237 research outputs found
Canonically conjugate pairs and phase operators
For quantum mechanics on a lattice the position (``particle number'')
operator and the quasi-momentum (``phase'') operator obey canonical commutation
relations (CCR) only on a dense set of the Hilbert space. We compare exact
numerical results for a particle in simple potentials on the lattice with the
expectations, when the CCR are assumed to be strictly obeyed. Only for
sufficiently smooth eigenfunctions this leads to reasonable results. In the
long time limit the use of the CCR can lead to a qualitativel wrong dynamics
even if the initial state is in the dense set.Comment: 4 pages, 5 figures. Phys. Rev. A, in pres
Bound State and Order Parameter Mixing Effect by Nonmagnetic Impurity Scattering in Two-band Superconductors
We investigate nonmagnetic impurity effects in two-band superconductors,
focusing on the effects of interband scatterings. Within the Born
approximation, it is known that interband scatterings mix order parameters in
the two bands. In particular, only one averaged energy gap appears in the
excitation spectrum in the dirty limit. [G. Gusman: J. Phys. Chem. Solids {\bf
28} (1967) 2327.] In this paper, we take into account the interband scattering
within the -matrix approximation beyond the Born approximation in the
previous work. We show that, although the interband scattering is responsible
for the mixing effect, this effect becomes weak when the interband scattering
becomes very strong. In the strong interband scattering limit, a two-gap
structure corresponding to two order parameters recovers in the superconducting
density of states. We also show that a bound state appears around a nonmagnetic
impurity depending on the phase of interband scattering potential.Comment: 28pages, 10 figure
Vortex nucleation through edge states in finite Bose-Einstein condensates
We study the vortex nucleation in a finite Bose-Einstein condensate. Using a
set of non-local and chiral boundary conditions to solve the
Schrdinger equation of non-interacting bosons in a rotating trap, we
obtain a quantitative expression for the characteristic angular velocity for
vortex nucleation in a condensate which is found to be 35% of the transverse
harmonic trapping frequency.Comment: 24 pages, 8 figures. Both figures and the text have been revise
C-axis resistivity and high Tc superconductivity
Recently we had proposed a mechanism for the normal-state C-axis resistivity
of the high-T layered cuprates that involved blocking of the
single-particle tunneling between the weakly coupled planes by strong
intra-planar electron-electron scattering. This gave a C-axis resistivity that
tracks the ab-plane T-linear resistivity, as observed in the high-temperature
limit. In this work this mechanism is examined further for its implication for
the ground-state energy and superconductivity of the layered cuprates. It is
now argued that, unlike the single-particle tunneling, the tunneling of a
boson-like pair between the planes prepared in the BCS-type coherent trial
state remains unblocked inasmuch as the latter is by construction an eigenstate
of the pair annihilation operator. The resulting pair-delocalization along the
C-axis offers energetically a comparative advantage to the paired-up trial
state, and, thus stabilizes superconductivity. In this scheme the strongly
correlated nature of the layered system enters only through the blocking
effect, namely that a given electron is effectively repeatedly monitored
(intra-planarly scattered) by the other electrons acting as an environment, on
a time-scale shorter than the inter-planar tunneling time. Possible
relationship to other inter-layer pairing mechanisms proposed by several
workers in the field is also briefly discussed.Comment: typos in equations corrected, contents unchange
Laser-induced collective excitations in a two-component Fermi gas
We consider the linear density response of a two-component (superfluid) Fermi
gas of atoms when the perturbation is caused by laser light. We show that
various types of laser excitation schemes can be transformed into linear
density perturbations, however, a Bragg spectroscopy scheme is needed for
transferring energy and momentum into a collective mode. This makes other types
of laser probing schemes insensitive for collective excitations and therefore
well suited for the detection of the superfluid order parameter. We show that
for the special case when laser light is coupled between the two components of
the Fermi gas, density response is always absent in a homogeneous system.Comment: 6 pages, no figure
A Method for Modeling Decoherence on a Quantum Information Processor
We develop and implement a method for modeling decoherence processes on an
N-dimensional quantum system that requires only an -dimensional quantum
environment and random classical fields. This model offers the advantage that
it may be implemented on small quantum information processors in order to
explore the intermediate regime between semiclassical and fully quantum models.
