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Title: Motion of a distinguishable Impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking

Abstract

We consider the real-time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion—a period of quasistationary behavior. In conclusion, when the impurity is injected with a finite center-of-mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newton’s cradlelike scenario where momentum is exchanged back and forth between the impurity and the background gas.

Authors:
;  [1];  [2]
  1. Univ. of Amsterdam, Amsterdam (The Netherlands)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1263909
Alternate Identifier(s):
OSTI ID: 1246179
Report Number(s):
BNL-112265-2016-JA
Journal ID: ISSN 0031-9007; PRLTAO; R&D Project: PO015; KC0202030
Grant/Contract Number:  
SC00112704; AC02-98CH10886; SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 116; Journal Issue: 14; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Neil J. Robinson, Caux, Jean -Sebastien, and Konik, Robert M. Motion of a distinguishable Impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking. United States: N. p., 2016. Web. doi:10.1103/PhysRevLett.116.145302.
Neil J. Robinson, Caux, Jean -Sebastien, & Konik, Robert M. Motion of a distinguishable Impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking. United States. https://doi.org/10.1103/PhysRevLett.116.145302
Neil J. Robinson, Caux, Jean -Sebastien, and Konik, Robert M. Thu . "Motion of a distinguishable Impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking". United States. https://doi.org/10.1103/PhysRevLett.116.145302. https://www.osti.gov/servlets/purl/1263909.
@article{osti_1263909,
title = {Motion of a distinguishable Impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking},
author = {Neil J. Robinson and Caux, Jean -Sebastien and Konik, Robert M.},
abstractNote = {We consider the real-time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion—a period of quasistationary behavior. In conclusion, when the impurity is injected with a finite center-of-mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newton’s cradlelike scenario where momentum is exchanged back and forth between the impurity and the background gas.},
doi = {10.1103/PhysRevLett.116.145302},
journal = {Physical Review Letters},
number = 14,
volume = 116,
place = {United States},
year = {Thu Apr 07 00:00:00 EDT 2016},
month = {Thu Apr 07 00:00:00 EDT 2016}
}

Journal Article:

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Cited by: 22 works
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Works referenced in this record:

Relaxation and Prethermalization in an Isolated Quantum System
journal, September 2012


On form factors in nested Bethe Ansatz systems
journal, October 2012

  • Pozsgay, Balázs; van Gerven Oei, Willem-Victor; Kormos, Márton
  • Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 46
  • DOI: 10.1088/1751-8113/45/46/465007

The Hubbard chain: Lieb–Wu equations and norm of the eigenfunctions
journal, December 1999


Dynamics, dephasing and clustering of impurity atoms in Bose–Einstein condensates
journal, November 2007


An eccentrically perturbed Tonks–Girardeau gas
journal, September 2010


Correspondence between dark solitons and the type II excitations of the Lieb-Liniger model
journal, January 2015


Form Factors in the Finite Volume
journal, October 1999

  • Korepin, V. E.; Slavnov, N. A.
  • International Journal of Modern Physics B, Vol. 13, Issue 24n25
  • DOI: 10.1142/s0217979299002769

Prethermalization revealed by the relaxation dynamics of full distribution functions
journal, July 2013


Prethermalization in one-dimensional Bose gases: Description by a stochastic Ornstein-Uhlenbeck process
journal, February 2013

  • Langen, Tim; Gring, Michael; Kuhnert, Maximilian
  • The European Physical Journal Special Topics, Vol. 217, Issue 1
  • DOI: 10.1140/epjst/e2013-01752-0

Dynamical Arrest of Ultracold Lattice Fermions
journal, February 2013


Determinant Representation for Dynamical Correlation Functions of the Quantum Nonlinear Schrödinger Equation
journal, October 1997

  • Kojima, T.; Korepin, V. E.; Slavnov, N. A.
  • Communications in Mathematical Physics, Vol. 188, Issue 3
  • DOI: 10.1007/s002200050182

Exact quantum dynamics of yrast states in the finite 1D Bose gas
journal, April 2014


Quantum flutter of supersonic particles in one-dimensional quantum liquids
journal, October 2012

  • Mathy, Charles J. M.; Zvonarev, Mikhail B.; Demler, Eugene
  • Nature Physics, Vol. 8, Issue 12
  • DOI: 10.1038/nphys2455

Three-dimensional localization of ultracold atoms in an optical disordered potential
journal, March 2012

  • Jendrzejewski, F.; Bernard, A.; Müller, K.
  • Nature Physics, Vol. 8, Issue 5
  • DOI: 10.1038/nphys2256

