Separation of Time Scales in a Quantum Newton’s Cradle
Abstract
For strongly repulsive bosons in one dimension, we provide detailed modeling of the Bragg pulse used in quantum Newton's cradle-like settings or in Bragg spectroscopy experiments. By employing the Fermi-Bose mapping for a nite harmonically trapped gas and the Quench Action approach for a thermodynamic system on a ring, we reconstruct the exact post-pulse many-body time evolution of Lieb-Liniger gases in the Tonks-Girardeau limit, together with their changing local density pro le and momentum distribution. Our results display a clear separation of timescales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behaviour.
- Authors:
-
- Univ. of Amsterdam (Netherlands)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1412758
- Alternate Identifier(s):
- OSTI ID: 1255317
- Report Number(s):
- BNL-114731-2017-JA
Journal ID: ISSN 0031-9007; PRLTAO; R&D Project: PO015; KC0202030; TRN: US1800350
- Grant/Contract Number:
- SC0012704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 116; Journal Issue: 22; 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
van den Berg, R., Wouters, B., Eliëns, S., De Nardis, J., Konik, R. M., and Caux, J. -S. Separation of Time Scales in a Quantum Newton’s Cradle. United States: N. p., 2016.
Web. doi:10.1103/PhysRevLett.116.225302.
van den Berg, R., Wouters, B., Eliëns, S., De Nardis, J., Konik, R. M., & Caux, J. -S. Separation of Time Scales in a Quantum Newton’s Cradle. United States. https://doi.org/10.1103/PhysRevLett.116.225302
van den Berg, R., Wouters, B., Eliëns, S., De Nardis, J., Konik, R. M., and Caux, J. -S. Wed .
"Separation of Time Scales in a Quantum Newton’s Cradle". United States. https://doi.org/10.1103/PhysRevLett.116.225302. https://www.osti.gov/servlets/purl/1412758.
@article{osti_1412758,
title = {Separation of Time Scales in a Quantum Newton’s Cradle},
author = {van den Berg, R. and Wouters, B. and Eliëns, S. and De Nardis, J. and Konik, R. M. and Caux, J. -S.},
abstractNote = {For strongly repulsive bosons in one dimension, we provide detailed modeling of the Bragg pulse used in quantum Newton's cradle-like settings or in Bragg spectroscopy experiments. By employing the Fermi-Bose mapping for a nite harmonically trapped gas and the Quench Action approach for a thermodynamic system on a ring, we reconstruct the exact post-pulse many-body time evolution of Lieb-Liniger gases in the Tonks-Girardeau limit, together with their changing local density pro le and momentum distribution. Our results display a clear separation of timescales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behaviour.},
doi = {10.1103/PhysRevLett.116.225302},
journal = {Physical Review Letters},
number = 22,
volume = 116,
place = {United States},
year = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}
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Works referenced in this record:
Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008
- Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
- Nature, Vol. 452, Issue 7189
Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
journal, December 2014
- De Nardis, J.; Caux, J-S
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 12
Many-body physics with ultracold gases
journal, July 2008
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- Reviews of Modern Physics, Vol. 80, Issue 3
Colloquium : Nonequilibrium dynamics of closed interacting quantum systems
journal, August 2011
- Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro
- Reviews of Modern Physics, Vol. 83, Issue 3
On the development of a function of any number of variables according to higher-order Laplace functions.; Ueber die Entwicklung einer Function von beliebig vielen Variablen nach Laplaceschen Functionen höherer Ordnung.
journal, July 1866
- Mehler, F. G.
- Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1866, Issue 66, p. 161-176
Splitting matter waves using an optimized standing-wave light-pulse sequence
journal, April 2005
- Wu, Saijun; Wang, Ying-Ju; Diot, Quentin
- Physical Review A, Vol. 71, Issue 4
Dynamical structure factor of one-dimensional Bose gases: Experimental signatures of beyond-Luttinger-liquid physics
journal, April 2015
- Fabbri, N.; Panfil, M.; Clément, D.
- Physical Review A, Vol. 91, Issue 4
Yang-Yang Thermodynamics on an Atom Chip
journal, March 2008
- van Amerongen, A. H.; van Es, J. J. P.; Wicke, P.
- Physical Review Letters, Vol. 100, Issue 9
Realization of an Excited, Strongly Correlated Quantum Gas Phase
journal, September 2009
- Haller, E.; Gustavsson, M.; Mark, M. J.
- Science, Vol. 325, Issue 5945
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
journal, November 1960
- Girardeau, M.
- Journal of Mathematical Physics, Vol. 1, Issue 6
Mapping out the quasicondensate transition through the dimensional crossover from one to three dimensions
journal, February 2011
- Armijo, J.; Jacqmin, T.; Kheruntsyan, K.
- Physical Review A, Vol. 83, Issue 2
Sub-Poissonian Fluctuations in a 1D Bose Gas: From the Quantum Quasicondensate to the Strongly Interacting Regime
journal, June 2011
- Jacqmin, Thibaut; Armijo, Julien; Berrada, Tarik
- Physical Review Letters, Vol. 106, Issue 23
Nonadiabatic creation of macroscopic superpositions with strongly correlated one-dimensional bosons in a ring trap
journal, November 2011
- Schenke, C.; Minguzzi, A.; Hekking, F. W. J.
