5,477 research outputs found
Dymanics of Generalized Coherent States
We show that generalized coherent states follow Schr\"{o}dinger dynamics in
time-dependent potentials. The normalized wave-packets follow a classical
evolution without spreading; in turn, the Schr\"{o}dinger potential depends on
the state through the classical trajectory. This feedback mechanism with
continuous dynamical re-adjustement allows the packets to remain coherent
indefinetely.Comment: 8 pages, plain latex, no figure
Wave interactions in localizing media - a coin with many faces
A variety of heterogeneous potentials are capable of localizing linear
non-interacting waves. In this work, we review different examples of
heterogeneous localizing potentials which were realized in experiments. We then
discuss the impact of nonlinearity induced by wave interactions, in particular
its destructive effect on the localizing properties of the heterogeneous
potentials.Comment: Review submitted to Intl. Journal of Bifurcation and Chaos Special
Issue edited by G. Nicolis, M. Robnik, V. Rothos and Ch. Skokos 21 Pages, 8
Figure
Bohmian Trajectories of Airy Packets
The discovery of Berry and Balazs in 1979 that the free-particle
Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet
solution has taken the folklore of quantum mechanics by surprise. Over the
years, this intriguing class of wave packets has sparked enormous theoretical
and experimental activities in related areas of optics and atom physics. Within
the Bohmian mechanics framework, we present new features of Airy wave packet
solutions to Schr\"odinger equation with time-dependent quadratic potentials.
In particular, we provide some insights to the problem by calculating the
corresponding Bohmian trajectories. It is shown that by using general
space-time transformations, these trajectories can display a unique variety of
cases depending upon the initial position of the individual particle in the
Airy wave packet. Further, we report here a myriad of nontrivial Bohmian
trajectories associated to the Airy wave packet. These new features are worth
introducing to the subject's theoretical folklore in light of the fact that the
evolution of a quantum mechanical Airy wave packet governed by the
Schr\"odinger equation is analogous to the propagation of a finite energy Airy
beam satisfying the paraxial equation. Numerous experimental configurations of
optics and atom physics have shown that the dynamics of Airy beams depends
significantly on initial parameters and configurations of the experimental
set-up.Comment: 8 page
Observation of Nonspreading Wave Packets in an Imaginary Potential
We propose and experimentally demonstrate a method to prepare a nonspreading
atomic wave packet. Our technique relies on a spatially modulated absorption
constantly chiseling away from an initially broad de Broglie wave. The
resulting contraction is balanced by dispersion due to Heisenberg's uncertainty
principle. This quantum evolution results in the formation of a nonspreading
wave packet of Gaussian form with a spatially quadratic phase. Experimentally,
we confirm these predictions by observing the evolution of the momentum
distribution. Moreover, by employing interferometric techniques, we measure the
predicted quadratic phase across the wave packet. Nonspreading wave packets of
this kind also exist in two space dimensions and we can control their amplitude
and phase using optical elements.Comment: 4 figure
Well-dressed states for wave-packet dynamics in cavity QED
The quantization of atomic center-of-mass motion is considered within the context of cavity QED with particular emphasis on the dynamics of localized wave packets. “Well-dressed” states are introduced as an eigenbasis that incorporates both the quantized atom-field interaction and the external bound states of a potential well. The interplay of internal and external time scales generates qualitatively new dynamics such as novel “collapses” and “revivals.
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