499 research outputs found
Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback
We apply quantum filtering and control to a particle in a harmonic trap under
continuous position measurement, and show that a simple static feedback law can
be used to cool the system. The final steady state is Gaussian and dependent on
the feedback strength and coupling between the system and probe. In the limit
of weak coupling this final state becomes the ground state. An earlier model by
Haine et. al. (PRA 69, 2004) without measurement back-action showed dark
states: states that did not display error signals, thus remaining unaffected by
the control. This paper shows that for a realistic measurement process this is
not true, which indicates that a Bose-Einstein condensate may be driven towards
the ground state from any arbitrary initial state.Comment: 1 Tex, 4 PS pictures, 1 bbl fil
Stability, Gain, and Robustness in Quantum Feedback Networks
This paper concerns the problem of stability for quantum feedback networks.
We demonstrate in the context of quantum optics how stability of quantum
feedback networks can be guaranteed using only simple gain inequalities for
network components and algebraic relationships determined by the network.
Quantum feedback networks are shown to be stable if the loop gain is less than
one-this is an extension of the famous small gain theorem of classical control
theory. We illustrate the simplicity and power of the small gain approach with
applications to important problems of robust stability and robust
stabilization.Comment: 16 page
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom
Nonperturbative and perturbative treatments of parametric heating in atom traps
We study the quantum description of parametric heating in harmonic potentials
both nonperturbatively and perturbatively, having in mind atom traps. The first
approach establishes an explicit connection between classical and quantum
descriptions; it also gives analytic expressions for properties such as the
width of fractional frequency parametric resonances. The second approach gives
an alternative insight into the problem and can be directly extended to take
into account nonlinear effects. This is specially important for shallow traps.Comment: 12 pages, 2 figure
Casimir force acting on magnetodielectric bodies embedded in media
Within the framework of macroscopic quantum electrodynamics, general
expressions for the Casimir force acting on linearly and causally responding
magnetodielectric bodies that can be embedded in another linear and causal
magnetodielectric medium are derived. Consistency with microscopic
harmonic-oscillator models of the matter is shown. The theory is applied to
planar structures and proper generalizations of Casimir's and Lifshitz-type
formulas are given.Comment: 15 pages, 2 figures; minor additions and corrections, to appear in
PR
Quantum projection filter for a highly nonlinear model in cavity QED
Both in classical and quantum stochastic control theory a major role is
played by the filtering equation, which recursively updates the information
state of the system under observation. Unfortunately, the theory is plagued by
infinite-dimensionality of the information state which severely limits its
practical applicability, except in a few select cases (e.g. the linear Gaussian
case.) One solution proposed in classical filtering theory is that of the
projection filter. In this scheme, the filter is constrained to evolve in a
finite-dimensional family of densities through orthogonal projection on the
tangent space with respect to the Fisher metric. Here we apply this approach to
the simple but highly nonlinear quantum model of optical phase bistability of a
stongly coupled two-level atom in an optical cavity. We observe near-optimal
performance of the quantum projection filter, demonstrating the utility of such
an approach.Comment: 19 pages, 6 figures. A version with high quality images can be found
at http://minty.caltech.edu/papers.ph
Dynamical Stability and Quantum Chaos of Ions in a Linear Trap
The realization of a paradigm chaotic system, namely the harmonically driven
oscillator, in the quantum domain using cold trapped ions driven by lasers is
theoretically investigated. The simplest characteristics of regular and chaotic
dynamics are calculated. The possibilities of experimental realization are
discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev
Laser Cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit
We study laser cooling of two ions that are trapped in a harmonic potential
and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is
shown to work analogously to sideband cooling of a single ion. Outside the
Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes
result in a quasi-continuous energy spectrum that significantly alters the
cooling dynamics. The cooling time decreases nonlinearly with the linewidth of
the cooling transition, and the effect of trapping states which may slow down
the cooling is considerably reduced. We show that cooling to the ground state
is possible also outside the Lamb-Dicke regime. We develop the model and use
Quantum Monte Carlo calculations for specific examples. We show that a rate
equation treatment is a good approximation in all cases.Comment: 13 pages, 10 figure
Algorithm for normal random numbers
We propose a simple algorithm for generating normally distributed pseudo
random numbers. The algorithm simulates N molecules that exchange energy among
themselves following a simple stochastic rule. We prove that the system is
ergodic, and that a Maxwell like distribution that may be used as a source of
normally distributed random deviates follows when N tends to infinity. The
algorithm passes various performance tests, including Monte Carlo simulation of
a finite 2D Ising model using Wolff's algorithm. It only requires four simple
lines of computer code, and is approximately ten times faster than the
Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to
Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf
- …