We consider in particular system-environment couplings which
induce coherence (phase) damping, though the model is directly extendable to
other coupling Hamiltonians. Effective, irreversible phase-damping of the
system is obtained by applying an additional stochastic Hamiltonian on the
environment alone, periodically redressing it and thereby irreversibliy
randomizing the system phase information that has leaked into the environment
as a result of the coupling. This model is exactly solvable in the case of
phase-damping, and we use this solution to describe the model's behavior in
some limiting cases. In the limit of small stochastic phase kicks the system's
coherence decays exponentially at a rate which increases linearly with the kick
frequency. In the case of strong kicks we observe an effective decoupling of
the system from the environment. We present a detailed implementation of the
method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure
Tunneling in Decaying Cosmologies and the Cosmological Constant Problem
The tunneling rate, with exact prefactor, is calculated to first order in
for an empty closed Friedmann-Robertson-Walker (FRW) universe with
decaying cosmological term ( is the scale factor and
is a parameter ). This model is equivalent to a cosmology
with the equation of state . The calculations are
performed by applying the dilute-instanton approximation on the corresponding
Duru-Kleinert path integral.
It is shown that the highest tunneling rate occurs for corresponding to
the cosmic string matter universe. The obtained most probable cosmological
term, like one obtained by Strominger, accounts for a possible solution to the
cosmological constant problem.Comment: 21 pages, REVTEX, The section 3 is considerably completed including
some physical mechanisms supporting the time variation of the cosmological
constant, added references for the section 3. Accepted to be published in
Phys. Rev.
Interference of Bose-Einstein condensates in momentum space
We suggest an experiment to investigate the linear superposition of two
spatially separated Bose-Einstein condensates. Due to the coherent combination
of the two wave functions, the dynamic structure factor, measurable through
inelastic photon scattering at high momentum transfer , is predicted to
exhibit interference fringes with frequency period where
is the distance between the condensates. We show that the coherent
configuration corresponds to an eigenstate of the physical observable measured
in the experiment and that the relative phase of the condensates is hence
created through the measurement process.Comment: 4 pages and 2 eps figure
Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard
model is derived in the framework of the slave-boson mean-field approximation.
The expansion can be obtained in terms of moments of the density of states of
freely hopping electrons on a lattice, which in turn are obtained for
hypercubic lattices in arbitrary dimension. The expansion is given for the case
of half-filling and for the energy up to fifth order in the ratio of hopping
integral over on-site interaction , but can straightforwardly be
generalized to the non-half-filled case and be extended to higher orders in
. For the energy the expansion is found to have an accuracy of better than
for . A comparison is given with an earlier perturbation
expansion based on the Linear Spin Wave approximation and with a similar
expansion based on the Hartree-Fock approximation. The case of an infinite
number of spatial dimensions is discussed.Comment: 12 pages, LaTeX2e, to be published in Phys. Rev.
Quantum-state control in optical lattices
We study the means to prepare and coherently manipulate atomic wave packets
in optical lattices, with particular emphasis on alkali atoms in the
far-detuned limit. We derive a general, basis independent expression for the
lattice operator, and show that its off-diagonal elements can be tailored to
couple the vibrational manifolds of separate magnetic sublevels. Using these
couplings one can evolve the state of a trapped atom in a quantum coherent
fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We
explore the use of atoms bound in optical lattices to study quantum tunneling
and the generation of macroscopic superposition states in a double-well
potential. Far-off-resonance optical potentials lend themselves particularly
well to reservoir engineering via well controlled fluctuations in the
potential, making the atom/lattice system attractive for the study of
decoherence and the connection between classical and quantum physics.Comment: 35 pages including 8 figures. To appear in Phys. Rev. A. March 199
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