5,020 research outputs found
Open Quantum System Stochastic Dynamics and the Rotating Wave Approximation
We study the stochastic dynamics of a two-level quantum system interacting
with a stochastic magnetic field, and a single frequency electromagnetic field,
with and without making the rotating wave approximation (RWA). The
transformation to the rotating frame does not commute with the stochastic
Hamiltonian if the stochastic field has nonvanishing components in the
transverse direction. Hence, making the RWA modifies the stochastic terms in
the Hamiltonian. Modification of the decay terms is also required in a master
equation approach (i.e., the Liouville--von Neumann density matrix equation)
for describing the dynamics. For isotropic Gaussian white noise, the RWA
dynamics remains Markovian, although the Lindblad terms in the master equation
for the density matrix become time-dependent when the non-commutation of the
RWA transformation and the noise Hamiltonian is properly accounted for. We also
treat Ornstein--Uhlenbeck noise, and find, in contra-distinction to the white
noise case, a significant difference in the dynamics calculated with the RWA
when the non-commutation of the RWA transformation and the noise Hamiltonian is
taken into account. These findings are applicable to the modeling of any open
quantum system coupled to an electromagentic field.Comment: 11 pages, 22 figures. Accepted for publication in J. Phys.
The Dynamics of an Electric Dipole Moment in a Stochastic Electric Field
The mean-field dynamics of an electric dipole moment in a deterministic and a
fluctuating electric field is solved to obtain the average over fluctuations of
the dipole moment and the angular mo- mentum as a function of time for a
Gaussian white noise stochastic electric field. The components of the average
electric dipole moment and the average angular momentum along the deterministic
electric field direction do not decay to zero, despite fluctuations in all
three components of the elec- tric field. This is in contrast to the decay of
the average over fluctuations of a magnetic moment in a stochastic magnetic
field with Gaussian white noise in all three components. The components of the
average electric dipole moment and the average angular momentum perpendicular
to the deterministic electric field direction oscillate with time but decay to
zero, and their variance grows with time.Comment: 10 pages, 10 figure
Simple spin-orbit based devices for electron spin polarization
We propose quantum devices having spin-orbit coupling (but no magnetic fields
or magnetic materials) that, when attached to leads, yield a high degree of
transmitted electron polarization. An example of such a simple device is
treated within a tight binding model composed of two 1D chains coupled by
several consecutive rungs (i.e., a ladder) and subject to a gate voltage. The
ensuing scattering problem (with Rashba spin-orbit coupling) is solved, and a
sizable polarization is predicted. When the ladder is twisted into a helix (as
in DNA), the curvature energy augments the polarization. For a system with
random spin-orbit coupling, the distribution of polarization is broad, hence a
high degree of polarization can be obtained in a measurement of a given
disorder-realization. When disorder occurs in a double helix structure then,
depending on scattering energy, the variance of the polarization distribution
can increase even further due to helix curvature.Comment: 9 PRB page
Coherence of an Interacting Bose Gas: from a Single to a Double Well
The low energy properties of a trapped bose gas split by a potential barrier
are determined over the whole range of barrier heights. We derive a
self-consistent two-mode model which reduces, for large , to a Bogoliubov
model for low barriers and to a Josephson model for any (asymmetric) double
well potential, with explicitly calculated tunneling and pair interaction
parameters. We compare the numerical results to analytical results that
precisely specify the role of number squeezing and finite temperatures in the
loss of coherence
Correlation and Entanglement of Multipartite States
We derive a classification and a measure of classical- and
quantum-correlation of multipartite qubit, qutrit, and in general, -level
systems, in terms of SU representations of density matrices. We compare
the measure for the case of bipartite correlation with concurrence and the
entropy of entanglement. The characterization of correlation is in terms of the
number of nonzero singular values of the correlation matrix, but that of mixed
state entanglement requires additional invariant parameters in the density
matrix. For the bipartite qubit case, the condition for mixed state
entanglement is written explicitly in terms of the invariant paramters in the
density matrix. For identical particle systems we analyze the effects of
exchange symmetry on classical and quantum correlation.Comment: 5 pages, 4 figure
Decoherence of Nitrogen Vacancy Centers in Diamond
