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Morera I, Ołdziejewski R, Astrakharchik GE, Juliá-Díaz B. Superexchange Liquefaction of Strongly Correlated Lattice Dipolar Bosons. PHYSICAL REVIEW LETTERS 2023; 130:023602. [PMID: 36706388 DOI: 10.1103/physrevlett.130.023602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 11/03/2022] [Accepted: 12/07/2022] [Indexed: 06/18/2023]
Abstract
We propose a mechanism for liquid formation in strongly correlated lattice systems. The mechanism is based on an interplay between long-range attraction and superexchange processes. As an example, we study dipolar bosons in one-dimensional optical lattices. We present a perturbative theory and validate it in comparison with full density-matrix renormalization group simulations for the energetic and structural properties of different phases of the system, i.e., self-bound Mott insulator, liquid, and gas. We analyze the nonequilibrium properties and calculate the dynamic structure factor. Its structure differs in compressible and insulating phases. In particular, the low-energy excitations in compressible phases are linear phonons. We extract the speed of sound and analyze its dependence on dipolar interaction and density. We show that it exhibits a nontrivial behavior owing to the breaking of Galilean invariance. We argue that an experimental detection of this previously unknown quantum liquid could provide a fingerprint of the superexchange process and open intriguing possibilities for investigating non-Galilean invariant liquids.
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Affiliation(s)
- Ivan Morera
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Rafał Ołdziejewski
- Max Planck Institute of Quantum Optics, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 Munich, Germany
| | - Grigori E Astrakharchik
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
| | - Bruno Juliá-Díaz
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
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Takayoshi S, Giamarchi T. Dynamical conductivity of disordered quantum chains. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2022; 76:213. [PMID: 36397821 PMCID: PMC9640472 DOI: 10.1140/epjd/s10053-022-00524-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 10/07/2022] [Indexed: 06/16/2023]
Abstract
ABSTRACT We study the transport properties of a one-dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest-neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high-frequency regime, the conductivity decays as a power law, with an interaction-dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low-frequency regime, we find a behavior consistent with the one of the noninteracting system ω 2 ( ln ω ) 2 independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases.
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Affiliation(s)
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, University of Geneva, 1211 Geneva, Switzerland
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Anderson R, Wang F, Xu P, Venu V, Trotzky S, Chevy F, Thywissen JH. Conductivity Spectrum of Ultracold Atoms in an Optical Lattice. PHYSICAL REVIEW LETTERS 2019; 122:153602. [PMID: 31050527 DOI: 10.1103/physrevlett.122.153602] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2018] [Indexed: 06/09/2023]
Abstract
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
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Affiliation(s)
- Rhys Anderson
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Fudong Wang
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Peihang Xu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Vijin Venu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Stefan Trotzky
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
| | - Joseph H Thywissen
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1 Canada
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Lucas A, Gazit S, Podolsky D, Witczak-Krempa W. Dynamical Response near Quantum Critical Points. PHYSICAL REVIEW LETTERS 2017; 118:056601. [PMID: 28211720 DOI: 10.1103/physrevlett.118.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Indexed: 06/06/2023]
Abstract
We study high-frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from quantum field theory allow us to fix the high-frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality and numerically via quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high-frequency optical conductivity and the corresponding sum rule.
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Affiliation(s)
- Andrew Lucas
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Snir Gazit
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | | | - William Witczak-Krempa
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Département de Physique, Université de Montréal, Montréal (Québec), H3C 3J7, Canada
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Bukov M, Kolodrubetz M, Polkovnikov A. Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields. PHYSICAL REVIEW LETTERS 2016; 116:125301. [PMID: 27058085 DOI: 10.1103/physrevlett.116.125301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.
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Affiliation(s)
- Marin Bukov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Michael Kolodrubetz
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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Observation of coherent quench dynamics in a metallic many-body state of fermionic atoms. Nat Commun 2015; 6:6009. [DOI: 10.1038/ncomms7009] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Accepted: 12/01/2014] [Indexed: 11/09/2022] Open
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Cai Z, Schollwöck U, Pollet L. Identifying a bath-induced bose liquid in interacting spin-boson models. PHYSICAL REVIEW LETTERS 2014; 113:260403. [PMID: 25615290 DOI: 10.1103/physrevlett.113.260403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 06/04/2023]
Abstract
We study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing spin-boson models to interacting spin-boson systems. We show that a bath-induced Bose liquid phase can occur in the ground state phase diagram away from half filling. This phase is compressible, gapless, and conducting but not superfluid. At half filling, only a Luttinger liquid and a charge density wave are found. The phase transition between them is of Kosterlitz-Thouless type where the Luttinger parameter takes a nonuniversal value. The applied quantum Monte Carlo method can be used for all open bosonic and unfrustrated spin systems, regardless of their dimension, filling factor, and spectrum of the dissipation as long as the quantum system couples to the bath via the density operators.
