1,152 research outputs found
Keplerian Squeezed States and Rydberg Wave Packets
We construct minimum-uncertainty solutions of the three-dimensional
Schr\"odinger equation with a Coulomb potential. These wave packets are
localized in radial and angular coordinates and are squeezed states in three
dimensions. They move on elliptical keplerian trajectories and are appropriate
for the description of the corresponding Rydberg wave packets, the production
of which is the focus of current experimental effort. We extend our analysis to
incorporate the effects of quantum defects in alkali-metal atoms, which are
used in experiments.Comment: accepted for publication in Physical Review
Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect
The quantum Hall effect is necessarily accompanied by low-energy excitations
localized at the edge of a two-dimensional electron system. For the case of
electrons interacting via the long-range Coulomb interaction, these excitations
are edge magnetoplasmons. We address the time evolution of localized
edge-magnetoplasmon wave packets. On short times the wave packets move along
the edge with classical E cross B drift. We show that on longer times the wave
packets can have properties similar to those of the Rydberg wave packets that
are produced in atoms using short-pulsed lasers. In particular, we show that
edge-magnetoplasmon wave packets can exhibit periodic revivals in which a
dispersed wave packet reassembles into a localized one. We propose the study of
edge-magnetoplasmon wave packets as a tool to investigate dynamical properties
of integer and fractional quantum-Hall edges. Various scenarios are discussed
for preparing the initial wave packet and for detecting it at a later time. We
comment on the importance of magnetoplasmon-phonon coupling and on quantum and
thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was
originally 3Mbyte and had to be bitmapped for submission to archive; in the
process it acquired distracting artifacts, to upload the better version, see
http://physics.indiana.edu/~uli/publ/projects.htm
Elliptical Squeezed States and Rydberg Wave Packets
We present a theoretical construction for closest-to-classical wave packets
localized in both angular and radial coordinates and moving on a keplerian
orbit. The method produces a family of elliptical squeezed states for the
planar Coulomb problem that minimize appropriate uncertainty relations in
radial and angular coordinates. The time evolution of these states is studied
for orbits with different semimajor axes and eccentricities. The elliptical
squeezed states may be useful for a description of the motion of Rydberg wave
packets excited by short-pulsed lasers in the presence of external fields,
which experiments are attempting to produce. We outline an extension of the
method to include certain effects of quantum defects appearing in the
alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199
Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms
This paper begins with an examination of the revival structure and long-term
evolution of Rydberg wave packets for hydrogen. We show that after the initial
cycle of collapse and fractional/full revivals, which occurs on the time scale
, a new sequence of revivals begins. We find that the structure of
the new revivals is different from that of the fractional revivals. The new
revivals are characterized by periodicities in the motion of the wave packet
with periods that are fractions of the revival time scale . These
long-term periodicities result in the autocorrelation function at times greater
than having a self-similar resemblance to its structure for times
less than . The new sequence of revivals culminates with the
formation of a single wave packet that more closely resembles the initial wave
packet than does the full revival at time , i.e., a superrevival
forms. Explicit examples of the superrevival structure for both circular and
radial wave packets are given. We then study wave packets in alkali-metal
atoms, which are typically used in experiments. The behavior of these packets
is affected by the presence of quantum defects that modify the hydrogenic
revival time scales and periodicities. Their behavior can be treated
analytically using supersymmetry-based quantum-defect theory. We illustrate our
results for alkali-metal atoms with explicit examples of the revival structure
for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199
Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values
Uncertainty relations between a bounded coordinate operator and a conjugate
momentum operator frequently appear in quantum mechanics. We prove that
physically reasonable minimum-uncertainty solutions to such relations have
quantized expectation values of the conjugate momentum. This implies, for
example, that the mean angular momentum is quantized for any
minimum-uncertainty state obtained from any uncertainty relation involving the
angular-momentum operator and a conjugate coordinate. Experiments specifically
seeking to create minimum-uncertainty states localized in angular coordinates
therefore must produce packets with integer angular momentum.Comment: accepted for publication in Physical Review
Possible Spontaneous Breaking of Lorentz and CPT Symmetry
One possible ramification of unified theories of nature such as string theory
that may underlie the conventional standard model is the possible spontaneous
breakdown of Lorentz and CPT symmetry. In this talk, the formalism for
inclusion of such effects into a low-energy effective field theory is
presented. An extension of the standard model that includes Lorentz- and
CPT-breaking terms is developed. The restriction of the standard model
extension to the QED sector is then discussed.Comment: Talk presented at Non-Accelerator New Physics, Dubna, Russia, July
199
Optical cavity tests of Lorentz invariance for the electron
A hypothetical violation of Lorentz invariance in the electrons' equation of
motion (expressed within the Lorentz-violating extension of the standard model)
leads to a change of the geometry of crystals and thus shifts the resonance
frequency of an electromagnetic cavity. This allows experimental tests of
Lorentz invariance of the electron sector of the standard model. The material
dependence of the effect allows to separate it from an additional shift caused
by Lorentz violation in electrodynamics, and to place independent limits on
both effects. From present experiments, upper limits on Lorentz violation in
the electrons' kinetic energy term are deduced.Comment: 17 pages revte
Superrevivals in the quantum dynamics of a particle confined in a finite square well potential
We examine the revival features in wave packet dynamics of a particle
confined in a finite square well potential. The possibility of tunneling
modifies the revival pattern as compared to an infinite square well potential.
We study the dependence of the revival times on the depth of the square well
and predict the existence of superrevivals. The nature of these superrevivals
is compared with similar features seen in the dynamics of wavepackets in an
anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in
Physical Review
Dynamic Nuclear Polarization in Double Quantum Dots
We theoretically investigate the controlled dynamic polarization of lattice
nuclear spins in GaAs double quantum dots containing two electrons. Three
regimes of long-term dynamics are identified, including the build up of a large
difference in the Overhauser fields across the dots, the saturation of the
nuclear polarization process associated with formation of so-called "dark
states," and the elimination of the difference field. We show that in the case
of unequal dots, build up of difference fields generally accompanies the
nuclear polarization process, whereas for nearly identical dots, build up of
difference fields competes with polarization saturation in dark states. The
elimination of the difference field does not, in general, correspond to a
stable steady state of the polarization process.Comment: 4 pages, 2 figure
Gravitational physics with antimatter
The production of low-energy antimatter provides unique opportunities to
search for new physics in an unexplored regime. Testing gravitational
interactions with antimatter is one such opportunity. Here a scenario based on
Lorentz and CPT violation in the Standard- Model Extension is considered in
which anomalous gravitational effects in antimatter could arise.Comment: 5 pages, presented at the International Conference on Exotic Atoms
(EXA 2008) and the 9th International Conference on Low Energy Antiproton
Physics (LEAP 2008), Vienna, Austria, September 200
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