- Physical Review A, Vol. 84, Issue 5
Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons
journal, February 2007
- Rigol, Marcos; Dunjko, Vanja; Yurovsky, Vladimir
- Physical Review Letters, Vol. 98, Issue 5
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
Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
journal, March 2015
- Campbell, A. S.; Gangardt, D. M.; Kheruntsyan, K. V.
- Physical Review Letters, Vol. 114, Issue 12
Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas
journal, May 2005
- Kheruntsyan, K. V.; Gangardt, D. M.; Drummond, P. D.
- Physical Review A, Vol. 71, Issue 5
Bragg scattering of atoms from a standing light wave
journal, February 1988
- Martin, Peter; Oldaker, Bruce; Miklich, Andrew
- Physical Review Letters, Vol. 60, Issue 6
Relaxation dynamics of local observables in integrable systems
journal, October 2015
- Nardis, J. De; Piroli, L.; Caux, J-S
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 43
Perturbation Theory for Singular Potentials in Quantum Mechanics
journal, April 1999
- Sen, Diptiman
- International Journal of Modern Physics A, Vol. 14, Issue 11
Exact Coherent States of a Harmonically Confined Tonks-Girardeau Gas
journal, June 2005
- Minguzzi, A.; Gangardt, D. M.
- Physical Review Letters, Vol. 94, Issue 24
Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
journal, August 1998
- Olshanii, M.
- Physical Review Letters, Vol. 81, Issue 5
Universal Theory of Nonlinear Luttinger Liquids
journal, January 2009
- Imambekov, A.; Glazman, L. I.
- Science, Vol. 323, Issue 5911
Bragg Spectroscopy of a Bose-Einstein Condensate
journal, June 1999
- Stenger, J.; Inouye, S.; Chikkatur, A. P.
- Physical Review Letters, Vol. 82, Issue 23
The reflection of electrons from standing light waves
journal, May 1933
- Kapitza, P. L.; Dirac, P. A. M.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 29, Issue 2
Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
journal, February 2006
- Cherny, Alexander Yu.; Brand, Joachim
- Physical Review A, Vol. 73, Issue 2
Fermionization dynamics of a strongly interacting one-dimensional Bose gas after an interaction quench
journal, August 2010
- Muth, Dominik; Schmidt, Bernd; Fleischhauer, Michael
- New Journal of Physics, Vol. 12, Issue 8
The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres
journal, November 1936
- Tonks, Lewi
- Physical Review, Vol. 50, Issue 10
Colloquium : Bulk Bogoliubov excitations in a Bose-Einstein condensate
journal, April 2005
- Ozeri, R.; Katz, N.; Steinhauer, J.
- Reviews of Modern Physics, Vol. 77, Issue 1
A new class of sum rules for products of Bessel functions
journal, March 2011
- Bevilacqua, G.; Biancalana, V.; Dancheva, Y.
- Journal of Mathematical Physics, Vol. 52, Issue 3
Density-density propagator for one-dimensional interacting spinless fermions with nonlinear dispersion and calculation of the Coulomb drag resistivity
journal, March 2008
- Rozhkov, A. V.
- Physical Review B, Vol. 77, Issue 12
Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
journal, August 2015
- Meinert, F.; Panfil, M.; Mark, M. J.
- Physical Review Letters, Vol. 115, Issue 8
Time Dependence of Correlation Functions Following a Quantum Quench
journal, April 2006
- Calabrese, Pasquale; Cardy, John
- Physical Review Letters, Vol. 96, Issue 13
Atom interferometry using Kapitza-Dirac scattering in a magnetic trap
journal, April 2009
- Sapiro, R. E.; Zhang, R.; Raithel, G.
- Physical Review A, Vol. 79, Issue 4
Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions
journal, March 1999
- Cheon, Taksu; Shigehara, T.
- Physical Review Letters, Vol. 82, Issue 12
Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate
journal, March 2005
- Wang, Ying-Ju; Anderson, Dana Z.; Bright, Victor M.
- Physical Review Letters, Vol. 94, Issue 9
Dynamical depinning of a Tonks-Girardeau gas
journal, December 2015
- Cartarius, Florian; Kawasaki, Eiji; Minguzzi, Anna
- Physical Review A, Vol. 92, Issue 6
Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas
journal, March 2014
- Panfil, Miłosz; Caux, Jean-Sébastien
- Physical Review A, Vol. 89, Issue 3
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963
- Lieb, Elliott H.; Liniger, Werner
- Physical Review, Vol. 130, Issue 4
Solution for an interaction quench in the Lieb-Liniger Bose gas
journal, March 2014
- De Nardis, Jacopo; Wouters, Bram; Brockmann, Michael
- Physical Review A, Vol. 89, Issue 3
Dynamic polarizability of a one-dimensional harmonically confined strongly interacting Bose gas
journal, May 2006
- Gattobigio, Mario
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 39, Issue 10
Time Evolution of Local Observables After Quenching to an Integrable Model
journal, June 2013
- Caux, Jean-Sébastien; Essler, Fabian H. L.
