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Abstract
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
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Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium. ATOMS 2021. [DOI: 10.3390/atoms9010018] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.
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Yan Z, Patel PB, Mukherjee B, Fletcher RJ, Struck J, Zwierlein MW. Boiling a Unitary Fermi Liquid. PHYSICAL REVIEW LETTERS 2019; 122:093401. [PMID: 30932518 DOI: 10.1103/physrevlett.122.093401] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2018] [Indexed: 06/09/2023]
Abstract
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T^{2} dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝T^{-1/2}. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.
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Affiliation(s)
- Zhenjie Yan
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Parth B Patel
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Biswaroop Mukherjee
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Richard J Fletcher
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Julian Struck
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Département de Physique, Ecole Normale Supérieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Martin W Zwierlein
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Camacho-Guardian A, Peña Ardila LA, Pohl T, Bruun GM. Bipolarons in a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2018; 121:013401. [PMID: 30028169 DOI: 10.1103/physrevlett.121.013401] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Indexed: 06/08/2023]
Abstract
Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schrödinger equation describing this for an arbitrarily strong impurity-boson interaction. We furthermore compare with quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments, and we describe a procedure to probe their properties.
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Affiliation(s)
- A Camacho-Guardian
- Center for Quantum Optics and Quantum Matter, Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark
| | - L A Peña Ardila
- Center for Quantum Optics and Quantum Matter, Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark
| | - T Pohl
- Center for Quantum Optics and Quantum Matter, Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark
| | - G M Bruun
- Center for Quantum Optics and Quantum Matter, Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark
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Scazza F, Valtolina G, Massignan P, Recati A, Amico A, Burchianti A, Fort C, Inguscio M, Zaccanti M, Roati G. Repulsive Fermi Polarons in a Resonant Mixture of Ultracold ^{6}Li Atoms. PHYSICAL REVIEW LETTERS 2017; 118:083602. [PMID: 28282175 DOI: 10.1103/physrevlett.118.083602] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2016] [Indexed: 06/06/2023]
Abstract
We employ radio-frequency spectroscopy to investigate a polarized spin mixture of ultracold ^{6}Li atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy E_{+}, the effective mass m^{*}, the residue Z, and the decay rate Γ. Above a critical interaction, E_{+} is found to exceed the Fermi energy of the bath, while m^{*} diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.
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Affiliation(s)
- F Scazza
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - G Valtolina
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - P Massignan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
| | - A Recati
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
- Ludwig-Maximilians-Universität München, 80333 München, Germany
| | - A Amico
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - A Burchianti
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - C Fort
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - M Zaccanti
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - G Roati
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (INO-CNR), 50019 Sesto Fiorentino, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
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Cetina M, Jag M, Lous RS, Fritsche I, Walraven JTM, Grimm R, Levinsen J, Parish MM, Schmidt R, Knap M, Demler E. Ultrafast many-body interferometry of impurities coupled to a Fermi sea. Science 2016; 354:96-99. [PMID: 27846498 DOI: 10.1126/science.aaf5134] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2016] [Accepted: 09/06/2016] [Indexed: 11/02/2022]
Abstract
The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed matter systems, the time scale for such "ultrafast" processes is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we observed nonequilibrium dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the nonperturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasi-particles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods applied to strongly interacting quantum gases enable the study of the dynamics of quantum matter under extreme nonequilibrium conditions.
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Affiliation(s)
- Marko Cetina
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Michael Jag
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Rianne S Lous
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Isabella Fritsche
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Jook T M Walraven
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - Rudolf Grimm
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria.
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Jesper Levinsen
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Meera M Parish
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Richard Schmidt
- Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Michael Knap
- Department of Physics, Walter Schottky Institute and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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Massignan P, Zaccanti M, Bruun GM. Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:034401. [PMID: 24553400 DOI: 10.1088/0034-4885/77/3/034401] [Citation(s) in RCA: 62] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions--the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.
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Affiliation(s)
- Pietro Massignan
- ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels, Barcelona, Spain
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Bertaina G, Fratini E, Giorgini S, Pieri P. Quantum Monte Carlo study of a resonant Bose-Fermi mixture. PHYSICAL REVIEW LETTERS 2013; 110:115303. [PMID: 25166551 DOI: 10.1103/physrevlett.110.115303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2012] [Indexed: 06/03/2023]
Abstract
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density n(B) is smaller than the fermion density n(F), for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing n(B).
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Affiliation(s)
- G Bertaina
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne EPFL, CH-1015 Lausanne, Switzerland
| | - E Fratini
- School of Science and Technology, Physics Division, University of Camerino and CNISM, I-62032 Camerino, Italy
| | - S Giorgini
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
| | - P Pieri
- School of Science and Technology, Physics Division, University of Camerino and CNISM, I-62032 Camerino, Italy and INFN, Sezione di Perugia, Perugia, Italy
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Nascimbène S, Navon N, Pilati S, Chevy F, Giorgini S, Georges A, Salomon C. Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms. PHYSICAL REVIEW LETTERS 2011; 106:215303. [PMID: 21699311 DOI: 10.1103/physrevlett.106.215303] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2011] [Revised: 04/06/2011] [Indexed: 05/31/2023]
Abstract
We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.
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Affiliation(s)
- S Nascimbène
- Laboratoire Kastler Brossel, CNRS, UPMC, École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.
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Yu Z, Zöllner S, Pethick CJ. Comment on "Normal phase of an imbalanced Fermi gas". PHYSICAL REVIEW LETTERS 2010; 105:188901. [PMID: 21231143 DOI: 10.1103/physrevlett.105.188901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2010] [Indexed: 05/30/2023]
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