Fermi-Edge Singularity in the Vicinity of the Resonant Scattering Condition

Vv, Mkhitaryan; Me, Raikh

doi:10.1103/physrevlett.106.197003

Cited by 6 publications

(5 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Describing the OC requires the inclusion of the higherorder terms in the expansion (13) which poses a challenge for theory that attracted intensive interest starting with the work of Anderson [10]. Among other approaches [1,11,[126][127][128][129][130][131][132][133][134][135], for overviews we refer to [1,9,136,137], the FDA provides an efficient tool to address this problem and yields exact results for infinitely heavy impurities, also in the case of finite temperature where thermal averages have to be performed.…”

Section: A Reverse Rf Spectramentioning

confidence: 99%

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

et al. 2018

View full text Add to dashboard Cite

In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.

show abstract

Section: A Reverse Rf Spectramentioning

confidence: 99%

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Given the long illustrious history of the original problem, see Refs. [18][19][20][21][22][23][49][50][51][52][53][54][55] , it is useful to start by summarizing the new aspects of OC in cold atomic systems.…”

Section: Introductionmentioning

confidence: 99%

“…[18][19][20][21][22][23][51][52][53][54][55][56][57]), it is useful to start by summarizing the new aspects of the OC in cold atomic systems.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2012

View full text Add to dashboard Cite

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.

show abstract

“…The same physics that is behind the Fermi edge singularity describes for instance tunneling into and out of a small quantum dot coupled to an electron reservoir. 5 Recent studies have focused on non-equilibrium, [6][7][8][9][10][11][12] nonstationary, 13 and band structure 14 phenomena.…”

Section: Introductionmentioning

confidence: 99%

Fermi edge singularity and finite-frequency spectral features in a semi-infinite one-dimensional wire

Sheikhan

Snyman

2012

Phys. Rev. B

View full text Add to dashboard Cite

We theoretically study a charge qubit interacting with electrons in a semi-infinite 1D wire. The system displays the physics of the Fermi edge singularity. Our results generalize known results for the Fermi-edge system to the regime where excitations induced by the qubit can resolve the spatial structure of the scattering region. We find resonant features in the qubit tunneling rate as a function of the qubit level splitting. They occur at integer multiples of hvF /l. Here vF is the Fermi velocity of the electrons in the wire, and l is the distance from the tip of the wire to the point where it interacts with the qubit. These features are due to a single coherent charge fluctuation in the electron gas, with a half-wavelength that fits into l an integer number of times. As the coupling between the qubit and the wire is increased, the resonances are washed out. This is a clear signature of the increasingly violent Fermi-sea shake-up that accompanies strong coupling.

show abstract

Fermi-Edge Singularity in the Vicinity of the Resonant Scattering Condition

Cited by 6 publications

References 39 publications

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

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

Fermi edge singularity and finite-frequency spectral features in a semi-infinite one-dimensional wire

Contact Info

Product

Resources

About