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:cond-mat/0601018 · Physical Review Letters

Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate

André Eckardt, Tharanga Jinasundera, Christoph Weiß, Martin Holthaus

Published Nov 9, 2005• 131 citations
arXivHTMLPDF

Abstract

We study many-body tunneling of a small Bose-Einstein condensate in a periodically modulated, tilted double-well potential. Periodic modulation of the trapping potential leads to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there exist well-developed half-integer Shapiro-like resonances.

DOI
10.1103/physrevlett.95.200401

Related papers

Fractional-photon-assisted tunneling in an optical superlattice: Large contribution to particle transfer

Martin Esmann, Niklas Teichmann, Christoph Weiß

Fractional-photon-assisted tunneling is investigated both analytically and numerically for few interacting ultracold atoms in the double wells of an optical superlattice. This can be realized experimentally by adding periodic shaking to an existing experimental setup [Cheinet et al., Phys. Rev. Lett. 101, 090404 (2008)]. Photon-assisted tunneling is visible in the particle transfer between the wells of the individual double wells. In order to understand the physics of the photon-assisted tunneling, an effective model based on the rotating-wave approximation is introduced. The validity of this effective approach is tested for wide parameter ranges that are accessible to experiments in double-well lattices. The effective model goes well beyond previous perturbation theory approaches and is useful for investigating in particular the fractional-photon-assisted tunneling resonances. Analytic results on the level of the experimentally realizable two-particle quantum dynamics show very good agreement with the numerical solution of the time-dependent Schr\"odinger equation. Far from being a small effect, both the one-half-photon and the one-third-photon resonances are shown to have large effects on the particle transfer.

arXiv:1101.5272•Physical Review A•Jun 29, 2011•12 citations

Fractional photon-assisted tunneling for Bose-Einstein condensates in a double well

Niklas Teichmann, Martin Esmann, Christoph Weiß

Half-integer-photon resonances in a periodically shaken double well are investigated on the level of the $N$-particle quantum dynamics. Contrary to nonlinear mean-field equations, the linear $N$-particle Schr\"odinger equation does not contain any nonlinearity which could be the origin of such resonances. Nevertheless, analytic calculations on the $N$-particle level explain why such resonances can be observed even for particle numbers as low as $N=2$. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.

arXiv:0905.2838•Physical Review A•Jun 17, 2009•35 citations

Photon-assisted tunneling of a driven two-mode Bose-Einstein condensate

Qiongtao Xie, Shiguang Rong, Honghua Zhong +2 more

We investigate the photon-assisted tunneling of a Bose-Einstein condensate in a periodically driven double-well potential. It is shown that the energy levels become nonequidistant due to the presence of the interatomic interaction, thereby leading to the occurrences of the fractional photon resonances. Depending on whether the resonance frequency shifts with the interatomic interaction, two distinct types of resonances are identified: nonshifting resonances and shifting resonances. In particular, certain nonshifting fractional resonances show an odd-even sensitivity to the atom number.

Physical Review A•Aug 27, 2010•19 citations

Adiabatic tunneling of Bose—Einstein condensates with modulated atom interaction in a double-well potential

Xin Xiao-Tian, Fang Huang, Xu Zhi-Jun +1 more

We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.

Chinese Physics B•Jul 1, 2014•5 citations

Fractional photon-assisted tunneling of ultra-cold atoms in periodically shaken double-well lattices

Martin Esmann, Jonathan D. Pritchard, Christoph Weiß

Fractional photon-assisted tunneling is investigated both numerically and analytically in a double-well lattice. While integer photon-assisted tunneling is a single-particle effect, fractional photon-assisted tunneling is an interaction-induced many-body effect. Double-well lattices with few particles in each double well are ideal to study this effect far from the mean-field effects. It is predicted that the 1/4-resonance is observable in such systems. Fractional photon-assisted tunneling provides a physically relevant model, for which N -th order time-dependent perturbation theory can be large although all previous orders are small. All predicted effects will be observable with an existing experimental setup [1].

arXiv:1109.2735•Laser Physics Letters•Nov 10, 2011•9 citations

Laser-assisted coherent atomic tunneling between two trapped Bose-Einstein condensates

Noriaki Tsukada, Mitsunobu Gotoda, Y. Nomura +1 more

We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the $n\mathrm{th}$ LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.

Physical Review A•May 1, 1999•32 citations
We study many-body tunneling of a small Bose-Einstein condensate in a periodically modulated, tilted double-well potential. Periodic modulation of the trapping potential leads to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there exist well-developed half-integer Shapiro-like resonances.
Fractional-photon-assisted tunneling is investigated both analytically and numerically for few interacting ultracold atoms in the double wells of an optical superlattice. This can be realized experimentally by adding periodic shaking to an existing experimental setup [Cheinet et al., Phys. Rev. Lett. 101, 090404 (2008)]. Photon-assisted tunneling is visible in the particle transfer between the wells of the individual double wells. In order to understand the physics of the photon-assisted tunneling, an effective model based on the rotating-wave approximation is introduced. The validity of this effective approach is tested for wide parameter ranges that are accessible to experiments in double-well lattices. The effective model goes well beyond previous perturbation theory approaches and is useful for investigating in particular the fractional-photon-assisted tunneling resonances. Analytic results on the level of the experimentally realizable two-particle quantum dynamics show very good agreement with the numerical solution of the time-dependent Schr\"odinger equation. Far from being a small effect, both the one-half-photon and the one-third-photon resonances are shown to have large effects on the particle transfer.
Half-integer-photon resonances in a periodically shaken double well are investigated on the level of the NNN-particle quantum dynamics. Contrary to nonlinear mean-field equations, the linear NNN-particle Schr\"odinger equation does not contain any nonlinearity which could be the origin of such resonances. Nevertheless, analytic calculations on the NNN-particle level explain why such resonances can be observed even for particle numbers as low as N=2N=2N=2. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.
We investigate the photon-assisted tunneling of a Bose-Einstein condensate in a periodically driven double-well potential. It is shown that the energy levels become nonequidistant due to the presence of the interatomic interaction, thereby leading to the occurrences of the fractional photon resonances. Depending on whether the resonance frequency shifts with the interatomic interaction, two distinct types of resonances are identified: nonshifting resonances and shifting resonances. In particular, certain nonshifting fractional resonances show an odd-even sensitivity to the atom number.
We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.
Fractional photon-assisted tunneling is investigated both numerically and analytically in a double-well lattice. While integer photon-assisted tunneling is a single-particle effect, fractional photon-assisted tunneling is an interaction-induced many-body effect. Double-well lattices with few particles in each double well are ideal to study this effect far from the mean-field effects. It is predicted that the 1/4-resonance is observable in such systems. Fractional photon-assisted tunneling provides a physically relevant model, for which N -th order time-dependent perturbation theory can be large although all previous orders are small. All predicted effects will be observable with an existing experimental setup [1].
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.