We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile’s rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that the 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to and the other at , where is the trapping frequency. The breathing mode at dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at , on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.
Nous étudions les oscillations de respiration (monopolaires) et leur amortissement dans un gaz de bosons unidimensionnel (1D) harmoniquement piégé dans le régime de quasi-condensat en utilisant une méthode de champ classique à température non nulle. En caractérisant les oscillations par le comportement de la largeur quadratique moyenne du profil de densité sur des temps longs, nous constatons que celle-ci présente un battement de deux fréquences distinctes. Ceci signifie que le gaz de bosons 1D n’oscille pas à la fréquence d’un seul mode de respiration, comme l’ont trouvé les études précédentes, mais sous l’effet de deux modes de respiration superposés, l’un oscillant à une pulsation proche de et l’autre à , où est la pulsation de piégeage. Le mode de respiration à domine le battement à basse température, dans le régime fortement quasi-condensé, et est attribué aux oscillations de la partie centrale de la distribution de densité, composée de particules occupant les niveaux de basse énergie fortement peuplés. Le mode de respiration à , en revanche, domine le battement à des températures plus élevées, proches du régime du gaz de bosons presque parfait, et est attribué aux oscillations des ailes de la distribution de densité, composées de particules thermiques dans des niveaux de plus haute énergie. Les deux modes de respiration ont des taux d’amortissement distincts, celui de la composante centrale étant environ quatre fois plus grand que celui des ailes.
Revised:
Accepted:
Online First:
Published online:
Mot clés : Atomes ultrafroids, Dynamique des gaz de Bose 1D, Simulations de champs classiques, Oscillations du mode respiratoire, Amortissement des oscillations collectives
Francis A. Bayocboc, Jr. 1; Karen V. Kheruntsyan 1
@article{CRPHYS_2023__24_S3_15_0, author = {Francis A. Bayocboc, Jr. and Karen V. Kheruntsyan}, title = {Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate}, journal = {Comptes Rendus. Physique}, pages = {15--38}, publisher = {Acad\'emie des sciences, Paris}, volume = {24}, number = {S3}, year = {2023}, doi = {10.5802/crphys.131}, language = {en}, }
TY - JOUR AU - Francis A. Bayocboc, Jr. AU - Karen V. Kheruntsyan TI - Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate JO - Comptes Rendus. Physique PY - 2023 SP - 15 EP - 38 VL - 24 IS - S3 PB - Académie des sciences, Paris DO - 10.5802/crphys.131 LA - en ID - CRPHYS_2023__24_S3_15_0 ER -
%0 Journal Article %A Francis A. Bayocboc, Jr. %A Karen V. Kheruntsyan %T Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate %J Comptes Rendus. Physique %D 2023 %P 15-38 %V 24 %N S3 %I Académie des sciences, Paris %R 10.5802/crphys.131 %G en %F CRPHYS_2023__24_S3_15_0
Francis A. Bayocboc, Jr.; Karen V. Kheruntsyan. Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate. Comptes Rendus. Physique, Volume 24 (2023) no. S3, pp. 15-38. doi : 10.5802/crphys.131. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.131/
[1] Collective Excitations of a Bose–Einstein Condensate in a Dilute Gas, Phys. Rev. Lett., Volume 77 (1996) no. 3, pp. 420-423 | DOI
[2] Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose–Einstein Condensate, Phys. Rev. Lett., Volume 78 (1997) no. 5, pp. 764-767 | DOI
