Quantum system driven by rapidly varying periodic perturbation

Grozdanov, T. P.; Rakovic, M J

doi:10.1103/physreva.38.1739

Cited by 59 publications

(82 citation statements)

References 3 publications

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“…The actual calculation ofĜ might be complicated. Such an operator was calculated in [22] and in [13] by introducing expansions forP andĜ. The result turns out to depend on the phase of the periodic part of the Hamiltonian or on the initial time.…”

Section: Floquet Theory and The Effective Hamiltonianmentioning

confidence: 99%

“…III an adaption of the Floquet theory to the problem is reviewed. An effective (time independent) Hamiltonian operator is defined following and generalizing [13]. The eigenvalues of this operator are the quasienergies of the system.…”

Section: Introductionmentioning

confidence: 99%

“…IV. The restrictions introduced in [13] are avoided and consequently detailed expressions for the various terms of the effective Hamiltonian are calculated explicitly. The classical effective Hamiltonian of Sec.…”

Section: Introductionmentioning

confidence: 99%

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Effective Hamiltonians for periodically driven systems

2003

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The dynamics of classical and quantum systems which are driven by a high frequency (ω) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed perturbatively in powers of ω −1 to order ω −4 and the corresponding time independent Hamiltonian is calculated. Such an effective Hamiltonian for the corresponding quantum problem is computed to order ω −4 in a high frequency expansion. Its spectrum is the quasienergy spectrum of the time dependent quantum system. The classical limit of this effective Hamiltonian is the classical effective time independent Hamiltonian. It is demonstrated that this effective Hamiltonian gives the exact quasienergies and quasienergy states of some simple examples as well as the lowest resonance of a non trivial model for an atom trap. The theory that is developed in the paper is useful for the analysis of atomic motion in atom traps of various shapes.

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Section: Floquet Theory and The Effective Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective Hamiltonians for periodically driven systems

2003

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“…A common approach in the analysis of periodically driven quantum systems is to search for a timeindependent effective Hamiltonian with an energy spectrum approximating the quasienergies of the Floquet Hamiltonian of the system [9][10][11]. The accomplishment of this task typically requires to restrict oneself to specific classes of driving operators.…”

Section: Introductionmentioning

confidence: 99%

Effective time-independent description of optical lattices with periodic driving

Hemmerich

2010

Phys. Rev. A

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For a periodically driven quantum system an effective time-independent Hamiltonian is derived with an eigen-energy spectrum, which in the regime of large driving frequencies approximates the quasi-energies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a twodimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In case of the 1D scenario the rescaling of the tunneling energy, previously considered by Eckardt et al. in Phys. Rev. Lett. 95, 260404 (2005), is reproduced. The 2D lattice with well depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. in Phys. Rev. Lett. 100, 130402 (2008) is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.

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“…Within this approximation, off-resonant high-frequency weak drive, corresponding to vertical driving of the pendulum axis, results in an effective potential V eff = (1/4)q 2 Kj sin 2 (ϕ) [18,19,20,21]. Sufficiently strong driving (q 2 > 2) stabilizes the ϕ = π fixed-point, producing the Kapitza inverted pendulum effect.…”

Section: Harmonic Driving -Kapitza Effectmentioning

confidence: 99%

Suppression of collision-induced dephasing by periodic, erratic, or noisy driving

Khripkov

Vardi

Cohen

2013

Eur. Phys. J. Spec. Top.

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Abstract. We compare different driving scenarios for controlling the loss of single particle coherence of an initially coherent preparation in the vicinity of the hyperbolic instability of the two-mode bose-Hubbard model. In particular we contrast the quantum Zeno suppression of decoherence by broad-band erratic or noisy driving, with the Kapitza effect obtained for high frequency periodic monochromatic driving.

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Quantum system driven by rapidly varying periodic perturbation

Cited by 59 publications

References 3 publications

Effective Hamiltonians for periodically driven systems

Effective Hamiltonians for periodically driven systems

Effective time-independent description of optical lattices with periodic driving

Suppression of collision-induced dephasing by periodic, erratic, or noisy driving

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