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Affiliation(s)
- Zi Cai
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Ulrich Schollwöck
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
| | - Lode Pollet
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
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Gazit S, Podolsky D, Auerbach A. Critical capacitance and charge-vortex duality near the superfluid-to-insulator transition. PHYSICAL REVIEW LETTERS 2014; 113:240601. [PMID: 25541760 DOI: 10.1103/physrevlett.113.240601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2014] [Indexed: 06/04/2023]
Abstract
Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies in two space dimensions, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2) model. The product of dynamical conductivities at mirror points is used as a quantitative measure of deviations from self-duality between charge and vortex theories. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral lattice bosons.
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Affiliation(s)
- Snir Gazit
- Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel
| | - Daniel Podolsky
- Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel
| | - Assa Auerbach
- Physics Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel
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Chen K, Liu L, Deng Y, Pollet L, Prokof'ev N. Universal conductivity in a two-dimensional superfluid-to-insulator quantum critical system. PHYSICAL REVIEW LETTERS 2014; 112:030402. [PMID: 24484123 DOI: 10.1103/physrevlett.112.030402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2013] [Indexed: 06/03/2023]
Abstract
We compute the universal conductivity of the (2+1)-dimensional XY universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical (2+1)-dimensional J-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, σ(∞) = 0.359(4)σQ with σQ the conductivity quantum. The universal conductivity curve is the standard example with the lowest number of components where the bottoms-up AdS/CFT correspondence from string theory can be tested and made to use [R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D 83, 066017 (2011)]. For the first time, the shape of the σ(iω(n)) - σ(∞) function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particlelike nature of charge transport. We find that the holographic gauge-gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation.
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Affiliation(s)
- Kun Chen
- National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Longxiang Liu
- National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Youjin Deng
- National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Lode Pollet
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Nikolay Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA and Russian Research Center "Kurchatov Institute", 123182 Moscow, Russia
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Knap M, Kantian A, Giamarchi T, Bloch I, Lukin MD, Demler E. Probing real-space and time-resolved correlation functions with many-body Ramsey interferometry. PHYSICAL REVIEW LETTERS 2013; 111:147205. [PMID: 24138270 DOI: 10.1103/physrevlett.111.147205] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2013] [Revised: 09/18/2013] [Indexed: 06/02/2023]
Abstract
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
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Affiliation(s)
- Michael Knap
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
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Eggel T, Cazalilla MA, Oshikawa M. Dynamical theory of superfluidity in one dimension. PHYSICAL REVIEW LETTERS 2011; 107:275302. [PMID: 22243315 DOI: 10.1103/physrevlett.107.275302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2011] [Revised: 07/13/2011] [Indexed: 05/31/2023]
Abstract
A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function. Applications of these results to the understanding of the superfluid properties of helium confined in 1D pores with nanometer diameter, dislocations in solid 4He, and ultracold atomic gases are also briefly discussed.
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Affiliation(s)
- Thomas Eggel
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Japan
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Sadgrove M, Nakagawa K. Fast, externally triggered, digital phase controller for an optical lattice. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2011; 82:113104. [PMID: 22128963 DOI: 10.1063/1.3655447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present a method to control the phase of an optical lattice according to an external trigger signal. The method has a latency of less than 30 μs. Two phase locked digital synthesizers provide the driving signal for two acousto-optic modulators which control the frequency and phase of the counter-propagating beams which form a standing wave (optical lattice). A micro-controller with an external interrupt function is connected to the desired external signal, and updates the phase register of one of the synthesizers when the external signal changes. The standing wave (period λ/2 = 390 nm) can be moved by units of 49 nm with a mean jitter of 28 nm. The phase change is well known due to the digital nature of the synthesizer, and does not need calibration. The uses of the scheme include coherent control of atomic matter-wave dynamics.
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Affiliation(s)
- Mark Sadgrove
- Institute for Laser Science, The University of Electro-Communication, 1-5-1 Chofugaoka, Chofu, Japan.
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