531 research outputs found
An open systems approach to calculating time dependent spectra
A new method to calculate the spectrum using cascaded open systems and master
equations is presented. The method uses two state analyzer atoms which are
coupled to the system of interest, whose spectrum of radiation is read from the
excitation of these analyzer atoms. The ordinary definitions of a spectrum uses
two-time averages and Fourier-transforms. The present method uses only one-time
averages. The method can be used to calculate time dependent as well as
stationary spectra.Comment: 8 pages, revtex, 18 figures, to be published in J.Mod.Op
Weisskopf-Wigner model for wave packet excitation
We consider a laser induced molecular excitation process as a decay of a
single energy state into a continuum. The analytic results based on
Weisskopf-Wigner approach and perturbation calculations are compared with
numerical wave packet results. We find that the decay model describes the
excitation process well within the expected parameter region.Comment: 14 pages, Latex2.09, 9 Postscript figures embedded using psfig, see
also http://www.physics.helsinki.fi/~kasuomin
Coupled eigenmodes in a two-component Bose-Einstein condensate
We have studied the elementary excitations in a two-component Bose-Einstein
condensate. We concentrate on the breathing modes and find the elementary
excitations to possess avoided crossings and regions of coalescing oscillations
where both components of the condensates oscillate with same frequency. For
large repulsive interactions between the condensates, their oscillational modes
tend to decouple due to decreased overlap. A thorough investigation of the
eigenmodes near the avoided crossings is presented.Comment: Replacement, 17 pages, 9 figure
Preservation of Positivity by Dynamical Coarse-Graining
We compare different quantum Master equations for the time evolution of the
reduced density matrix. The widely applied secular approximation (rotating wave
approximation) applied in combination with the Born-Markov approximation
generates a Lindblad type master equation ensuring for completely positive and
stable evolution and is typically well applicable for optical baths. For phonon
baths however, the secular approximation is expected to be invalid. The usual
Markovian master equation does not generally preserve positivity of the density
matrix. As a solution we propose a coarse-graining approach with a dynamically
adapted coarse graining time scale. For some simple examples we demonstrate
that this preserves the accuracy of the integro-differential Born equation. For
large times we analytically show that the secular approximation master equation
is recovered. The method can in principle be extended to systems with a
dynamically changing system Hamiltonian, which is of special interest for
adiabatic quantum computation. We give some numerical examples for the
spin-boson model of cases where a spin system thermalizes rapidly, and other
examples where thermalization is not reached.Comment: 18 pages, 7 figures, reviewers suggestions included and tightened
presentation; accepted for publication in PR
Observing the spin of a free electron
Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions
Open system dynamics with non-Markovian quantum jumps
We discuss in detail how non-Markovian open system dynamics can be described
in terms of quantum jumps [J. Piilo et al., Phys. Rev. Lett. 100, 180402
(2008)]. Our results demonstrate that it is possible to have a jump description
contained in the physical Hilbert space of the reduced system. The developed
non-Markovian quantum jump (NMQJ) approach is a generalization of the Markovian
Monte Carlo Wave Function (MCWF) method into the non-Markovian regime. The
method conserves both the probabilities in the density matrix and the norms of
the state vectors exactly, and sheds new light on non-Markovian dynamics. The
dynamics of the pure state ensemble illustrates how local-in-time master
equation can describe memory effects and how the current state of the system
carries information on its earlier state. Our approach solves the problem of
negative jump probabilities of the Markovian MCWF method in the non-Markovian
regime by defining the corresponding jump process with positive probability.
The results demonstrate that in the theoretical description of non-Markovian
open systems, there occurs quantum jumps which recreate seemingly lost
superpositions due to the memory.Comment: 19 pages, 10 figures. V2: Published version. Discussion section
shortened and some other minor changes according to the referee's suggestion
Systematic Perturbation Theory for Dynamical Coarse-Graining
We demonstrate how the dynamical coarse-graining approach can be
systematically extended to higher orders in the coupling between system and
reservoir. Up to second order in the coupling constant we explicitly show that
dynamical coarse-graining unconditionally preserves positivity of the density
matrix -- even for bath density matrices that are not in equilibrium and also
for time-dependent system Hamiltonians. By construction, the approach correctly
captures the short-time dynamics, i.e., it is suitable to analyze non-Markovian
effects. We compare the dynamics with the exact solution for highly
non-Markovian systems and find a remarkable quality of the coarse-graining
approach. The extension to higher orders is straightforward but rather tedious.
The approach is especially useful for bath correlation functions of simple
structure and for small system dimensions.Comment: 17 pages, 5 figures, version accepted for publication in PR
Sudden death and sudden birth of entanglement in common structured reservoirs
We study the exact entanglement dynamics of two qubits in a common structured
reservoir. We demonstrate that, for certain classes of entangled states,
entanglement sudden death occurs, while for certain initially factorized
states, entanglement sudden birth takes place. The backaction of the
non-Markovian reservoir is responsible for revivals of entanglement after
sudden death has occurred, and also for periods of disentanglement following
entanglement sudden birth.Comment: 4 pages, 2 figure
Validity of adiabaticity in Cavity QED
This paper deals with the concept of adiabaticity for fully quantum
mechanically cavity QED models. The physically interesting cases of Gaussian
and standing wave shapes of the cavity mode are considered. An analytical
approximate measure for adiabaticity is given and compared with numerical wave
packet simulations. Good agreement is obtained where the approximations are
expected to be valid. Usually for cavity QED systems, the large atom-field
detuning case is considered as the adiabatic limit. We, however, show that
adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit.
Effective semiclassical time dependent models, which do not take into account
the shape of the wave packet, are derived. Corrections to such an effective
theory, which are purely quantum mechanical, are discussed. It is shown that
many of the results presented can be applied to time dependent two-level
systems.Comment: 10 pages, 9 figure
Driven harmonic oscillator as a quantum simulator for open systems
We show theoretically how a driven harmonic oscillator can be used as a
quantum simulator for non-Markovian damped harmonic oscillator. In the general
framework, the results demonstrate the possibility to use a closed system as a
simulator for open quantum systems. The quantum simulator is based on sets of
controlled drives of the closed harmonic oscillator with appropriately tailored
electric field pulses. The non-Markovian dynamics of the damped harmonic
oscillator is obtained by using the information about the spectral density of
the open system when averaging over the drives of the closed oscillator. We
consider single trapped ions as a specific physical implementation of the
simulator, and we show how the simulator approach reveals new physical insight
into the open system dynamics, e.g. the characteristic quantum mechanical
non-Markovian oscillatory behavior of the energy of the damped oscillator,
usually obtained by the non-Lindblad-type master equation, can have a simple
semiclassical interpretation.Comment: 10 pages, 4 figures. V2: Minor modifications and added 2 appendixes
for more details about calculation
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