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Mitchison MT, Fogarty T, Guarnieri G, Campbell S, Busch T, Goold J. In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities. PHYSICAL REVIEW LETTERS 2020; 125:080402. [PMID: 32909771 DOI: 10.1103/physrevlett.125.080402] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 07/27/2020] [Indexed: 06/11/2023]
Abstract
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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Affiliation(s)
- Mark T Mitchison
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Giacomo Guarnieri
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
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2
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De Nardis J, Panfil M. Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States. PHYSICAL REVIEW LETTERS 2018; 120:217206. [PMID: 29883179 DOI: 10.1103/physrevlett.120.217206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Indexed: 06/08/2023]
Abstract
The singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very difficult in most cold atomic experimental settings. Moreover the presence of a finite temperature destroys another feature of one-dimensional quantum liquids: the real space quasilong-range order in which the spatial correlation functions exhibit power-law decay. We consider a nonequilibrium protocol where two interacting Bose gases are prepared either at different temperatures or chemical potentials and then joined. We show that the nonequilibrium steady state emerging at large times around the junction displays edge singularities in the response function and quasilong-range order.
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Affiliation(s)
- Jacopo De Nardis
- Département de Physique, École Normale Supérieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Miłosz Panfil
- Institute of Theoretical Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
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Benjamin D, Klich I, Demler E. Single-band model of resonant inelastic x-ray scattering by quasiparticles in high-T(c) cuprate superconductors. PHYSICAL REVIEW LETTERS 2014; 112:247002. [PMID: 24996103 DOI: 10.1103/physrevlett.112.247002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Indexed: 06/03/2023]
Abstract
We show that a simple model of noninteracting quasiparticles accurately describes resonant inelastic x-ray scattering (RIXS) experiments in the hole-doped cuprate superconductors. Band structure alone yields signatures previously attributed to collective magnetic modes, such as the dispersing peaks and nontrivial polarization dependence found in several experiments. We conclude that RIXS data can be explained without positing the existence of magnetic excitations that persist with increasing doping. In so doing we develop a formalism for RIXS in itinerant electron systems that accounts for the positively charged core hole exactly and discover a mechanism by which the core hole produces polarization dependence mimicking that of a magnetic system.
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Affiliation(s)
- David Benjamin
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Israel Klich
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Eugene Demler
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Schiró M, Mitra A. Transient orthogonality catastrophe in a time-dependent nonequilibrium environment. PHYSICAL REVIEW LETTERS 2014; 112:246401. [PMID: 24996096 DOI: 10.1103/physrevlett.112.246401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2013] [Indexed: 06/03/2023]
Abstract
We study the response of a highly excited time-dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient nonequilibrium environment. To this extent we consider, as a key quantity, the overlap between time-dependent wave functions, which we write in terms of a novel two-time correlator generalizing the standard Loschmidt echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through nonequilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one-dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power-law structure even in the presence of a large nonequilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of nonlinearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.
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Affiliation(s)
- Marco Schiró
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA; Department of Chemistry, Columbia University, New York, New York 10027, USA; and Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191 Gif-sur-Yvette, France
| | - Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
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Protopopov IV, Gutman DB, Mirlin AD. Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants. PHYSICAL REVIEW LETTERS 2013; 110:216404. [PMID: 23745901 DOI: 10.1103/physrevlett.110.216404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Indexed: 06/02/2023]
Abstract
We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(1+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.
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Affiliation(s)
- I V Protopopov
- Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
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Benjamin D, Abanin D, Abbamonte P, Demler E. Microscopic theory of resonant soft-x-ray scattering in materials with charge order: the example of charge stripes in high-temperature cuprate superconductors. PHYSICAL REVIEW LETTERS 2013; 110:137002. [PMID: 23581360 DOI: 10.1103/physrevlett.110.137002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2012] [Indexed: 06/02/2023]
Abstract
We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.
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Affiliation(s)
- David Benjamin
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Kovrizhin DL, Chalker JT. Relaxation in driven integer quantum Hall edge states. PHYSICAL REVIEW LETTERS 2012; 109:106403. [PMID: 23005309 DOI: 10.1103/physrevlett.109.106403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2011] [Indexed: 06/01/2023]
Abstract
A highly nonthermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al., Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.