We model the decoherence and dephasing of nitrogen vacancy (NV) centers in
diamond due to a noisy paramagnetic bath, with and without the presence of a rf
field that couples levels of the ground electronic state manifold, using a
simple quantum mechanical model that allows for analytical solutions. The model
treats the NV three-level ground state system in the presence of fluctuating
magnetic fields that arise from the environment, and that result in
decoherence, dephasing and dissipation. We show that all 9 eigenmodes of the
three-level system are coupled to each other due to interaction with the
environment, and we discuss consequences for fitting experiments in which
decoherence plays a role.Comment: 13 pages, and 13 figure
Bose-Einstein Condensates in Time-Dependent Light Potentials: Adiabatic and Nonadiabatic Behavior of Nonlinear Wave Equations
The criteria for validity of adiabaticity for nonlinear wave equations are
considered within the context of atomic matter-waves tunneling from
macroscopically populated optical standing-wave traps loaded from a
Bose-Einstein condensate. We show that even when the optical standing wave is
slowly turned on and the condensate behaves adiabatically during this turn-on,
once the tunneling-time between wells in the optical lattice becomes longer
than the nonlinear time-scale, adiabaticity breaks down and a significant
spatially varying phase develops across the condensate wave function from well
to well. This phase drastically affects the contrast of the fringe pattern in
Josephson-effect interference experiments, and the condensate coherence
properties in general.Comment: 5 pages, 3 figure
Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping
An analysis of a single-domain magnetic needle in the presence of an external
magnetic field is carried out with the aim of achieving a high
precision magnetometer. We determine the uncertainty of such a
device due to Gilbert dissipation and the associated internal magnetic field
fluctuations that gives rise to diffusion of the magnetic needle axis direction
and the needle orbital angular momentum. The levitation of the
magnetic needle in a magnetic trap and its stability are also analyzed
Feshbach Resonance in a Tight-Binding Model
The physics of Feshbach resonance is analyzed using an analytic expression
for the -wave scattering phase-shift and the scattering length which we
derive within a two-channel tight-binding model. Employing a unified treatment
of bound states and resonances in terms of the Jost function, it is shown that
for strong inter-channel coupling, Feshbach resonance can occur even when the
closed channel does not have a bound state. This may extend the range of
ultra-cold atomic systems that can be manipulated by Feshbach resonance. The
dependence of the sign of on the coupling strength in the unitary limit is
elucidated. As a by-product, analytic expressions are derived for the
background scattering length, the external magnetic field at which resonance
occurs, and the energy shift , where
is the scattering energy and is the bound state energy in the
closed channel (when there is one).Comment: 5 pages with 1 figures + 6 supplementary material pages with 4
figures. Substantial changes compared with previous versio
Sound waves and modulational instabilities on continuous wave solutions in spinor Bose-Einstein condensates
We analyze sound waves (phonons, Bogoliubov excitations) propagating on
continuous wave (cw) solutions of repulsive spinor Bose-Einstein
condensates (BECs), such as Na (which is antiferromagnetic or polar) and
Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic
field is included. All cw solutions to ferromagnetic BECs with vanishing
particle density and non-zero components in both fields are
subject to modulational instability (MI). MI increases with increasing particle
density. MI also increases with differences in the components' wavenumbers;
this effect is larger at lower densities but becomes insignificant at higher
particle densities. CW solutions to antiferromagnetic (polar) BECS with
vanishing particle density and non-zero components in both
fields do not suffer MI if the wavenumbers of the components are the same. If
there is a wavenumber difference, MI initially increases with increasing
particle density, then peaks before dropping to zero beyond a given particle
density. The cw solutions with particles in both components and
nonvanishing components do not have MI if the wavenumbers of the
components are the same, but do exhibit MI when the wavenumbers are different.
Direct numerical simulations of a cw with weak white noise confirm that weak
noise grows fastest at wavenumbers with the largest MI, and shows some of the
results beyond small amplitude perturbations. Phonon dispersion curves are
computed numerically; we find analytic solutions for the phonon dispersion in a
variety of limiting cases.Comment: 22 pages, 20 figure
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