Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2006.15326 · Physical Review Letters

What is a Quantum Shock Wave?

S. A. Simmons, Francis A. Bayocboc, Jason C. Pillay, David Colas, Ian P. McCulloch, Karen V. Kheruntsyan

Published Oct 26, 2020• 38 citations
arXivHTMLPDF

Abstract

Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.

DOI
10.1103/physrevlett.125.180401

Related papers

Fate of the vacuum point and of gray solitons in dispersive quantum shock waves in a one-dimensional Bose gas

S. A. Simmons, Jason C. Pillay, Karen V. Kheruntsyan

We continue the study of dispersive quantum shock waves in a one-dimensional Bose gas beyond the mean-field approximation. In a recent work by Simmons et al. [Phys. Rev. Lett. 125, 180401 (2020)], the oscillatory shock wave train developing in this system from an initial localized density bump on a uniform background was interpreted as a result of quantum mechanical self-interference, wherein the interference contrast would diminish with the loss of matter-wave phase coherence. Such loss of coherence, relative to the mean-field Gross-Pitaevskii description, occurs due to either quantum or thermal fluctuations, as well as in the strongly interacting regime. In this work we extend the analysis of dispersive quantum shock waves in this context to other dynamical scenarios. More specifically, the scenarios studied include evolution of a sufficiently high-density bump, known to lead to the so-called ``vacuum point'' in the mean-field description, and evolution of an initial density dip, known to shed a train of gray solitons in the same mean-field approximation. We study the fate of these nonlinear wave structures in the presence of quantum and thermal fluctuations, as well as at intermediate and strong interactions, and show that both the vacuum point and gray solitons cease to manifest themselves beyond the mean-field approach. On the other hand, we find that a vacuum point can occur in an ideal (noninteracting) Bose gas evolving from a ground state of a localized dimple potential. Due to the ubiquity of dispersive shock waves in nature, our results should provide useful insights and perspectives for a variety of other physical systems known to display nonlinear wave phenomena.

arXiv:2305.17647•Physical Review A•Jul 25, 2023•2 citations

Direct observation of long-range many-body coherence in quasi-one-dimensional attractive Bose gases

Hikaru Tamura, Sambit Banerjee, Rongjie Li +3 more

Macroscopic coherence is an important feature of quantum many-body systems exhibiting collective behaviors, with examples ranging from atomic Bose-Einstein condensates, and quantum liquids to superconductors. Probing many-body coherence in a dynamically unstable regime, however, presents an intriguing and outstanding challenge in out-of-equilibrium quantum many-body physics. Here, we experimentally study the first- and second-order coherence of degenerate quasi-one-dimensional (1D) Bose gases quenched from repulsive to modulationally unstable attractive interaction regimes. The resulting dynamics, monitored by in situ density and matter-wave interference imaging, reveals phase-coherent density wave evolutions, clearly distinguished from iconic soliton trains previously observed in attractive gases. This arises from the interplay between noise-amplified density modulations and dispersive shock waves of broad interest in nonlinear physics, plasmas, granular systems, and beyond. At longer times, the gases become phase-scrambled, exhibiting a finite correlation length. Interestingly, following an interaction quench back to the repulsive regime, we observe that quasi-long-range coherence can be spontaneously re-established. This captivating rephasing dynamics can be attributed to the nucleation and annihilation of density defects in the quasi-1D geometry. These results shed light on out-of-equilibrium phase coherence in quantum many-body systems in a regime where beyond mean-field effects may arise and theoretical approaches have not been well-established. Attractive Bose gases are modulationally unstable yet exhibit rich nonlinear many-body behaviors, owing to the interplay between their coherence and unstable collective excitations. Here, the authors probe out-of-equilibrium dynamics in quasi-1D Bose-Einstein condensates subject to quench dynamics between repulsive and attractive interactions.

arXiv:2506.13597•Nature Communications•Jun 27, 2026•1 citation

Universal shock-wave propagation in one-dimensional Bose fluids

Romain Dubessy, Juan Polo, Hélène Perrin +2 more

We propose a protocol for creating moving, robust dispersive shock waves in interacting one-dimensional Bose fluids.The fluid is prepared in a moving state by phase imprinting and sent against the walls of a box trap.We demonstrate that the thus formed shock wave oscillates for several periods and is robust against thermal fluctuations.We show that this large amplitude dynamics is universal across the whole spectrum of the interatomic interaction strength, from weak to strong interactions, and it is fully controlled by the sound velocity inside the fluid.Our work provides a generalization of the dispersive-shock-wave paradigm to the many-body regime.The shock waves we propose are within reach for ultracold atom experiments.

arXiv:2007.05252•Physical Review Research•Jan 29, 2021•17 citations

Finite-temperature dynamics of shock waves in an ultracold Fermi gas

Ria Rushin Joseph, L. Rosales-Zárate, P. D. Drummond

The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.