[3] Collisionless and Hydrodynamic Excitations of a Bose–Einstein Condensate, Phys. Rev. Lett., Volume 81 (1998) no. 3, pp. 500-503 | DOI
[4] Temperature Dependence of Damping and Frequency Shifts of the Scissors Mode of a Trapped Bose–Einstein Condensate, Phys. Rev. Lett., Volume 86 (2001) no. 18, pp. 3938-3941 | DOI
[5] Transverse Breathing Mode of an Elongated Bose–Einstein Condensate, Phys. Rev. Lett., Volume 88 (2002) no. 25, 250402, 4 pages | DOI
[6] Damping of Low-Energy Excitations of a Trapped Bose–Einstein Condensate at Finite Temperatures, Phys. Rev. Lett., Volume 80 (1998) no. 11, pp. 2269-2272 | DOI
[7] Landau damping in dilute Bose gases, Phys. Lett., A, Volume 235 (1997) no. 4, pp. 398-402 | DOI
[8] Elementary Excitations in Trapped Bose–Einstein Condensed Gases Beyond the Mean-Field Approximation, Phys. Rev. Lett., Volume 81 (1998) no. 21, pp. 4541-4544 | DOI
[9] Collisionless modes of a trapped Bose gas, Phys. Rev. A, Volume 60 (1999) no. 5, pp. 3973-3981 | DOI
[10] Kinetic theory of collective excitations and damping in Bose–Einstein condensed gases, Phys. Rev. A, Volume 62 (2000) no. 5, 053602, 10 pages | DOI
[11] Temperature-induced resonances and Landau damping of collective modes in Bose–Einstein condensed gases in spherical traps, Phys. Rev. A, Volume 61 (1999) no. 1, 013602, 10 pages | DOI
[12] Damping and revivals of collective oscillations in a finite-temperature model of trapped Bose–Einstein condensation, Phys. Rev. A, Volume 63 (2001) no. 5, 053606, 5 pages | DOI
[13] Quadrupole Collective Modes in Trapped Finite-Temperature Bose–Einstein Condensates, Phys. Rev. Lett., Volume 88 (2002) no. 18, 180402, 4 pages | DOI
[14] Modeling Bose–Einstein condensed gases at finite temperatures with N-body simulations, Phys. Rev. A, Volume 66 (2002) no. 3, 033606, 18 pages | DOI
[15] Accidental Suppression of Landau Damping of the Transverse Breathing Mode in Elongated Bose–Einstein Condensates, Phys. Rev. Lett., Volume 89 (2002) no. 15, 150402, 4 pages | DOI
[16] Landau damping in trapped Bose condensed gases, New J. Phys., Volume 5 (2003), 88, 23 pages | DOI
[17] Landau damping of transverse quadrupole oscillations of an elongated Bose–Einstein condensate, Phys. Rev. A, Volume 67 (2003) no. 5, 053607, 5 pages | DOI
[18] Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor, Science, Volume 269 (1995) no. 5221, pp. 198-201 | DOI
[19] Evidence of Bose–Einstein Condensation in an Atomic Gas with Attractive Interactions, Phys. Rev. Lett., Volume 75 (1995) no. 9, pp. 1687-1690 | DOI
[20] Bose–Einstein Condensation in a Gas of Sodium Atoms, Phys. Rev. Lett., Volume 75 (1995) no. 22, pp. 3969-3973 | DOI
[21] Bose-Condensed Gases at Finite Temperatures, Cambridge University Press, 2009
[22] Energy spectrum of a non-ideal Bose gas, Sov. Phys., JETP, Volume 34 (1958) no. 2, pp. 299-307
[23] Quench-Induced Breathing Mode of One-Dimensional Bose Gases, Phys. Rev. Lett., Volume 113 (2014) no. 3, 035301, 5 pages | DOI
[24] A quantum Newton’s cradle, Nature, Volume 440 (2006) no. 7086, pp. 900-903 | DOI
[25] Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys. Rev., Volume 130 (1963) no. 4, pp. 1605-1616 | DOI
[26] Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Phys. Rev., Volume 130 (1963), pp. 1616-1624 | DOI
[27] Thermalization and its mechanism for generic isolated quantum systems, Nature, Volume 452 (2008), pp. 854-858 | DOI
[28] Breakdown of Thermalization in Finite One-Dimensional Systems, Phys. Rev. Lett., Volume 103 (2009) no. 10, 100403, 4 pages | DOI
[29] Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys., Volume 83 (2011) no. 3, pp. 863-883 | DOI
