5,060 research outputs found
Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems
The state matrix for an open quantum system with Markovian evolution
obeys a master equation. The master equation evolution can be unraveled into
stochastic nonlinear trajectories for a pure state , such that on average
reproduces . Here we give for the first time a complete
parameterization of all diffusive unravelings (in which evolves
continuously but non-differentiably in time). We give an explicit measurement
theory interpretation for these quantum trajectories, in terms of monitoring
the system's environment. We also introduce new classes of diffusive
unravelings that are invariant under the linear operator transformations under
which the master equation is invariant. We illustrate these invariant
unravelings by numerical simulations. Finally, we discuss generalized gauge
transformations as a method of connecting apparently disparate descriptions of
the same trajectories by stochastic Schr\"odinger equations, and their
invariance properties.Comment: 10 pages, including 5 figures, submitted to J. Chem Phys special
issue on open quantum system
Reducing the linewidth of an atom laser by feedback
A continuous atom laser will almost certainly have a linewidth dominated by
the effect of the atomic interaction energy, which turns fluctuations in the
condensate atom number into fluctuations in the condensate frequency. These
correlated fluctuations mean that information about the atom number could be
used to reduce the frequency fluctuations, by controlling a spatially uniform
potential. We show that feedback based on a physically reasonable quantum
non-demolition measurement of the atom number of the condensate in situ can
reduce the linewidth enormously.Comment: 5 pages, 1 figur
Effects of twin-beam squashed light on a three-level atom
An electro-optical feedback loop can make in-loop light (squashed light)
which produces a photocurrent with noise below the standard quantum limit (such
as squeezed light). We investigate the effect of squashed light interacting
with a three-level atom in the cascade configuration and compare it to the
effects produced by squeezed light and classical noise. It turns out that one
master equation can be formulated for all three types of light and that this
unified formalism can also be applied to the evolution of a two-level atom. We
show that squashed light does not mimic all aspects of squeezed light, and in
particular, it does not produce the characteristic linear intensity dependence
of the population of the upper-most level of the cascade three-level atom.
Nevertheless, it has nonclassical transient effects in the de-excitation.Comment: 12 pages, 6 figure
The pointer basis and the feedback stabilization of quantum systems
The dynamics for an open quantum system can be `unravelled' in infinitely
many ways, depending on how the environment is monitored, yielding different
sorts of conditioned states, evolving stochastically. In the case of ideal
monitoring these states are pure, and the set of states for a given monitoring
forms a basis (which is overcomplete in general) for the system. It has been
argued elsewhere [D. Atkins et al., Europhys. Lett. 69, 163 (2005)] that the
`pointer basis' as introduced by Zurek and Paz [Phys. Rev. Lett 70,
1187(1993)], should be identified with the unravelling-induced basis which
decoheres most slowly. Here we show the applicability of this concept of
pointer basis to the problem of state stabilization for quantum systems. In
particular we prove that for linear Gaussian quantum systems, if the feedback
control is assumed to be strong compared to the decoherence of the pointer
basis, then the system can be stabilized in one of the pointer basis states
with a fidelity close to one (the infidelity varies inversely with the control
strength). Moreover, if the aim of the feedback is to maximize the fidelity of
the unconditioned system state with a pure state that is one of its conditioned
states, then the optimal unravelling for stabilizing the system in this way is
that which induces the pointer basis for the conditioned states. We illustrate
these results with a model system: quantum Brownian motion. We show that even
if the feedback control strength is comparable to the decoherence, the optimal
unravelling still induces a basis very close to the pointer basis. However if
the feedback control is weak compared to the decoherence, this is not the case
Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States
As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state
of an optical or atom laser far above threshold is a mixture of coherent field
states with random phase, or, equivalently, a Poissonian mixture of number
states. We are interested in which, if either, of these descriptions of
, is more natural. In the preceding paper we concentrated upon
whether descriptions such as these are physically realizable (PR). In this
paper we investigate another relevant aspect of these ensembles, their
robustness. A robust ensemble is one for which the pure states that comprise it
survive relatively unchanged for a long time under the system evolution. We
determine numerically the most robust ensembles as a function of the parameters
in the laser model: the self-energy of the bosons in the laser mode, and
the excess phase noise . We find that these most robust ensembles are PR
ensembles, or similar to PR ensembles, for all values of these parameters. In
the ideal laser limit (), the most robust states are coherent
states. As the phase noise or phase dispersion is increased, the
most robust states become increasingly amplitude-squeezed. We find scaling laws
for these states. As the phase diffusion or dispersion becomes so large that
the laser output is no longer quantum coherent, the most robust states become
so squeezed that they cease to have a well-defined coherent amplitude. That is,
the quantum coherence of the laser output is manifest in the most robust PR
states having a well-defined coherent amplitude. This lends support to the idea
that robust PR ensembles are the most natural description of the state of the
laser mode. It also has interesting implications for atom lasers in particular,
for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as
Part II of a two-part paper. The original version of quant-ph/9906125 is
shortly to be replaced by a new version which is Part I of the two-part
paper. This paper (Part II) also contains some material from the original
version of quant-ph/990612
Measuring measurement--disturbance relationships with weak values
Using formal definitions for measurement precision {\epsilon} and disturbance
(measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has
shown that Heisenberg's claimed relation between these quantities is false in
general. Here we show that the quantities introduced by Ozawa can be determined
experimentally, using no prior knowledge of the measurement under investigation
--- both quantities correspond to the root-mean-squared difference given by a
weak-valued probability distribution. We propose a simple three-qubit
experiment which would illustrate the failure of Heisenberg's
measurement--disturbance relation, and the validity of an alternative relation
proposed by Ozawa
Adiabatic Elimination in Compound Quantum Systems with Feedback
Feedback in compound quantum systems is effected by using the output from one
sub-system (``the system'') to control the evolution of a second sub-system
(``the ancilla'') which is reversibly coupled to the system. In the limit where
the ancilla responds to fluctuations on a much shorter time scale than does the
system, we show that it can be adiabatically eliminated, yielding a master
equation for the system alone. This is very significant as it decreases the
necessary basis size for numerical simulation and allows the effect of the
ancilla to be understood more easily. We consider two types of ancilla: a
two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g.
an optical mode). For each, we consider two forms of feedback: coherent (for
which a quantum mechanical description of the feedback loop is required) and
incoherent (for which a classical description is sufficient). We test the
master equations we obtain using numerical simulation of the full dynamics of
the compound system. For the system (a parametric oscillator) and feedback
(intensity-dependent detuning) we choose, good agreement is found in the limit
of heavy damping of the ancilla. We discuss the relation of our work to
previous work on feedback in compound quantum systems, and also to previous
work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment
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