Smooth double barriers in quantum mechanics

Dutt, Avik; Kar, Sayan

doi:10.1119/1.3481701

Cited by 24 publications

(22 citation statements)

References 22 publications

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“…Recently, a revival of interest in the paradox is arisen [15][16][17] due to the research in tunneling through double barrier. [18][19][20] The simplest case is the one-dimensional rectangular double barrier (RDB), and it has been found that even in the free propagation region between two barriers, the velocity of the tunneling particle can still be far larger than its typical value in free space.…”

Section: Introductionmentioning

confidence: 99%

Resonant tunneling dynamics and the related tunneling time

Xiao

Huang

2015

Int. J. Mod. Phys. B

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In close analogy with optical Fabry-Pérot (FP) interferometer, we rederive the transmission and reflection coefficients of tunneling through a rectangular double barrier (RDB). Based on the same analogy, we also get an analytic finesse formula for its filtering capability of matter waves, and with this formula, we reproduce the RDB transmission rate in exactly the same form as that of FP interferometer. Compared with the numerical results obtained from the original finesse definition, we find the formula works well. Next, we turn to the elusive time issue in tunneling, and show that the "generalized Hartman effect" can be regarded as an artifact of the opaque limit βl → ∞. In the thin barrier approximation, phase (or dwell) time does depend on the free inter-barrier distance d asymptotically. Further, the analysis of transmission rate in the neighborhood of resonance shows that, phase (or dwell) time could be a good estimate of the resonance lifetime. The numerical results from the uncertainty principle support this statement. This fact can be viewed as a support to the idea that, phase (or dwell) time is a measure of lifetime of energy stored beneath the barrier. To confirm this result, we shrink RDB to a double Dirac δ-barrier. The landscape of the phase (or dwell) time in k and d axes fits excellently well with the lifetime estimates near the resonance. As a supplementary check, we also apply phase (or dwell) time formula to the rectangular well, where no obstacle exists to the propagation of particle. However, due to the self-interference induced by the common cavity-like structure, phase (or dwell) time calculation leads to a counterintuitive "slowing down" effect, which can be explained appropriately by the lifetime assumptions.

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Section: Introductionmentioning

confidence: 99%

Resonant tunneling dynamics and the related tunneling time

Xiao

Huang

2015

Int. J. Mod. Phys. B

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“…Model potentials of a double well are indeed treated in most textbooks, and even in many pedagogical-style articles. [7][8][9][10][11][12] The treatment of a double well potential in textbooks will vary from qualitative discussion (see, for example, Problem 2.47 in Griffiths, 1 ) to an analytical solution (for example, Section 8.5 in Merzbacher, 13 where, however, advanced mathematical steps are required). More often, the Wentzel-Kramers-Brillouin (WKB) approximation is used (see, for example, Problem 8.15 in Griffiths, 1 and Problem 7.2, and 8.10 in Merzbacher.…”

Section: Introductionmentioning

confidence: 99%

The double-well potential in quantum mechanics: a simple, numerically exact formulation

Jelic

Marsiglio

2012

Eur. J. Phys.

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The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of 'classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.

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“…First, they provide a new subwavelength potential landscape. Quasi-bound states and resonant tunnelings of multibarrier potentials can be studied using Wentzel-Kramers-Brillouin (WKB) approximation [47,48]. The potentials can also form multi-barrier lattices since f (x) has a period of λ, thus they are useful for the study of band structures, and even trapping atoms through the quasi-bound states.…”

Section: Additional Tunabilitymentioning

confidence: 99%

Dark-state optical potential barriers with nanoscale spacing

Zubairy

2020

Phys. Rev. A

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Optical potentials have been a versatile tool for the study of atomic motions and many-body interactions in cold atoms. Recently, optical subwavelength single barriers were proposed to enhance the atomic interaction energy scale, which is based on non-adiabatic corrections to Born-Oppenheimer potentials. Here we present a study for creating a new landscape of non-adiabatic potentials-multiple barriers with subwavelength spacing at tens of nanometers. To realize these potentials, spatially rapid-varying dark states of atomic Λ-configurations are formed by controlling the spatial intensities of the driving lasers. As an application, we show that bound states of two and three atoms via magnetic dipolar interactions with weak magnetic moments can be realized in our scheme. Imperfections and experimental realizations of the multiple barriers are also discussed.

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Smooth double barriers in quantum mechanics

Cited by 24 publications

References 22 publications

Resonant tunneling dynamics and the related tunneling time

Resonant tunneling dynamics and the related tunneling time

The double-well potential in quantum mechanics: a simple, numerically exact formulation

Dark-state optical potential barriers with nanoscale spacing

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