Physical Review A•Jul 31, 2018•10 citations

Universal shock-wave propagation in one-dimensional Bose fluids

Romain Dubessy, Juan Polo, Hélène Perrin +2 more

We propose a protocol for creating moving, robust dispersive shock waves in interacting one-dimensional Bose fluids. The fluid is prepared in a moving state by phase imprinting and sent against the walls of a box trap. We demonstrate that the thus formed shock wave oscillates for several periods and is robust against thermal fluctuations. We show that this large amplitude dynamics is universal across the whole spectrum of the interatomic interaction strength, from weak to strong interactions, and it is fully controlled by the sound velocity inside the fluid. Our work provides a generalization of the dispersive-shock-wave paradigm to the many-body regime. The shock waves we propose are within reach for ultracold atom experiments.6 MoreReceived 8 July 2020Accepted 5 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013098Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesCold atoms & matter wavesPhysical Systems1-dimensional systemsBose-Einstein condensatesNonlinear DynamicsAtomic, Molecular & Optical

•Jul 9, 2020•16 citations

Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics

Mark A. Hoefer, Mark J. Ablowitz, Ian R. Coddington +3 more

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

arXiv:cond-mat/0603389•Physical Review A•Aug 29, 2006•318 citations
Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.
We continue the study of dispersive quantum shock waves in a one-dimensional Bose gas beyond the mean-field approximation. In a recent work by Simmons et al. [Phys. Rev. Lett. 125, 180401 (2020)], the oscillatory shock wave train developing in this system from an initial localized density bump on a uniform background was interpreted as a result of quantum mechanical self-interference, wherein the interference contrast would diminish with the loss of matter-wave phase coherence. Such loss of coherence, relative to the mean-field Gross-Pitaevskii description, occurs due to either quantum or thermal fluctuations, as well as in the strongly interacting regime. In this work we extend the analysis of dispersive quantum shock waves in this context to other dynamical scenarios. More specifically, the scenarios studied include evolution of a sufficiently high-density bump, known to lead to the so-called ``vacuum point'' in the mean-field description, and evolution of an initial density dip, known to shed a train of gray solitons in the same mean-field approximation. We study the fate of these nonlinear wave structures in the presence of quantum and thermal fluctuations, as well as at intermediate and strong interactions, and show that both the vacuum point and gray solitons cease to manifest themselves beyond the mean-field approach. On the other hand, we find that a vacuum point can occur in an ideal (noninteracting) Bose gas evolving from a ground state of a localized dimple potential. Due to the ubiquity of dispersive shock waves in nature, our results should provide useful insights and perspectives for a variety of other physical systems known to display nonlinear wave phenomena.
Macroscopic coherence is an important feature of quantum many-body systems exhibiting collective behaviors, with examples ranging from atomic Bose-Einstein condensates, and quantum liquids to superconductors. Probing many-body coherence in a dynamically unstable regime, however, presents an intriguing and outstanding challenge in out-of-equilibrium quantum many-body physics. Here, we experimentally study the first- and second-order coherence of degenerate quasi-one-dimensional (1D) Bose gases quenched from repulsive to modulationally unstable attractive interaction regimes. The resulting dynamics, monitored by in situ density and matter-wave interference imaging, reveals phase-coherent density wave evolutions, clearly distinguished from iconic soliton trains previously observed in attractive gases. This arises from the interplay between noise-amplified density modulations and dispersive shock waves of broad interest in nonlinear physics, plasmas, granular systems, and beyond. At longer times, the gases become phase-scrambled, exhibiting a finite correlation length. Interestingly, following an interaction quench back to the repulsive regime, we observe that quasi-long-range coherence can be spontaneously re-established. This captivating rephasing dynamics can be attributed to the nucleation and annihilation of density defects in the quasi-1D geometry. These results shed light on out-of-equilibrium phase coherence in quantum many-body systems in a regime where beyond mean-field effects may arise and theoretical approaches have not been well-established. Attractive Bose gases are modulationally unstable yet exhibit rich nonlinear many-body behaviors, owing to the interplay between their coherence and unstable collective excitations. Here, the authors probe out-of-equilibrium dynamics in quasi-1D Bose-Einstein condensates subject to quench dynamics between repulsive and attractive interactions.
We propose a protocol for creating moving, robust dispersive shock waves in interacting one-dimensional Bose fluids.The fluid is prepared in a moving state by phase imprinting and sent against the walls of a box trap.We demonstrate that the thus formed shock wave oscillates for several periods and is robust against thermal fluctuations.We show that this large amplitude dynamics is universal across the whole spectrum of the interatomic interaction strength, from weak to strong interactions, and it is fully controlled by the sound velocity inside the fluid.Our work provides a generalization of the dispersive-shock-wave paradigm to the many-body regime.The shock waves we propose are within reach for ultracold atom experiments.
The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.
We propose a protocol for creating moving, robust dispersive shock waves in interacting one-dimensional Bose fluids. The fluid is prepared in a moving state by phase imprinting and sent against the walls of a box trap. We demonstrate that the thus formed shock wave oscillates for several periods and is robust against thermal fluctuations. We show that this large amplitude dynamics is universal across the whole spectrum of the interatomic interaction strength, from weak to strong interactions, and it is fully controlled by the sound velocity inside the fluid. Our work provides a generalization of the dispersive-shock-wave paradigm to the many-body regime. The shock waves we propose are within reach for ultracold atom experiments.6 MoreReceived 8 July 2020Accepted 5 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013098Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesCold atoms & matter wavesPhysical Systems1-dimensional systemsBose-Einstein condensatesNonlinear DynamicsAtomic, Molecular & Optical
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.