Dynamics of a quantum wave emitted by a decaying and evanescent point source

Delgado, Fernando; Muga, J. G.

doi:10.1016/j.physe.2015.06.018

Cited by 3 publications

(15 citation statements)

References 37 publications

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“…This expression yields a formal solution for the Husimi amplitude corresponding to the transmitted state Ψ(x, t). The physics that is embedded in f can be for instance accessed by numerically computing the integral in (22). Here the challenge, and the main aim of our study, is to analytically compute this integral.…”

Section: Husimi Distributionmentioning

confidence: 99%

“…To this end, we rewrite the Husimi amplitude (22) in an alternative form. Combining (22) with ( 4)-( 6) and (18), we show (details may be found in appendix A) that, in the frozen Gaussian regime (7), f can be written in the form…”

Section: Husimi Distributionmentioning

confidence: 99%

“…points where F 2slit vanishes. To further ensure that (112) indeed accurately describes the phase-space structure of the actual Husimi distribution, we then superimpose on figure 5(b) the phase-space points (112) for k = −4, −2, 0, 2, 4 onto the corresponding Husimi distribution obtained by numerically evaluating the integral (22) for the aperture function (99) and for the exact same numerical parameters as on figure 5(a). This clearly confirms the accuracy of our analytic result (112) to describe the position of the diffraction peaks in phase space.…”

Section: (108)mentioning

confidence: 99%

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Phase-space representation of diffraction in time: analytic results

Barbier

Goussev

2022

New J. Phys.

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Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variations of transmission properties. Here we analytically describe the phase-space structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an analytic expression for the Husimi distribution representing the state of the system in the case of time gratings comprising a succession of Lorentzian-like slits. In particular, for a double-slit scenario, we derive a simple and intuitive expression that accurately captures the position of interference fringes in phase space.

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Section: Husimi Distributionmentioning

confidence: 99%

Section: Husimi Distributionmentioning

confidence: 99%

Section: (108)mentioning

confidence: 99%

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Phase-space representation of diffraction in time: analytic results

Barbier

Goussev

2022

New J. Phys.

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“…We emphasize that ( 22) is valid for an arbitrary time-dependent aperture function χ(τ ). The expression (22) of K can now be used to construct the transmitted state Ψ(x, t). Indeed, substituting (10) and ( 22) into (15) yields the following expression of Ψ [38]:…”

Section: Modelmentioning

confidence: 99%

“…This approach is very popular in diffraction-in-time studies and has been extensively used in the literature (see, e.g., Refs. [9,18,19,20,21,22]). What it does not take into account however is the back-action of the transmitted matter wave on the incoming wave in the incident region.…”

Section: Introductionmentioning

confidence: 99%

Phase-space representation of diffraction in time: Analytic results

Barbier,

Goussev

2021

Preprint

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Diffraction in time manifests itself as the appearance of probabilitydensity fringes when a matter wave passes through an opaque screen with abrupt temporal variation of transmission properties. Here we analytically describe the phasespace structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an analytic expression for the Husimi distribution representing the state of the system in the case of time gratings comprising a succession of Lorentzianlike slits. In particular, for a double-slit scenario, we derive a simple and intuitive expression that accurately captures the position of interference fringes in phase space.

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Absorption dynamics and delay time in complex potentials

2018

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The dynamics of absorption is analyzed by using an exactly solvable model that deals with an analytical solution to Schrödinger's equation for cutoff initial plane waves incident on a complex absorbing potential. A dynamical absorption coefficient which allows us to explore the dynamical loss of particles from the transient to the stationary regime is derived. We find that the absorption process is characterized by the emission of a series of damped periodic pulses in time domain, associated with damped Rabi-type oscillations with a characteristic frequency, ω=(E+ò)/ÿ, where E is the energy of the incident waves and −ò is energy of the quasidiscrete state of the system induced by the absorptive part of the Hamiltonian; the width γ of this resonance governs the amplitude of the pulses. The resemblance of the time-dependent absorption coefficient with a real decay process is discussed, in particular the transition from exponential to nonexponential regimes, a well-known feature of quantum decay. We have also analyzed the effect of the absorptive part of the potential on the dynamical delay time, which behaves differently from the one observed in attractive real delta potentials, exhibiting two regimes: time advance and time delay.

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Dynamics of a quantum wave emitted by a decaying and evanescent point source

Cited by 3 publications

References 37 publications

Phase-space representation of diffraction in time: analytic results

Phase-space representation of diffraction in time: analytic results

Phase-space representation of diffraction in time: Analytic results

Absorption dynamics and delay time in complex potentials

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