Coherent control of the self-trapping transition

Holthaus, Martin; Stenholm, Stig

doi:10.1007/pl00011106

Cited by 78 publications

(112 citation statements)

References 25 publications

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“…For a discussion of the relation between mean-field and Nparticle behavior see, e.g., [18,19] and references therein and [20] for its control by external driving fields. The self-trapping transition occurs at g = −v/N s and is connected to a bifurcation of the stationary states, the fixed points of the Hamiltonian (5), in the mean-field approximation.…”

Section: Two-mode Bose-hubbard Model and Mean-field Approximationmentioning

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: Two-mode Bose-hubbard Model and Mean-field Approximationmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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“…Here V (x) is the magnetic trap holding the condensate; typically V (x) is a quadratic function of x. In this paper we consider the case where the control is again given by the dipole term E(t) · x (see, e.g., [17]). However, other parameters, such as trap frequency and scattering length, can also be influenced and tuned in the laboratory.…”

Section: Examplesmentioning

confidence: 99%

Limitations on the control of Schrödinger equations

2006

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Abstract.We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical "No-go" result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control (E(t) · x)u is not controllable in finite or infinite time. Finally, in Section 3, we give criteria for additive controllability of linear Schrödinger equations, and we give a distributed additive controllability result for the nonlinear Schrödinger equation if the data are small.Mathematics Subject Classification. 35Q40, 35Q55, 81Q99, 93B05.

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“…[25], where the energy spectrum is drawn for other purposes). The evolutions of the energy spectrum for different atom numbers are qualitatively very similar.…”

Section: Merging Of Condensates In the Practical Non-adiabatic Cirmentioning

confidence: 99%

Adiabatic and nonadiabatic merging of independent Bose-Einstein condensates

Duan

2005

Phys. Rev. A

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Motivated by a recent experiment [Chikkatur et al. Science, 296, 2193] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate) . In the non-adiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still get a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the non-adiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on merging of condensates.

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Coherent control of the self-trapping transition

Cited by 78 publications

References 25 publications

Semiclassical quantization of anN-particle Bose-Hubbard model

Semiclassical quantization of anN-particle Bose-Hubbard model

Limitations on the control of Schrödinger equations

Adiabatic and nonadiabatic merging of independent Bose-Einstein condensates

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