Universal Many-Body Response of Heavy Impurities Coupled to a Fermi
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Reports on Progress in Physics REPORT ON PROGRESS Related content - Polarons, dressed molecules and itinerant Universal many-body response of heavy impurities ferromagnetism in ultracold Fermi gases Pietro Massignan, Matteo Zaccanti and coupled to a Fermi sea: a review of recent Georg M Bruun - Comparing and contrasting nuclei and cold progress atomic gases N T Zinner and A S Jensen To cite this article: Richard Schmidt et al 2018 Rep. Prog. Phys. 81 024401 - Recent developments in quantum Monte Carlo simulations with applications for cold gases Lode Pollet View the article online for updates and enhancements. This content was downloaded from IP address 128.103.149.52 on 03/02/2018 at 21:40 IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 81 (2018) 024401 (37pp) https://doi.org/10.1088/1361-6633/aa9593 81 Report on Progress 2018 Universal many-body response of heavy © 2018 IOP Publishing Ltd impurities coupled to a Fermi sea: RPPHAG a review of recent progress 024401 Richard Schmidt1,2,3 , Michael Knap4 , Dmitri A Ivanov5,6 , Richard Schmidt et al Jhih-Shih You1, Marko Cetina7,8,9 and Eugene Demler1 1 Department of Physics, Harvard University, Cambridge MA 02138, United States of America Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress 2 ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, United States of America 3 Institute of Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland Printed in the UK 4 Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany 5 Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland ROP 6 Department of Physics, University of Zürich, 8057 Zürich, Switzerland 7 Institut für Quantenoptik und Quanteninformation (IQOQI), Österreichische Akademie der 10.1088/1361-6633/aa9593 Wissenschaften, 6020 Innsbruck, Austria 8 Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria 9 Joint Quantum Institute and University of Maryland Department of Physics, College Park, 1361-6633 Maryland 20742, United States of America E-mail: [email protected] 2 Received 12 January 2017, revised 27 September 2017 Accepted for publication 24 October 2017 Published 5 January 2018 Corresponding Editor Professor Maciej Lewenstein Abstract 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 γ = πkBT/4. 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 T/TF 0.2 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 3He and the formation of Fermi polarons. The presented results are in excellent agreement with recent 1361-6633/18/024401+37$33.00 1 © 2018 IOP Publishing Ltd Printed in the UK Rep. Prog. Phys. 81 (2018) 024401 Report on Progress experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology. Keywords: quantum impurities, Feshbach resonances, Fermi gas, non-equilibrium dynamics, orthogonality catastrophe, functional determinants (Some figures may appear in colour only in the online journal) Contents D.2. Bottom-of-the-band and bound-state contributions.................................................................. 28 1. Introduction ......................................................................2 Appendix E. Asymptotic long-time response ............... 29 1.1. Progress towards studying real-time impurity E.1 Finite temperature ................................................... 29 dynamics .................................................................3 E.2. Zero temperature ................................................... 30 1.2. Outline .....................................................................4 Appendix F. Bi-exponential crossover .......................... 31 2. Anderson–Fano model with ultracold atoms ...................5 Appendix G. Subleading branches of Toeplitz 2.1. Feshbach resonances ...............................................5 determinants .................................................................. 31 2.2. Interaction regimes ..................................................6 References ..................................................................... 32 2.3. Anderson–Fano model ............................................6 3. Dynamic many-body responses .......................................7 3.1. Radio-frequency spectroscopy ................................7 3.1.1. ‘Standard’ RF spectroscopy. .........................7 3.1.2. ‘Reverse’ RF spectroscopy.. .........................8 3.2. Real-time responses ................................................8 1. Introduction 3.2.1. Ramsey interferometry. ................................8 3.2.2. Spin-echo interferometry .............................8 Exactly solvable models are a rare commodity in many-body 3.3. Functional determinant approach ............................8 physics [1]. Yet they provide a unique basis to develop a pro- 4. Universal many-body response: radio-frequency spectra 9 found understanding of physical systems and can serve as a 4.1. Reverse RF spectra ..................................................9 benchmark for approximate theoretical approaches. Examples 4.1.1. From Fermi polarons to the orthogonality include the Ising model [2], one-dimensional systems [3, 4], catastrophe. ................................................10 the Kitaev model [5, 6], or the Dicke model [7] which became 4.1.2. Single-particle interpretation. ....................11 paradigms of condensed matter physics and quantum optics. 4.1.3. Comparison to experiments.. .....................13 Heavy impurities interacting with a Fermi gas are another 4.2. Standard RF spectra ..............................................14 paradigmatic example that is exactly solvable and yet retains 5. Universal many-body response: dephasing dynamics ...14 the complexity of an interacting many-body system exhibiting 5.1. Exact numerical solution .......................................15 rich physics [8, 9]. Most prominently it features the orthogo- 5.2. Analytical results ..................................................16 nality catastrophe which defies a simple perturbative descrip- 5.2.1. Excitation branches. ...................................16 tion and signals the absence of quasiparticles even at weak 5.2.2. Temperature independent contributions. ....16 interactions, as first investigated by Anderson [10]. 5.2.3. Fermi-surface contributions.. .....................17 The Anderson orthogonality catastrophe manifests itself not 5.2.4. Bosonization. .............................................17 only in ground state properties but also in the non-equilibrium 5.2.5. Toeplitz-determinant approach.. ............... 20 dynamics. At long times, the power-law decay of coherence 5.3. Universal scaling relations ................................... 22 (for a definition see equation (10) and [11–13]) is one of its 5.4. Comparison to experiments ................................. 22 key manifestations which universally depends only on the scat- 6. Universal short-time, high-frequency response ............ 24 tering phase shift close to the Fermi surface. In contrast, the 6.1. RF response with finite initial and final state description of the short-time dynamics, being testament of the interactions ........................................................... 24 short-distance physics, suffers typically from the microscopic 6.2. Analytical high-frequency response..................... 24 unknown. In particular in conventional solid-state systems 6.2.1. Relation to the long-time evolution.. ........ 25 physics depends on the details of chemical bonding, the core- 7. Summary and outlook ................................................... 25 hole potentials, as well as their screening and relaxation, which Acknowledgments ......................................................... 26 leads to highly non-universal short-time