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:2406.12192 · Physics Letters A

Driven - dissipative dynamics of ultracold atoms trapped in an array of harmonic potentials

Roland Cristopher F. Caballar

Published Jan 7, 2025• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physleta.2024.130220

Related papers

Quantum dynamics of trapped ultracold atoms

Roberto B. Diener

•Jan 1, 2003•1 citation

Emergence of Unique Steady Edge States in Trapped Ultracold Atom Systems

Roland Cristopher F. Caballar

We show that, for a one - dimensional open quantum system of ultracold atoms trapped in an array of harmonic potentials that is weakly coupled to a background Bose - Einstein Condensate (BEC), a unique steady state emerges at either of the two edges of the array due to the combined effects of excitation via lasers of these ultracold atoms and decay back to their initial energy levels via emission of excitations into the BEC, acting as an excitation reservoir. We then demonstrate the existence of steady states of the master equation that describes the dynamics of this open quantum system with respect to the expectation value of the position of the harmonic potential containing these states, and show that these steady states occur at the edges of the array of harmonic potentials trapping these atoms. Using the open quantum system's master equation to evolve initial states of the system that are trapped in other harmonic potentials in the array numerically over time, we verify the analytic calculations demonstrating the existence of these steady states at the edge of the system, and further demonstrate that these steady states will emerge regardless of the number of atoms trapped in each of the harmonic potentials in the array. We note that the emergence of these edge states irrespective of the initial state of the system is similar to the non-Hermitian skin effect seen in other open quantum systems, and are of fundamental importance in quantum technological applications such as quantum transport and quantum batteries.

cond-mat.quant-gasCross-listedarXiv:2603.20763•Annals of Physics•Mar 24, 2026•0 citations

Chaotic escape dynamics of ultracold and Bose-condensed atoms

Kevin Mitchell, D. Steck

Bulletin of the American Physical Society•Jun 9, 2007•0 citations

Regulation of resonance and anti-resonance of soliton in ultracold atomic gases

He Zhang-Ming, Dexun ZHAI, Qianquan ZHU +1 more

Kapitza’s pendulum is an inverted pendulum that is dynamically stabilized by rapidly driving its pivot point. Many applications of Kapitza stabilization in quantum systems have been proposed, such as optical molasses, the stability of optical resonators, preparation of molecular ions, the breaking of translation symmetry, the periodically driven sine-Gordon model, polariton Rabi oscillation, and the stabilization of bright solitons in a Bose-Einstein condensate. In particular, Kapitza stabilization can be used to trap particles. The most notable example of such an application is the Paul trap. Recently, the Kapitza trap was created by superimposing time-tuned focused laser beams to produce a periodically driven harmonic potential for ultracold atomic gases. This work opens up new possibilities to study Floquet systems of ultracold atomic gases. So we consider the periodically driven harmonic potential, and investigate the properties of soliton in ultracold atomic gases by numerical simulations. It is found interestingly that when a soliton is located at the center of the harmonic potential, a resonance phenomenon of soliton amplitude oscillation occurs at a specific driven frequency. In addition, the oscillation amplitude increases with the increase of the trapping frequency of the harmonic potential, and the resonance frequency increases with theaugment of soliton initial amplitude. The change of driven frequency and initial phase has a significant effect on soliton motion when the soliton is located at the edge of the harmonic potential. When the initial phase is zero, there is a characteristic driven frequency. For the case where the driven frequency is equal to the characteristic frequency, soliton motion exhibits periodic oscillations. For the case where the driven frequency is slightly lower than the characteristic frequency, the resonance of soliton oscillation can be found. When the driven frequency is slightly higher than the characteristic frequency, the anti-resonance of soliton oscillation can be found. In addition, it is found that the characteristic driven frequency increases linearly with the increase of the trapping frequency of the harmonic potential. When the initial phase is not equal to zero, the irregular oscillation, quasi-periodic oscillation, and periodic oscillation can be observed with the increase of driven frequency. When the driven frequency is equal to a specific value, the resonance of soliton oscillation can also obtained. Furthermore, the fast driving has no effect on the motion trajectory of solitons. These results can help to precisely control ultracold atomic gases.

