Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas

Goold, John; Fogarty, Thomás; Gullo, Nicola; Paternostro, Mauro; Busch, Thomas

doi:10.1103/physreva.84.063632

Cited by 123 publications

(184 citation statements)

References 27 publications

(39 reference statements)

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“…[66]): Initially, the impurity is prepared in the down state j #i, and the fermions are in the ground state jc 0 i. Then, the Ramsey interferometry is performed: At time t ¼ 0, a =2 pulse is applied, such that the system is driven into the superposition state j#iþj"i ffiffi 2 p jc 0 i.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

et al. 2012

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“…Also, while the LE for local perturbations -the X-ray edge singularity problem -is well understood, its behavior in generic many-body systems is poorly described [7]. Studies so far mostly focused on local perturbations and simple refermionizable spin chain models [8][9][10].…”

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confidence: 99%

“…Alternatively, the LE can be measured using Ramsey interferometry [8,9]: initializing the qubit in the | state with weak interactions to the cold atoms, yields a wavefunction | ⊗ |Ψ 0 at t = 0. By applying a π/2 rf pulse [33], a superposition of the two qubit states is produced (| + | )/ √ 2 ⊗ |Ψ 0 , yielding distinct, qubit state dependent time evolution for |Ψ 0 .…”

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confidence: 99%

Loschmidt Echo and the Many-Body Orthogonality Catastrophe in a Qubit-Coupled Luttinger Liquid

et al. 2013

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We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behaviour: the steady state exponent after quenching back and forth n-times between 2 LLs (bang-bang protocol) is 2n-times bigger than that of the adiabatic overlap, and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry. Introduction. The long coherence times and the possibility to control parameters very accurately in optical lattices allow to simulate exciting non-equilibrium effects in quantum many body systems. Particular attention has been devoted to the evolution of quantum stated after quenches [1] in which a parameter in the Hamiltonian is changed either suddenly or gradually. By measuring the Loschmidt echo (LE), it is possible to get insight into the dynamical properties of the quantum-many body state.The LE is defined as the overlap of two wave functions, |Ψ 0 (t) and |Ψ(t) , evolved from the same initial state, but with different Hamiltonians, H 0 and H,

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“…By now impurities have been used to investigate the atomic density distribution [11], as well as exotic quasi-particles such as Fröhlich polarons [12]. These results show that impurities are very robust and reliable tools to investigate the underlying condensate behaviour, and many proposals for further investigations exist [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 96%

Topological defect dynamics of vortex lattices in Bose-Einstein condensates

O’Riordan

Busch

2016

Phys. Rev. A

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Vortex lattices in rapidly rotating Bose-Einstein condensates are systems of topological excitations that arrange themselves into periodic patterns. Here we show how phase-imprinting techniques can be used to create a controllable number of defects in these lattices and examine the resulting dynamics. Even though we describe our system using the mean-field Gross-Pitaevskii theory, the full range of many particle effects among the vortices can be studied. In particular we find the existence of localized vacancies that are quasi-stable over long periods of time, and characterize the effects on the background lattice through use of the orientational correlation function, and Delaunay triangulation.

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Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas

Cited by 123 publications

References 27 publications

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

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

Loschmidt Echo and the Many-Body Orthogonality Catastrophe in a Qubit-Coupled Luttinger Liquid

Topological defect dynamics of vortex lattices in Bose-Einstein condensates

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