- Physical Review Letters, Vol. 110, Issue 25
Dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit
journal, September 2005
- Brand, Joachim; Cherny, Alexander Yu.
- Physical Review A, Vol. 72, Issue 3
Correlations in an expanding gas of hard-core bosons
journal, April 2008
- Gangardt, D. M.; Pustilnik, M.
- Physical Review A, Vol. 77, Issue 4
One dimensional bosons: From condensed matter systems to ultracold gases
journal, December 2011
- Cazalilla, M. A.; Citro, R.; Giamarchi, T.
- Reviews of Modern Physics, Vol. 83, Issue 4
Equilibration of a Tonks-Girardeau Gas Following a Trap Release
journal, June 2013
- Collura, Mario; Sotiriadis, Spyros; Calabrese, Pasquale
- Physical Review Letters, Vol. 110, Issue 24
Modulated trapping of interacting bosons in one dimension
journal, November 2014
- Quinn, Eoin; Haque, Masudul
- Physical Review A, Vol. 90, Issue 5
Observation of the Kapitza–Dirac effect
journal, September 2001
- Freimund, Daniel L.; Aflatooni, Kayvan; Batelaan, Herman
- Nature, Vol. 413, Issue 6852
Lieb's soliton-like excitations in harmonic traps
journal, May 2013
- Astrakharchik, G. E.; Pitaevskii, L. P.
- EPL (Europhysics Letters), Vol. 102, Issue 3
A quantum Newton's cradle
journal, April 2006
- Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
- Nature, Vol. 440, Issue 7086
The reflection of electrons from standing light waves
journal, June 1967
- Schwarz, Helmut
- Zeitschrift für Physik A Hadrons and nuclei, Vol. 204, Issue 3
The Reflections of Electrons from Standing Light Waves
book, January 1964
- Kapitza, P. L.; Dirac, P. A. M.
- Collected Papers of P.L. Kapitza
Momentum distribution dynamics of a tonks-girardeau gas: Bragg reflections of a quantum many-body wavepacket
conference, May 2007
- Pezer, R.; Buljan, H.
- 2007 Quantum Electronics and Laser Science Conference
Many-Body Physics with Ultracold Gases
text, January 2007
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- arXiv
Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
text, January 2008
- Rozhkov, A. V.
- arXiv
One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
text, January 2011
- Cazalilla, M. A.; Citro, R.; Giamarchi, T.
- arXiv
Lieb's soliton-like excitations in harmonic trap
text, January 2012
- Astrakharchik, G. E.; Pitaevskii, L. P.
- arXiv
Time evolution of local observables after quenching to an integrable model
text, January 2013
- Caux, Jean-Sebastien; Essler, Fabian H. L.
- arXiv
Solution for an interaction quench in the Lieb-Liniger Bose gas
text, January 2013
- De Nardis, Jacopo; Wouters, Bram; Brockmann, Michael
- arXiv
Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
text, January 2014
- Fabbri, Nicole; Panfil, Milosz; Clément, David
- arXiv
Modulated trapping of interacting bosons in one dimension
text, January 2014
- Quinn, Eoin; Haque, Masudul
- arXiv
Dynamical depinning of a Tonks Girardeau gas
text, January 2015
- Cartarius, Florian; Kawasaki, Eiji; Minguzzi, Anna
- arXiv
Relaxation dynamics of local observables in integrable systems
text, January 2015
- De Nardis, Jacopo; Piroli, Lorenzo; Caux, Jean-Sébastien
- arXiv
Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
text, January 2015
- Meinert, Florian; Panfil, Milosz; Mark, Manfred J.
- arXiv
An Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate
text, January 2004
- Wang, Ying-Ju; Anderson, Dana Z.; Bright, Victor M.
- arXiv
Exact coherent states of a harmonically confined Tonks-Girardeau gas
text, January 2005
- Minguzzi, A.; Gangardt, D. M.
- arXiv
Time-dependence of correlation functions following a quantum quench
text, January 2006
- Calabrese, Pasquale; Cardy, John
- arXiv
Perturbation Theory for Singular Potentials in Quantum Mechanics
text, January 1998
- Sen, Diptiman
- arXiv
Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
text, January 1998
- Olshanii, Maxim
- arXiv
Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
text, January 1998
- Cheon, Taksu; Shigehara, T.
- arXiv
Works referencing / citing this record:
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journal, February 2017
- Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 2
Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
journal, January 2016
- Vlijm, Rogier; Eliens, Sebas; Caux, Jean-Sébastien
- SciPost Physics, Vol. 1, Issue 1
Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
text, January 2016
- Vlijm, R.; Eliëns, I. S.; Caux, J. -S.
- arXiv
Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases
text, January 2016
- Atas, Y. Y.; Gangardt, D. M.; Bouchoule, I.
- arXiv
From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
text, January 2016
- Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric
- arXiv
Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup
text, January 2017
- Caux, Jean-Sébastien; Doyon, Benjamin; Dubail, Jérôme
- arXiv