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Affiliation(s)
- D L Kovrizhin
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
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Ubbelohde N, Roszak K, Hohls F, Maire N, Haug RJ, Novotný T. Strong quantum memory at resonant Fermi edges revealed by shot noise. Sci Rep 2012; 2:374. [PMID: 22530093 PMCID: PMC3332523 DOI: 10.1038/srep00374] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2011] [Accepted: 04/02/2012] [Indexed: 12/01/2022] Open
Abstract
Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.
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Affiliation(s)
- N. Ubbelohde
- Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraβe 2, D-30167 Hannover, Germany
| | - K. Roszak
- Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, CZ-12116 Prague, Czech Republic
- Institute of Physics, Wroctaw University of Technology, PL-50370 Wroctaw, Poland
| | - F. Hohls
- Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraβe 2, D-30167 Hannover, Germany
- Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany
| | - N. Maire
- Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraβe 2, D-30167 Hannover, Germany
| | - R. J. Haug
- Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraβe 2, D-30167 Hannover, Germany
| | - T. Novotný
- Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, CZ-12116 Prague, Czech Republic
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Mkhitaryan VV, Raikh ME. Fermi-edge singularity in the vicinity of the resonant scattering condition. PHYSICAL REVIEW LETTERS 2011; 106:197003. [PMID: 21668193 DOI: 10.1103/physrevlett.106.197003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2010] [Indexed: 05/30/2023]
Abstract
Fermi-edge absorption theory predicting the spectrum A(ω) ∝ ω(-2δ(0)/π+δ(0)92)/π2) relies on the assumption that scattering phase δ(0) is frequency independent. The dependence of δ(0) on ω becomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, because of the finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate the finite time delay into the theory, solve the Dyson equation with a modified kernel, and find that, near the resonance, A(ω) behaves as ω(-3/4)|lnω|. Scattering off the core hole becomes resonant in 1D and 2D in the presence of an empty subband above the Fermi level; then a deep hole splits off a level from the bottom of this subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.
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Affiliation(s)
- V V Mkhitaryan
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
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Gutman DB, Gefen Y, Mirlin AD. Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing. PHYSICAL REVIEW LETTERS 2008; 101:126802. [PMID: 18851399 DOI: 10.1103/physrevlett.101.126802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2008] [Indexed: 05/26/2023]
Abstract
A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.
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Affiliation(s)
- D B Gutman
- Institut für Theorie der kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany
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Gutman DB, Gefen Y, Mirlin AD. Nonequilibrium zero-bias anomaly in disordered metals. PHYSICAL REVIEW LETTERS 2008; 100:086801. [PMID: 18352647 DOI: 10.1103/physrevlett.100.086801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2007] [Indexed: 05/26/2023]
Abstract
We extend the theory of a zero-bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film to out-of-equilibrium conditions. An effective action describing virtual fluctuations out of equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.
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Affiliation(s)
- D B Gutman
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
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Snyman I, Nazarov YV. Polarization of a charge qubit strongly coupled to a voltage-driven quantum point contact. PHYSICAL REVIEW LETTERS 2007; 99:096802. [PMID: 17931026 DOI: 10.1103/physrevlett.99.096802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2006] [Indexed: 05/25/2023]
Abstract
We study a charge qubit with level splitting epsilon, coupled to a quantum point contact driven by voltage V. In the limit of weak coupling, the qubit polarization shows cusps at epsilon=+/-eV. We show that, for stronger couplings, prominent peculiarities occur at fractions epsilon=+/-eV/2. Further increase of the coupling leads to a polarization corresponding to a pseudo Boltzmann distribution with an effective temperature approximately eV.
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Affiliation(s)
- I Snyman
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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Bettelheim E, Abanov AG, Wiegmann P. Orthogonality catastrophe and shock waves in a nonequilibrium Fermi gas. PHYSICAL REVIEW LETTERS 2006; 97:246402. [PMID: 17280305 DOI: 10.1103/physrevlett.97.246402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2006] [Indexed: 05/13/2023]
Abstract
A semiclassical wave packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock-wave phenomenon. The nonlinear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the orthogonality catastrophe. We study a generalization of this phenomenon to the nonequilibrium regime and show how the orthogonality catastrophe cures the gradient catastrophe, by providing a dispersive regularization mechanism.
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Affiliation(s)
- E Bettelheim
- James Frank Institute, University of Chicago, 5640 S. Ellis Ave., Chicago, Illinois 60637, USA
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