Form factors of local operators in a one-dimensional two-component Bose gas
journal, October 2015


Observation of a One-Dimensional Tonks-Girardeau Gas
journal, August 2004


Phonon resonances in atomic currents through Bose-Fermi mixtures in optical lattices
journal, October 2010


Tonks–Girardeau gas of ultracold atoms in an optical lattice
journal, May 2004

  • Paredes, Belén; Widera, Artur; Murg, Valentin
  • Nature, Vol. 429, Issue 6989
  • DOI: 10.1038/nature02530

Calculation of the norm of bethe vectors in models with SU(3)-symmetry
journal, July 1989

  • Reshetikhin, N. Yu.
  • Journal of Soviet Mathematics, Vol. 46, Issue 1
  • DOI: 10.1007/bf01099200

Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases
journal, February 2014


Coherent Interaction of a Single Fermion with a Small Bosonic Field
journal, March 2011


Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms
journal, January 2012

  • Schneider, Ulrich; Hackermüller, Lucia; Ronzheimer, Jens Philipp
  • Nature Physics, Vol. 8, Issue 3
  • DOI: 10.1038/nphys2205

Experimental observation of a generalized Gibbs ensemble
journal, April 2015


Breathing oscillations of a trapped impurity in a Bose gas
journal, April 2012


Dynamics of an impurity in a one-dimensional lattice
journal, April 2013


Non-equilibrium coherence dynamics in one-dimensional Bose gases
journal, September 2007

  • Hofferberth, S.; Lesanovsky, I.; Fischer, B.
  • Nature, Vol. 449, Issue 7160
  • DOI: 10.1038/nature06149

Correlation functions of integrable models: A description of the ABACUS algorithm
journal, September 2009

  • Caux, Jean-Sébastien
  • Journal of Mathematical Physics, Vol. 50, Issue 9
  • DOI: 10.1063/1.3216474

Slow Electrons in a Polar Crystal
journal, February 1955


Prethermalization in a Nonintegrable Quantum Spin Chain after a Quench
journal, November 2013


Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
journal, August 2011


Real-time evolution for weak interaction quenches in quantum systems
journal, October 2009


Spin-charge separation in two-component Bose gases
journal, January 2008


Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
journal, March 2007

  • Lewenstein, Maciej; Sanpera, Anna; Ahufinger, Veronica
  • Advances in Physics, Vol. 56, Issue 2
  • DOI: 10.1080/00018730701223200

Norms of Bethe wave functions for the nonlinear Schrödinger model of spin‐1/2 particles
journal, October 1990

  • Pang, Gen‐di; Pu, Fu‐cho; Zhao, Bao‐heng
  • Journal of Mathematical Physics, Vol. 31, Issue 10
  • DOI: 10.1063/1.528993

Self-localized state and solitons in a Bose-Einstein-condensate–impurity mixture at finite temperature
journal, July 2014


Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas
journal, February 2012

  • Trotzky, S.; Chen, Y-A.; Flesch, A.
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2232

A quantum Newton's cradle
journal, April 2006

  • Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
  • Nature, Vol. 440, Issue 7086
  • DOI: 10.1038/nature04693

Dynamical density-density correlations in the one-dimensional Bose gas
journal, September 2006


Quantum Transport through a Tonks-Girardeau Gas
journal, October 2009


One dimensional bosons: From condensed matter systems to ultracold gases
journal, December 2011


Quantum dynamics of impurities in a one-dimensional Bose gas
journal, February 2012


Real-time dynamics of an impurity in an ideal Bose gas in a trap
journal, August 2015


Dynamical depinning of a Tonks-Girardeau gas
journal, December 2015


Quantum distillation: Dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
journal, October 2009


Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs
journal, January 2012


Self-trapping in the two-dimensional Bose-Hubbard model
journal, September 2013


Expansion Dynamics of Interacting Bosons in Homogeneous Lattices in One and Two Dimensions
journal, May 2013


Sudden expansion of Mott insulators in one dimension
journal, December 2013


Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
journal, October 2015


Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
journal, June 2009


Excitons in Metals: Infinite Hole Mass
journal, November 1967


Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution
journal, February 1969


Infrared Catastrophe in Fermi Gases with Local Scattering Potentials
journal, June 1967


One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm
journal, September 2012

  • Imambekov, Adilet; Schmidt, Thomas L.; Glazman, Leonid I.
  • Reviews of Modern Physics, Vol. 84, Issue 3
  • DOI: 10.1103/RevModPhys.84.1253

Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas
journal, December 2007


Observation of Complex Bound States in the Spin- 1 / 2 Heisenberg X X Z Chain Using Local Quantum Quenches
journal, February 2012


Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas
journal, December 2011


Quantum Flutter: Signatures and Robustness
journal, January 2014


Momentum relaxation of a mobile impurity in a one-dimensional quantum gas
journal, April 2014


Quantum Boltzmann equation for a mobile impurity in a degenerate Tonks-Girardeau gas
journal, June 2014


Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas
journal, September 2014


Perpetual motion of a mobile impurity in a one-dimensional quantum gas
journal, March 2014


Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963


Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
journal, May 1963


Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
journal, December 1967


Further Results for the Many-Body Problem in One Dimension
journal, January 1968


Polarization suppression and nonmonotonic local two-body correlations in the two-component Bose gas in one dimension
journal, December 2009

  • Caux, Jean-Sébastien; Klauser, Antoine; van den Brink, Jeroen
  • Physical Review A, Vol. 80, Issue 6
  • DOI: 10.1103/PhysRevA.80.061605

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension
journal, September 2011


Exact yrast spectra of cold atoms on a ring
journal, March 2011


Exact Relaxation Dynamics of a Localized Many-Body State in the 1D Bose Gas
journal, March 2012


Recurrence Time in the Quantum Dynamics of the 1D Bose Gas
journal, June 2015

  • Kaminishi, Eriko; Sato, Jun; Deguchi, Tetsuo
  • Journal of the Physical Society of Japan, Vol. 84, Issue 6
  • DOI: 10.7566/JPSJ.84.064002

Nonequal-time current correlation function in a one-dimensional Bose gas
journal, March 1990

  • Slavnov, N. A.
  • Theoretical and Mathematical Physics, Vol. 82, Issue 3
  • DOI: 10.1007/BF01029221

Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
journal, November 2011


Interaction Quench in the Hubbard Model
journal, May 2008


Metastable Superfluidity of Repulsive Fermionic Atoms in Optical Lattices
journal, December 2008


Quench dynamics in a model with tuneable integrability breaking
journal, April 2014


Prethermalization of weakly interacting bosons after a sudden interaction quench
journal, May 2015


Pre-relaxation in weakly interacting models
journal, July 2015


Spontaneous Solitons in the Thermal Equilibrium of a Quasi-1D Bose Gas
journal, November 2012


Non-equilibrium coherence dynamics in one-dimensional Bose gases
text, January 2007


Dynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates
text, January 2007


Interaction Quench in the Hubbard model
text, January 2008


Phonon resonances in atomic currents through Bose-Fermi mixtures in optical lattices
text, January 2010


One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
text, January 2011


Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs
text, January 2011


Dynamical arrest of ultracold lattice fermions
text, January 2012


Dynamics of an impurity in a one-dimensional lattice
text, January 2012


Quantum Flutter: Signatures and Robustness
text, January 2013


Self trapping in the two-dimensional Bose-Hubbard model
text, January 2013


Polarons, Dressed Molecules, and Itinerant Ferromagnetism in ultracold Fermi gases
text, January 2013


Quench Dynamics in a Model with Tuneable Integrability Breaking
text, January 2013


Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas
text, January 2014


Pre-relaxation in weakly interacting models
text, January 2015


Real-Time Dynamics of an Impurity in an Ideal Bose Gas in a Trap
text, January 2015


Form factors of local operators in a one-dimensional two-component Bose gas
text, January 2015


Dynamical depinning of a Tonks Girardeau gas
text, January 2015


Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
text, January 2015


Works referencing / citing this record:

Effective approach to impurity dynamics in one-dimensional trapped Bose gases
journal, July 2019


Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid
journal, September 2016


Bose polaron as an instance of quantum Brownian motion
journal, September 2017


Correlated quantum dynamics of two quenched fermionic impurities immersed in a Bose-Einstein condensate
journal, August 2019


Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
journal, August 2018


Quench Dynamics and Orthogonality Catastrophe of Bose Polarons
journal, May 2019


Topological states in the Kronig–Penney model with arbitrary scattering potentials
journal, January 2019

  • Reshodko, Irina; Benseny, Albert; Romhányi, Judit
  • New Journal of Physics, Vol. 21, Issue 1
  • DOI: 10.1088/1367-2630/aaf9bf

Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid
text, January 2016


Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
text, January 2017


Topological states in the Kronig-Penney model with arbitrary scattering potentials
text, January 2018