theory and experiment for the lifetime of Fermi polarons in the strong-coupling regime, as long as they remain well-defined.

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Functional determinant approach investigations of heavy impurity physics

Wang

2023

AAPPS Bull.

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In this brief review, we report some new development in the functional determinant approach (FDA), an exact numerical method, in the studies of a heavy quantum impurity immersed in Fermi gases and manipulated with radio-frequency pulses. FDA has been successfully applied to investigate the universal dynamical responses of a heavy impurity in an ultracold ideal Fermi gas in both the time and frequency domain, which allows the exploration of the renowned Anderson’s orthogonality catastrophe (OC). In such a system, OC is induced by the multiple particle-hole excitations of the Fermi sea, which is beyond a simple perturbation picture and manifests itself as the absence of quasiparticles named polarons. More recently, two new directions for studying heavy impurity with FDA have been developed. One is to extend FDA to a strongly correlated background superfluid background, a Bardeen–Cooper–Schrieffer (BCS) superfluid. In this system, Anderson’s orthogonality catastrophe is prohibited due to the suppression of multiple particle-hole excitations by the superfluid gap, which leads to the existence of genuine polaron. The other direction is to generalize the FDA to the case of multiple RF pulses scheme, which extends the well-established 1D Ramsey spectroscopy in ultracold atoms into multidimensional, in the same spirit as the well-known multidimensional nuclear magnetic resonance and optical multidimensional coherent spectroscopy. Multidimensional Ramsey spectroscopy allows us to investigate correlations between spectral peaks of an impurity-medium system that is not accessible in the conventional one-dimensional spectrum.

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Theory of radio-frequency spectroscopy of impurities in quantum gases

Cited by 36 publications

References 86 publications

In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities

In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities

Fermi polarons at finite temperature: Spectral function and rf-spectroscopy

Functional determinant approach investigations of heavy impurity physics

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