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:1703.04662 · Science

Formation of matter-wave soliton trains by modulational instability

Jason H. V. Nguyen, De Luo, Randall G. Hulet

Published Apr 27, 2017• 224 citations
arXivHTMLPDF

Abstract

Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By exploiting a shallow zero-crossing of a Feshbach resonance, we characterize modulational instability and its role in the formation of matter-wave soliton trains from a Bose-Einstein condensate. We examine the universal scaling laws exhibited by the system and, through real-time imaging, address a long-standing question of whether the solitons in trains are created with effectively repulsive nearest-neighbor interactions or rather evolve into such a structure.

DOI
10.1126/science.aal3220

Related papers

Formation of matter-wave soliton trains by modulational instability

Randall G. Hulet, Jason Nguyen, De Luo

Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•5 citations

Spontaneous Soliton Formation and Modulational Instability in Bose-Einstein Condensates

Lincoln D. Carr, Joachim Brand

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Nature (London) 417, 150 (2002)]] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales.

arXiv:cond-mat/0303257•Physical Review Letters•Jan 28, 2004•214 citations

Formation of Bright Matter-Wave Solitons during the Collapse of Attractive Bose-Einstein Condensates

Simon L. Cornish, Sarah T. Thompson, Carl Wieman

We observe bright matter-wave solitons form during the collapse of (85)Rb condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.

arXiv:cond-mat/0601664•Physical Review Letters•May 3, 2006•496 citations

Bright matter wave solitons in Bose–Einstein condensates

Kevin E. Strecker, Guthrie B. Partridge, Andrew G. Truscott +1 more

We review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of 7 Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrödinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.

New Journal of Physics•Jun 16, 2003•213 citations

Modulational Instability and Complex Dynamics of Confined Matter-Wave Solitons

Luca Salasnich, Alberto Parola, L. Reatto

We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.

arXiv:cond-mat/0307206•Physical Review Letters•Aug 22, 2003•216 citations

Formation of soliton trains in Bose–Einstein condensates by temporal Talbot effect

Krzysztof Gawryluk, Mirosław Brewczyk, Mariusz Gajda +1 more

We study the formation of matter-wave soliton trains in Bose–Einstein condensates confined in a box-like potential. We find that the generation of ‘real’ solitons understood as multipeak structures undergoing elastic collisions is possible if the condensate is released from the box into the harmonic trap only within well-defined time intervals. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in recent experiment (Strecker et al 2002 Nature 417 150). Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.

arXiv:cond-mat/0409313•Journal of Physics B Atomic Molecular and Optical Physics•Dec 5, 2005•10 citations
Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By exploiting a shallow zero-crossing of a Feshbach resonance, we characterize modulational instability and its role in the formation of matter-wave soliton trains from a Bose-Einstein condensate. We examine the universal scaling laws exhibited by the system and, through real-time imaging, address a long-standing question of whether the solitons in trains are created with effectively repulsive nearest-neighbor interactions or rather evolve into such a structure.
Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.
The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Nature (London) 417, 150 (2002)]] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales.
We observe bright matter-wave solitons form during the collapse of (85)Rb condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.
We review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of 7 Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrödinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.
We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.
We study the formation of matter-wave soliton trains in Bose–Einstein condensates confined in a box-like potential. We find that the generation of ‘real’ solitons understood as multipeak structures undergoing elastic collisions is possible if the condensate is released from the box into the harmonic trap only within well-defined time intervals. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in recent experiment (Strecker et al 2002 Nature 417 150). Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.