Publications (2)0 Total impact
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ABSTRACT: We investigate the effect of anharmonicity and interactions on the dynamics
of an initially Gaussian wavepacket in a weakly anharmonic potential. We note
that depending on the strength and sign of interactions and anharmonicity, the
quantum state can be either localized or delocalized in the potential. We
formulate a classical model of this phenomenon and compare it to quantum
simulations done for a self consistent potential given by the Gross-Pitaevskii
Equation.
12/2012;
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ABSTRACT: We study echoes and what we call 'revival echoes' for a collection of atoms
that are described by a single quantum wavefunction and are confined in a
weakly anharmonic trap. The echoes and revival echoes are induced by applying
two, successive temporally localized potential perturbations to the confining
potential, one at time $t=0$, and a smaller one at time $t=\tau$. Pulse-like
responses in the expectation value of position $<x(t)>$ are predicted at $t
\approx n\tau$ ($n=2,3,...$) and are particularly evident at $t \approx 2\tau$.
A novel result of our study is the finding of 'revival echoes'. Revivals (but
not echoes) occur even if the second perturbation is absent. In particular, in
the absence of the second perturbation, the response to the first perturbation
dies away, but then reassembles, producing a response at revival times $mT_x$
($m=1,2,...$). Including the second perturbation at $t=\tau$, we find
temporally localized responses, revival echoes, both before and after $t\approx
mT_x$, e.g., at $t\approx m T_x-n \tau$ (pre-revival echoes) and at $t\approx
mT_x+n\tau$, (post-revival echoes), where $m$ and $n$ are $1,2,...$ . Depending
on the form of the perturbations, the 'principal' revival echoes at $t \approx
T_x \pm \tau$ can be much larger than the echo at $t \approx 2\tau$. We develop
a perturbative model for these phenomena, and compare its predictions to the
numerical solutions of the time-dependent Schr\"odinger Equation. The scaling
of the size of the various echoes and revival echoes as a function of the
symmetry and size of the perturbations applied at $t=0$ and $t=\tau$ is
investigated. We also study the presence of revivals and revival echoes in
higher moments of position, $<x^p (t)>$, $p>1$, and the effect of atom-atom
interactions on these phenomena.
06/2012;
