Towards a generalized Landau-Zener formula for an interacting Bose-Einstein condensate in a two-level system

Witthaut, Dirk; Graefe, Eva-Maria; Korsch, Hans Jürgen

doi:10.1103/physreva.73.063609

Cited by 83 publications

(95 citation statements)

References 18 publications

(32 reference statements)

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“…mean-field, dynamics. A generalized Landau-Zener formula for the mean-field description of interacting BECs in a two-mode system has been derived by studying the many particle system [5]. In [6] the commutability between the classical and the adiabatic limit for the same system is studied and first steps towards a semiclassical treatment of the problem are reported.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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A semiclassical Bohr-Sommerfeld approximation is derived for an N -particle, two-mode BoseHubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the 'classical' dynamics of the mean-field Gross-Pitaevskii equation and is expected to be valid for large N . We demonstrate the possibility to reconstruct quantum properties of the N -particle system from the mean-field dynamics. The resulting semiclassical eigenvalues and eigenstates are found to be in very good agreement with the exact ones, even for small values of N , both for subcritical and supercritical particle interaction strength where tunneling has to be taken into account.

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Section: Introductionmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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“…We make reference to the two-mode mean-field and Bose-Hubbard schemes inherited from the Gross-Pitaevskii and full quantum approaches [4][5][6][7][8][9]. As a result of incorporating the linear variation in time between the two levels, all of those treatments suggested a breakdown of the adiabatic limit, that is, that the LZ transition probability does not vanish even in the adiabatic limit.…”

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confidence: 99%

“…Tunnelling from the ground state to the excited state is enhanced by the nonlinearity, where as in the opposite direction it is suppressed. Even more, a LZ formula has been derived for the two mode many-particle scenario [7].…”

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confidence: 99%

Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids

Caballero-Benítez

Paredes

2012

Phys. Rev. A

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We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains, using a many-body generalization recently reported [Y.-A. Chen et al.], within the decoupling approximation and the one-level band scheme. The energy spectrum evidences the structure of the avoided level crossings as a function of the on-site inter particle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle LandauZener predictions. In the strong coupling regime, we find that there is a critical value of the on-site interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.

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“…In recent years, ultracold atomic gases have provided new opportunities for investigating a many-body extension of the simple two-level LZ tunneling process [9][10][11][12][13][14][15][16][17][18]. The remarkable controllability in these systems allows a clear study of the effect of the interatomic interaction on the LZ tunneling process.…”

Section: Introductionmentioning

confidence: 99%

Photon-induced sideband transitions in a many-body Landau-Zener process

et al. 2014

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We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the strong interaction regime, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different "photon" numbers.

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Towards a generalized Landau-Zener formula for an interacting Bose-Einstein condensate in a two-level system

Cited by 83 publications

References 18 publications

Semiclassical quantization of anN-particle Bose-Hubbard model

Semiclassical quantization of anN-particle Bose-Hubbard model

Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids

Photon-induced sideband transitions in a many-body Landau-Zener process

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