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:0805.1948 · New Journal of Physics

Avalanches of Bose–Einstein condensates in leaking optical lattices

Gim Seng Ng, H Hennig, Ragnar Fleischmann, Tsampikos Kottos, Theo Geisel

Published Jul 23, 2009• 37 citations
arXivHTMLPDF

Abstract

We study the decay of an atomic Bose–Einstein condensate (BEC) population N (τ) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Λ>Λ b , discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N (τ), which for a whole range of Λ-values follow a scale-free distribution P ( J =δ N )∼1/ J α . A theoretical analysis of the mixed phase space of the system indicates that 1<α<3, in agreement with our numerical findings.

DOI
10.1088/1367-2630/11/7/073045

Related papers

Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice

H. Hennig, Jérôme Dorignac, David K Campbell

We study the effect of discrete breathers (DBs) on the transfer of a Bose-Einstein condensate (BEC) in an optical lattice using the discrete nonlinear Schr\"odinger equation. In previous theoretical (primarily numerical) investigations of the dynamics of BECs in leaking optical lattices, collisions between a DB and a lattice excitation, e.g., a moving breather (MB) or phonon, were studied. These collisions led to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we develop an analytic understanding of this phenomenon, based on the study of a highly localized system---namely, a nonlinear trimer---which predicts that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. We then show numerically that a qualitatively similar threshold exists in extended lattices. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.

arXiv:1006.0943•Physical Review A•Nov 4, 2010•47 citations

Collision of discrete breathers in two-species Bose-Einstein condensates in optical lattices

Russell Campbell, Mateusz Borkowski, Gian‐Luca Oppo

The properties of Bose-Einstein condensates (BEC) can be studied and controlled effectively when trapped in optical lattices. In the limit of tight binding, BEC in optical lattices are well described by the discrete nonlinear Schrödinger equation (DNLSE). Spatially localised modes of excitations, known as discrete breathers or lattice solitons, can occur in the DNLSE. These have been shown to evolve from initial conditions of Gaussian wave-packets. Using this method with the addition of an initial momentum, mobile breathers that travel across the lattice with a constant velocity can also be formed.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Discrete breathers in Bose–Einstein condensates

Roberto Franzosi, Roberto Livi, Gian‐Luca Oppo +1 more

Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions.

Nonlinearity•Oct 28, 2011•71 citations

Interactions and collisions of discrete breathers in two-species Bose-Einstein condensates in optical lattices

Russell Campbell, Gian‐Luca Oppo, Mateusz Borkowski

The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.

arXiv:1403.5520•Physical Review E•Jan 13, 2015•5 citations

Confining and probing BEC dynamics in optical lattices via boundary dissipations

Gian‐Luca Oppo, Roberto Franzosi, Roberto Livi

A technique, based on boundary dissipation, capable to localise and probe the breather dynamics of Bose-Einstein condensates (BEC) in optical lattices is described. Numerical simulations of BEC in optical lattices with atomic losses at the trap ends are presented and the dynamical evolution of the atomic density starting from a uniform filling the lattice. The utilization of atomic losses at the boundaries to probe the dynamics of the localized structures inside the lattice is investigated.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•0 citations

Discrete breathers in BEC with two- and three-body interactions in optical lattice

F. Kh. Abdullaev, A. Bouketir, Azeddine Messikh +1 more

We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the condensate wavefunction is reduced to the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. This result is important to obtain the conditions for generation of discrete solitons(breathers) in optical lattice. Also using the Page approach, we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The numerical simulations conform with the analytical predictions.

arXiv:cond-mat/0605622•May 25, 2006•0 citations
We study the decay of an atomic Bose–Einstein condensate (BEC) population N (τ) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Λ>Λ b , discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N (τ), which for a whole range of Λ-values follow a scale-free distribution P ( J =δ N )∼1/ J α . A theoretical analysis of the mixed phase space of the system indicates that 1<α<3, in agreement with our numerical findings.
We study the effect of discrete breathers (DBs) on the transfer of a Bose-Einstein condensate (BEC) in an optical lattice using the discrete nonlinear Schr\"odinger equation. In previous theoretical (primarily numerical) investigations of the dynamics of BECs in leaking optical lattices, collisions between a DB and a lattice excitation, e.g., a moving breather (MB) or phonon, were studied. These collisions led to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we develop an analytic understanding of this phenomenon, based on the study of a highly localized system---namely, a nonlinear trimer---which predicts that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. We then show numerically that a qualitatively similar threshold exists in extended lattices. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.
The properties of Bose-Einstein condensates (BEC) can be studied and controlled effectively when trapped in optical lattices. In the limit of tight binding, BEC in optical lattices are well described by the discrete nonlinear Schrödinger equation (DNLSE). Spatially localised modes of excitations, known as discrete breathers or lattice solitons, can occur in the DNLSE. These have been shown to evolve from initial conditions of Gaussian wave-packets. Using this method with the addition of an initial momentum, mobile breathers that travel across the lattice with a constant velocity can also be formed.
Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions.
The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.
We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the condensate wavefunction is reduced to the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. This result is important to obtain the conditions for generation of discrete solitons(breathers) in optical lattice. Also using the Page approach, we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The numerical simulations conform with the analytical predictions.