205 research outputs found
Feedback cooling of atomic motion in cavity QED
We consider the problem of controlling the motion of an atom trapped in an
optical cavity using continuous feedback. In order to realize such a scheme
experimentally, one must be able to perform state estimation of the atomic
motion in real time. While in theory this estimate may be provided by a
stochastic master equation describing the full dynamics of the observed system,
integrating this equation in real time is impractical. Here we derive an
approximate estimation equation for this purpose, and use it as a drive in a
feedback algorithm designed to cool the motion of the atom. We examine the
effectiveness of such a procedure using full simulations of the cavity QED
system, including the quantized motion of the atom in one dimension.Comment: 22 pages, 17 figure
Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging
We show that well-separated quantum superposition states, measurements of
strongly nonlinear observables, and quantum dynamics driven by anomalous
diffusion can all be achieved for single atoms or molecules by imaging
spontaneous photons that they emit via resonance florescence. To generate
anomalous diffusion we introduce continuous measurements driven by L\'evy
processes, and prove a number of results regarding their properties. In
particular we present strong evidence that the only stable L\'evy density that
can realize a strictly continuous measurement is the Gaussian.Comment: revtex4-1, 17 pages, 7 eps figure
Quantum feedback control of atomic motion in an optical cavity
We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies
A simple formula for pooling knowledge about a quantum system
When various observers obtain information in an independent fashion about a
classical system, there is a simple rule which allows them to pool their
knowledge, and this requires only the states-of-knowledge of the respective
observers. Here we derive an equivalent quantum formula. While its realm of
applicability is necessarily more limited, it does apply to a large class of
measurements, and we show explicitly for a single qubit that it satisfies the
intuitive notions of what it means to pool knowledge about a quantum system.
This analysis also provides a physical interpretation for the trace of the
product of two density matrices.Comment: 5 pages, Revtex
The Quantum Emergence of Chaos
The dynamical status of isolated quantum systems, partly due to the linearity
of the Schrodinger equation is unclear: Conventional measures fail to detect
chaos in such systems. However, when quantum systems are subjected to
observation -- as all experimental systems must be -- their dynamics is no
longer linear and, in the appropriate limit(s), the evolution of expectation
values, conditioned on the observations, closely approaches the behavior of
classical trajectories. Here we show, by analyzing a specific example, that
microscopic continuously observed quantum systems, even far from any classical
limit, can have a positive Lyapunov exponent, and thus be truly chaotic.Comment: 4 pages, 4 figure
The approach to typicality in many-body quantum systems
The recent discovery that for large Hilbert spaces, almost all (that is,
typical) Hamiltonians have eigenstates that place small subsystems in thermal
equilibrium, has shed much light on the origins of irreversibility and
thermalization. Here we give numerical evidence that many-body lattice systems
generically approach typicality as the number of subsystems is increased, and
thus provide further support for the eigenstate thermalization hypothesis. Our
results indicate that the deviation of many-body systems from typicality
decreases exponentially with the number of systems. Further, by averaging over
a number of randomly-selected nearest-neighbor interactions, we obtain a
power-law for the atypicality as a function of the Hilbert space dimension,
distinct from the power-law possessed by random Hamiltonians.Comment: 6 pages, 2 png figures, revtex
Rapid state purification protocols for a Cooper pair box
We propose techniques for implementing two different rapid state purification
schemes, within the constraints present in a superconducting charge qubit
system. Both schemes use a continuous measurement of charge (z) measurements,
and seek to minimize the time required to purify the conditional state. Our
methods are designed to make the purification process relatively insensitive to
rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The
first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67,
030301(R) (2003)] uses the measurement results to control bias (z) pulses so as
to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second
proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90
(2006)] uses a simple feedback protocol which tightly rotates the Bloch vector
about an axis almost parallel with the measurement axis. We compare the
performance of these and other techniques by a number of different measures.Comment: 14 pages, 14 figures. v2: Revised version after referee comments.
Accepted for publication by Physical Review
A Straightforward Introduction to Continuous Quantum Measurement
We present a pedagogical treatment of the formalism of continuous quantum
measurement. Our aim is to show the reader how the equations describing such
measurements are derived and manipulated in a direct manner. We also give
elementary background material for those new to measurement theory, and
describe further various aspects of continuous measurements that should be
helpful to those wanting to use such measurements in applications.
Specifically, we use the simple and direct approach of generalized measurements
to derive the stochastic master equation describing the continuous measurements
of observables, give a tutorial on stochastic calculus, treat multiple
observers and inefficient detection, examine a general form of the measurement
master equation, and show how the master equation leads to information gain and
disturbance. To conclude, we give a detailed treatment of imaging the resonance
fluorescence from a single atom as a concrete example of how a continuous
position measurement arises in a physical system.Comment: 24 pages, 3 eps figues. To appear in Contemporary Physic
Feedback cooling of a nanomechanical resonator
Cooled, low-loss nanomechanical resonators offer the prospect of directly
observing the quantum dynamics of mesoscopic systems. However, the present
state of the art requires cooling down to the milliKelvin regime in order to
observe quantum effects. Here we present an active feedback strategy based on
continuous observation of the resonator position for the purpose of obtaining
these low temperatures. In addition, we apply this to an experimentally
realizable configuration, where the position monitoring is carried out by a
single-electron transistor. Our estimates indicate that with current technology
this technique is likely to bring the required low temperatures within reach.Comment: 10 pages, RevTex4, 4 color eps figure
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