[30] Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems, Phys. Rev. B, Volume 84 (2011) no. 5, 054304, 10 pages | DOI
[31] Constructing the Generalized Gibbs Ensemble after a Quantum Quench, Phys. Rev. Lett., Volume 109 (2012) no. 17, 175301, 5 pages | DOI
[32] Relaxation and Prethermalization in an Isolated Quantum System, Science, Volume 337 (2012) no. 6100, pp. 1318-1322 | DOI
[33] Experimental observation of a generalized Gibbs ensemble, Science, Volume 348 (2015) no. 6231, pp. 207-211 | DOI
[34] Integrability breakdown in longitudinaly trapped, one-dimensional bosonic gases, Eur. Phys. J. D, Volume 65 (2011) no. 1, pp. 43-47 | DOI
[35] Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas, Phys. Rev. Lett., Volume 100 (2008) no. 21, 210403, 4 pages | DOI
[36] Thermalization in a quasi-one-dimensional ultracold bosonic gas, New J. Phys., Volume 12 (2010) no. 5, 055023 | DOI
[37] Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas, Phys. Rev. Lett., Volume 105 (2010) no. 9, 090404, 4 pages | DOI
[38] Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime, Phys. Rev. Lett., Volume 126 (2021) no. 9, 090602, 8 pages | DOI
[39] Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential, J. Phys. B: At. Mol. Opt. Phys., Volume 51 (2018) no. 20, 205303 | DOI
[40] Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion, Phys. Rev. Lett., Volume 125 (2020) no. 24, 240604, 6 pages | DOI
[41] Thermalization of a quantum Newton’s cradle in a one-dimensional quasicondensate, Phys. Rev. A, Volume 103 (2021) no. 2, 023315, 13 pages | DOI
[42] Exciting Collective Oscillations in a Trapped 1D Gas, Phys. Rev. Lett., Volume 91 (2003) no. 25, 250402, 4 pages | DOI
[43] Realization of an Excited, Strongly Correlated Quantum Gas Phase, Science, Volume 325 (2009) no. 5945, pp. 1224-1227 | DOI
[44] Classical-Field Method for Time Dependent Bose–Einstein Condensed Gases, Phys. Rev. Lett., Volume 87 (2001) no. 21, 210404, 4 pages | DOI
[45] Collective oscillations of a one-dimensional trapped Bose–Einstein gas, Phys. Rev. A, Volume 66 (2002) no. 4, 043610, 6 pages | DOI
[46] Dynamics of a classical gas including dissipative and mean-field effects, Phys. Rev. A, Volume 68 (2003) no. 4, 043608, 4 pages | DOI
[47] Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems, Phys. Rev. A, Volume 88 (2013) no. 4, 043601, 9 pages | DOI
[48] Breathing mode in the Bose-Hubbard chain with a harmonic trapping potential, Phys. Rev. A, Volume 88 (2013) no. 6, 063636, 7 pages | DOI
[49] Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas, Phys. Rev. A, Volume 92 (2015) no. 2, 021601, 5 pages | DOI
[50] Monopole Excitations of a Harmonically Trapped One-Dimensional Bose Gas from the Ideal Gas to the Tonks–Girardeau Regime, Phys. Rev. Lett., Volume 115 (2015) no. 11, 115302, 5 pages | DOI
[51] Collective modes of a one-dimensional trapped atomic Bose gas at finite temperatures, Phys. Rev. A, Volume 90 (2014) no. 1, 013622, 7 pages | DOI
[52] Collective modes of a harmonically trapped one-dimensional Bose gas: The effects of finite particle number and nonzero temperature, Phys. Rev. A, Volume 91 (2015) no. 6, 063631, 9 pages | DOI
[53] Collective oscillations of a trapped quantum gas in low dimensions, Phys. Rev. A, Volume 92 (2015) no. 5, 053617, 10 pages | DOI
[54] Hydrodynamic versus collisionless dynamics of a one-dimensional harmonically trapped Bose gas, Phys. Rev. A, Volume 94 (2016) no. 6, 063605, 8 pages | DOI
[55] Finite-temperature hydrodynamics for one-dimensional Bose gases: Breathing-mode oscillations as a case study, Phys. Rev. A, Volume 94 (2016) no. 5, 051602, 5 pages | DOI
