Quantum theory of particle motion in a rapidly oscillating field

Cook, Richard J.; Shankland, Donn G.; Wells, Ann Laurie

doi:10.1103/physreva.31.564

Cited by 154 publications

(148 citation statements)

References 13 publications

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“…Similarly to the classical case, in the high modulation regime such a potential can be approximated by an effective time-independent potential [5,6] …”

Section: Imaginary Kapitza Pendulummentioning

confidence: 99%

“…It was first explained and demonstrated in classical physics by Pyotr Kapitza in 1951, who showed that an inverted pendulum can be stabilized by the addition of a vertical vibration [2]. Later nonlinear and quantum analogues of this phenomenon were studied in several papers [3][4][5][6] and found important applications, for example in Paul traps for charged particles [7], in driven bosonic Josephson junctions [8], and in nonlinear dispersion management and diffraction control of light in optics [3,9]. The main result underlying Kapitza stabilization is that the motion of a classical or quantum particle in an external rapidly oscillating potential can be described at leading order by an effective time-independent potential, which shows a local minimum (a well) while the non-oscillating potential did not.…”

Section: Introductionmentioning

confidence: 99%

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Imaginary Kapitza pendulum

2013

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We extend the theory of Kapitza stabilization within the complex domain, i.e. for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasi-energy spectrum is found to be entirely real-valued, however a substantial difference with respect to a real potential emerges, that is the formation of a truly bound state instead of a resonance. The predictions of the Kapitza averaging method and the transition from a complex to an entirely real-valued quasi-energy spectrum at high frequencies are confirmed by numerical simulations of the Schrödinger equation for an oscillating Gaussian potential. An application and a physical implementation of the imaginary Kapitza pendulum to the stability of optical resonators with variable reflectivity is discussed.

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“…Similarly to the classical case, in the high modulation regime such a potential can be approximated by an effective time-independent potential [5,6] …”

Section: Imaginary Kapitza Pendulummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Imaginary Kapitza pendulum

2013

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“…The time-scale separation allows us to consider Φ(x, t) as a slowly varying function of time [26]. Notice the explicit dependence on the parameter σ.…”

Section: From Classical To Quantum Adiabatic Approximationmentioning

confidence: 99%

Nonadiabatic effects in the dynamics of atoms confined in a cylindric time-orbiting-potential magnetic trap

2004

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In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed to an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the nonadiabatic effects arising from the spin dynamics about the local magnetic field. Geometric-like magnetic-fields determined by the Berry's phase appear within the quantum description. The application of a variational procedure on the original quantum equation leads to a set of dynamical evolution equations for the quantum average value of the position operator and of the spin variables. Within this approximation we derive the quantummechanical ground state configuration matching the classical adiabatic solution and perform some numerical simulations.

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“…Either of these would r~2Mr~ ( 6) A plot of a characteristic trajectory spiraling into the origin is indicated in Fig. 1 (10) The displacements in position and momentum on the right-hand sides represent the motion of a free particle exposed to the time-varying potential alone.…”

Section: Introductionmentioning

confidence: 99%

“…We are concerned with [6], Combescure [7], and Brown [g], aimed mainly at understanding ion motion in a Paul trap [9], which is governed by the Mathieu equation.…”

Section: Introductionmentioning

confidence: 99%