Acta Physica Sinica•Jan 1, 2025•0 citations

Equilibration and approximate conservation laws: Dipole oscillations and perfect drag of ultracold atoms in a harmonic trap

Robert Bamler, Achim Rosch

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum-generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\ensuremath{\delta}\ensuremath{\omega}$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by interspecies interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of interspecies interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\ensuremath{\tau}\ensuremath{\propto}{(\ensuremath{\delta}\ensuremath{\omega})}^{2}/\mathrm{\ensuremath{\Gamma}}$, where $\mathrm{\ensuremath{\Gamma}}$ is a single-particle scattering rate.

arXiv:1504.03375•Physical Review A•Jun 5, 2015•8 citations

Interplay of driving, nonlinearity and dissipation in nanoscale and ultracold atom systems

Mathematisch-naturwissenschaftlichen Fakultät I, Heinrich-Heine-Universität Düsseldorf

•Jan 1, 2006•0 citations
We show that, for a one - dimensional open quantum system of ultracold atoms trapped in an array of harmonic potentials that is weakly coupled to a background Bose - Einstein Condensate (BEC), a unique steady state emerges at either of the two edges of the array due to the combined effects of excitation via lasers of these ultracold atoms and decay back to their initial energy levels via emission of excitations into the BEC, acting as an excitation reservoir. We then demonstrate the existence of steady states of the master equation that describes the dynamics of this open quantum system with respect to the expectation value of the position of the harmonic potential containing these states, and show that these steady states occur at the edges of the array of harmonic potentials trapping these atoms. Using the open quantum system's master equation to evolve initial states of the system that are trapped in other harmonic potentials in the array numerically over time, we verify the analytic calculations demonstrating the existence of these steady states at the edge of the system, and further demonstrate that these steady states will emerge regardless of the number of atoms trapped in each of the harmonic potentials in the array. We note that the emergence of these edge states irrespective of the initial state of the system is similar to the non-Hermitian skin effect seen in other open quantum systems, and are of fundamental importance in quantum technological applications such as quantum transport and quantum batteries.
Kapitza’s pendulum is an inverted pendulum that is dynamically stabilized by rapidly driving its pivot point. Many applications of Kapitza stabilization in quantum systems have been proposed, such as optical molasses, the stability of optical resonators, preparation of molecular ions, the breaking of translation symmetry, the periodically driven sine-Gordon model, polariton Rabi oscillation, and the stabilization of bright solitons in a Bose-Einstein condensate. In particular, Kapitza stabilization can be used to trap particles. The most notable example of such an application is the Paul trap. Recently, the Kapitza trap was created by superimposing time-tuned focused laser beams to produce a periodically driven harmonic potential for ultracold atomic gases. This work opens up new possibilities to study Floquet systems of ultracold atomic gases. So we consider the periodically driven harmonic potential, and investigate the properties of soliton in ultracold atomic gases by numerical simulations. It is found interestingly that when a soliton is located at the center of the harmonic potential, a resonance phenomenon of soliton amplitude oscillation occurs at a specific driven frequency. In addition, the oscillation amplitude increases with the increase of the trapping frequency of the harmonic potential, and the resonance frequency increases with theaugment of soliton initial amplitude. The change of driven frequency and initial phase has a significant effect on soliton motion when the soliton is located at the edge of the harmonic potential. When the initial phase is zero, there is a characteristic driven frequency. For the case where the driven frequency is equal to the characteristic frequency, soliton motion exhibits periodic oscillations. For the case where the driven frequency is slightly lower than the characteristic frequency, the resonance of soliton oscillation can be found. When the driven frequency is slightly higher than the characteristic frequency, the anti-resonance of soliton oscillation can be found. In addition, it is found that the characteristic driven frequency increases linearly with the increase of the trapping frequency of the harmonic potential. When the initial phase is not equal to zero, the irregular oscillation, quasi-periodic oscillation, and periodic oscillation can be observed with the increase of driven frequency. When the driven frequency is equal to a specific value, the resonance of soliton oscillation can also obtained. Furthermore, the fast driving has no effect on the motion trajectory of solitons. These results can help to precisely control ultracold atomic gases.
The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum-generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\ensuremath{\delta}\ensuremath{\omega}$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by interspecies interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of interspecies interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\ensuremath{\tau}\ensuremath{\propto}{(\ensuremath{\delta}\ensuremath{\omega})}^{2}/\mathrm{\ensuremath{\Gamma}}$, where $\mathrm{\ensuremath{\Gamma}}$ is a single-particle scattering rate.