Intermode Traces ? Fundamental Interference Phenomenon
in Quantum and Wave Physics

Kaplan, A. E.; Stifter, P.; Leeuwen, K. A. H. van; Lamb, Willis E.; Schleich, Wolfgang P.

doi:10.1238/physica.topical.076a00093

Cited by 45 publications

(47 citation statements)

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“…As a result the fringe velocities in Fig. 1 are a few tens of percents larger than the linear trace velocities 4nv 0 for the canals with a symmetric initial state [12]. The nonlinear fringe velocities are still determined by the degenerate intermode traces and are approximately integer multiples of the minimum speed.…”

mentioning

confidence: 85%

“…After the turn-off of the MOT the kinetic energy term in GPE becomes dominant and the matter wave expands towards, and eventually reflects from, the box boundaries. Due to the macroscopic quantum coherence of a BEC different spatial regions of the matter field generate a complex self-interference pattern that exhibits canals analogously to the quantum carpet structures of the linear Schrödinger equation [12]. From Fig.…”

mentioning

confidence: 98%

“…One-dimensional case -The linear Schrödinger equation for the 1D box of length L exhibits [12] regular spatio-temporal patterns. These patterns consist of straight lines, so called traces, of different steepness corresponding to harmonics of a fundamental velocity, v 0 .…”

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confidence: 99%

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Interference of a Bose-Einstein condensate in a hard-wall trap: From the nonlinear Talbot effect to the formation of vorticity

et al. 2001

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We theoretically study the coherent expansion of a BoseEinstein condensate in the presence of a confining impenetrable hard-wall potential. The nonlinear dynamics of the macroscopically coherent matter field results in rich and complex spatio-temporal interference patterns demonstrating the formation of vorticity and solitonlike structures, and the fragmentation of the condensate into coherently coupled pieces. 03.75.Fi,05.30.Jp

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confidence: 85%

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confidence: 98%

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Interference of a Bose-Einstein condensate in a hard-wall trap: From the nonlinear Talbot effect to the formation of vorticity

et al. 2001

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“…If y is to be measured at a later time t 1 the system must move in time from 0 to t 1 , 19) according to (3.3). At t 1 a measurement is made, 20) according to (3.17).…”

Section: Quantum Distribution Functionsmentioning

confidence: 99%

“…The difference is in the motion: the two peaks drift back and forth against each other without spreading, eventually arriving at the origin. The interference term therefore has a different effect (sometimes called a "quantum carpet" [19]) but we have nevertheless introduced the attenuation coefficient in the same way as the ratio of the coefficient of the cosine to twice the geometric mean of the first two terms. For very short times, c(t) ∼ = x 2 − 1 2 ẋ 2 t 2 and [x(0), x(t)] ∼ = i t/m, so a(t) is of the same form (5.22) but now with…”

Section: Displaced Ground State Pairmentioning

confidence: 99%

Measured quantum probability distribution functions for Brownian motion

Ford

O’Connell

2007

Phys. Rev. A

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The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath..

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Quantum carpets of a slightly relativistic particle

Marzoli¹,

Kaplan

Saif

et al. 2008

Fortschritte der Physik

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We analyze the structures emerging in the spacetime representation of the probability density woven by a slightly relativistic particle caught in a one-dimensional box. In particular, we evaluate the relativistic effects on the revival time and the specific changes produced in the intermode traces, which quantum carpets consist of. Moreover, we present a detailed mathematical analysis of such quantum carpets pursuing the approach of a kernel. Here we represent the probability distribution as a superposition of interfering Airy function-type structures along straight world lines. We also show that this phenomenon can be enhanced by many orders of magnitude in semiconductors with narrow band-gap (e.g. as in InSb) and small effective mass of the electron, whereby due to the strong nonparabolicity of the semiconductor conduction band, the electron energy vs momentum dispersion relation behaves in a pseudo-relativistic way.Fortschr. Phys. 56, No. 10, 967 -992 (2008) We analyze the structures emerging in the spacetime representation of the probability density woven by a slightly relativistic particle caught in a one-dimensional box. In particular, we evaluate the relativistic effects on the revival time and the specific changes produced in the intermode traces, which quantum carpets consist of. Moreover, we present a detailed mathematical analysis of such quantum carpets pursuing the approach of a kernel. Here we represent the probability distribution as a superposition of interfering Airy functiontype structures along straight world lines. We also show that this phenomenon can be enhanced by many orders of magnitude in semiconductors with narrow band-gap (e.g. as in InSb) and small effective mass of the electron, whereby due to the strong nonparabolicity of the semiconductor conduction band, the electron energy vs momentum dispersion relation behaves in a pseudo-relativistic way.

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Intermode Traces ? Fundamental Interference Phenomenon in Quantum and Wave Physics

Cited by 45 publications

References 4 publications

Interference of a Bose-Einstein condensate in a hard-wall trap: From the nonlinear Talbot effect to the formation of vorticity

Interference of a Bose-Einstein condensate in a hard-wall trap: From the nonlinear Talbot effect to the formation of vorticity

Measured quantum probability distribution functions for Brownian motion

Quantum carpets of a slightly relativistic particle

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