[56] Collapse and revival of the monopole mode of a degenerate Bose gas in an isotropic harmonic trap, Phys. Rev. A, Volume 94 (2016) no. 4, 043640, 13 pages | DOI
[57] Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates, Phys. Rev. A, Volume 106 (2022) no. 2, 023320, 14 pages | DOI
[58] Coherence properties of a continuous atom laser, J. Mod. Opt., Volume 47 (2000) no. 14-15, pp. 2671-2695 | DOI
[59] Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques, Adv. Phys., Volume 57 (2008) no. 5, pp. 363-455 | DOI
[60] Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons, Phys. Rev. Lett., Volume 81 (1998) no. 5, pp. 938-941 | DOI
[61] XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations, Comput. Phys. Commun., Volume 184 (2013) no. 1, pp. 201-208 | DOI
[62] Properties of the stochastic Gross–Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation, J. Phys. B: At. Mol. Opt. Phys., Volume 38 (2005), pp. 4259-4280 | DOI
[63] Numerical method for evolving the projected Gross–Pitaevskii equation, Phys. Rev. E, Volume 78 (2008) no. 2, 026704, 12 pages | DOI
[64] Numerical method for the stochastic projected Gross–Pitaevskii equation, Phys. Rev. E, Volume 89 (2014) no. 1, 013302, 15 pages | DOI
[65] Two-body momentum correlations in a weakly interacting one-dimensional Bose gas, Phys. Rev. A, Volume 86 (2012) no. 3, 033626, 11 pages | DOI
[66] Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction, J. Math. Phys., Volume 10 (1969) no. 7, pp. 1115-1122 | DOI
[67] Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas, Phys. Rev. A, Volume 71 (2005) no. 5, 053615, 17 pages | DOI
[68] Classical field records of a quantum system: Their internal consistency and accuracy, Phys. Rev. A, Volume 92 (2015) no. 6, 063620, 10 pages | DOI
[69] Complex wave fields in the interacting one-dimensional Bose gas, Phys. Rev. A, Volume 97 (2018) no. 5, 053607, 11 pages | DOI
[70] Classical fields in the one-dimensional Bose gas: Applicability and determination of the optimal cutoff, Phys. Rev. A, Volume 98 (2018) no. 2, 023622, 12 pages | DOI
[71] Bose–Einstein Condensation and Liquid Helium, Phys. Rev., Volume 104 (1956) no. 3, pp. 576-584 | DOI
[72] Extension of Bogoliubov theory to quasicondensates, Phys. Rev. A, Volume 67 (2003) no. 5, 053615, 24 pages | DOI
[73] Bosonizing one-dimensional cold atomic gases, J. Phys. B: At. Mol. Opt. Phys., Volume 37 (2004) no. 7, S1, pp. 0953-4075 | DOI
[74] Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature, Phys. Rev. A, Volume 79 (2009) no. 4, 043619, 20 pages | DOI
[75] Damping in dilute Bose gases: A mean-field approach, Phys. Rev. A, Volume 57 (1998) no. 4, pp. 2949-2957 | DOI
[76] Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose–Einstein Condensate, Commun. Theor. Phys., Volume 57 (2012) no. 5, pp. 789-794 | DOI
[77] Dynamics of Trapped Bose Gases at Finite Temperatures, J. Low Temp. Phys., Volume 116 (1999) no. 3, pp. 277-345 | DOI
[78] Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping (2022) (https://arxiv.org/abs/2205.15826)
[79] Pair Correlations in a Finite-Temperature 1D Bose Gas, Phys. Rev. Lett., Volume 91 (2003) no. 4, 040403, 4 pages | DOI
[80] Regimes of Quantum Degeneracy in Trapped 1D Gases, Phys. Rev. Lett., Volume 85 (2000) no. 18, pp. 3745-3749 | DOI
[81] Spatial Nonlocal Pair Correlations in a Repulsive 1D Bose Gas, Phys. Rev. Lett., Volume 100 (2008) no. 6, 160406, 4 pages | DOI
[82] Interaction-induced crossover versus finite-size condensation in a weakly interacting trapped one-dimensional Bose gas, Phys. Rev. A, Volume 75 (2007) no. 3, 031606, 4 pages | DOI
Cited by Sources:
Comments - Policy