Localization and tunneling in periodically driven bistable systems

Dittrich, Thomas; Groβmann, F.; Jung, P.; Oelschlägel, B.; Hänggi, Peter

doi:10.1016/0378-4371(93)90351-4

Cited by 20 publications

(16 citation statements)

References 27 publications

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“…For example, coherent oscillations of the longitudinal magnetic field can be used to drive the "bias", or energy asymmetry between the wells. In that case it has been predicted that certain frequencies will completely suppress tunneling due to quantum interference [46], a phenomenon known as "dynamic localization" [47].…”

Section: Quantum Tunneling and Schrödinger Catsmentioning

confidence: 99%

Quantum-state control in optical lattices

1998

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We study the means to prepare and coherently manipulate atomic wave packets in optical lattices, with particular emphasis on alkali atoms in the far-detuned limit. We derive a general, basis independent expression for the lattice operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well controlled fluctuations in the potential, making the atom/lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

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Section: Quantum Tunneling and Schrödinger Catsmentioning

confidence: 99%

Quantum-state control in optical lattices

1998

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“…In the present work, wave packet localization in DWPs, symmetric, asymmetric as well as anharmonic, in the presence of oscillating fields is investigated. Unlike prior work, which is mostly concerned with tunneling and confinement in one of the wells, the present work (for the first time in the literature, to the best of our knowledge) shows localization of the wave packet on the barrier for specific parameters of the linear oscillating field. The time evolution of a bilobal wave packet is presented, where each of the lobes initially indicating a high probability density in each of the wells, merge into a single lobe at the peak rise of the pulse, with localization and stabilization on the barrier.…”

Section: Introductionmentioning

confidence: 56%

“…Several dynamical aspects of the driven double‐well system have been studied before . The particle‐tunneling time in an SDWP can be reduced with a specific frequency and electric field strength of a laser, leading to tunneling enhancement .…”

Section: Introductionmentioning

confidence: 99%

“…The particle‐tunneling time in an SDWP can be reduced with a specific frequency and electric field strength of a laser, leading to tunneling enhancement . Coherent destruction of tunneling is an opposite effect, where the tunneling time is increased to an extent such that it does not tunnel through the barrier . In chemistry, tunneling finds importance in H‐transfer reactions (eg, OH + H 2 S → H 2 O + HS, an atmospheric reaction), isomerization reactions where hydrogen shifts are involved (eg, [1,5] hydrogen shift reactions in cyclopentadiene), and so on.…”

Section: Introductionmentioning

confidence: 99%

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Atop‐the‐barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

Kumar

Raj

Balanarayan

2019

Int J of Quantum Chemistry

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The spatio‐temporal localization of a system in the presence of an oscillating electric field for a symmetric double‐well potential is examined via numerical simulations of the time‐dependent Schrödinger equation. For an initial state with equal probability densities in both the wells, stabilized localization atop the barrier can be achieved on a periodic high‐frequency driving. The barrier localization is characterized using Shannon information entropies in position and momentum spaces, defined as Sρ = − ∫ |ψ|2 ln |ψ|2 dx and Sγ = − ∫ |ϕ|2 ln |ϕ|2 dp, where ψ and ϕ refer to position and momentum space wave functions, respectively. The information entropy sum, Sρ + Sγ, goes through a minimum indicating the formation of the barrier‐localized state, when the peak intensity of the oscillating field is reached. The generalized uncertainty via the Białynicki‐Birula‐Mycielski inequality ( Sρ + Sγ ≥ 1 + lnπ) is saturated upon this minimization. This serves as a signature of the formation of the barrier‐atop localized state, in terms of Shannon entropies of measurable densities.

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“…An extensive review of this approach is given by Chu [20]. Within the framework of the Floquet formalism the time evolution is determined via successive application of a one-cycle unitary propagator C, which maps the wave function at time t into the wave function at time t + T. The eigenvalue problem for the propagator C may be written as C]A") = exp( -iE")1A"), (9) (& I&(T)) = ):(4g Ic14i ) (&i 14(o)) (io) and if we choose the initial state such that (4'~l@(o)) =~~, ' then where the E"arecalled quasienergies and for a bounded system are real numbers. The corresponding eigenfunctions 1A") are referred to as quasienergy states or Floquet states.…”

mentioning

confidence: 99%

Chaos-induced avoided level crossing and tunneling

1994

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We study the quantum effect of chaos on dynamical tunneling in the driven pendulum. We analyze the avoided level crossing between the Floquet states associated with the chaotic part of the phase space and a member of the quasidegenerate doublet. As a result of the interaction, the doublet state whose Husimi distribution was initially localized on symmetric Kolmogorov-Arnold-Moser islands exchanges its structure with the chaotic state. We investigate the implications of this kind of avoided crossing on the quantum dynamics of a wave packet initially centered on one of the symmetric islands.PACS number(s): 03.65.w, 05.45.+b, 73.40.Gk

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Localization and tunneling in periodically driven bistable systems

Cited by 20 publications

References 27 publications

Quantum-state control in optical lattices

Quantum-state control in optical lattices

Atop‐the‐barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

Chaos-induced avoided level crossing and tunneling

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