19,458 research outputs found
Optimal state estimation for cavity optomechanical systems
We demonstrate optimal state estimation for a cavity optomechanical system
through Kalman filtering. By taking into account nontrivial experimental noise
sources, such as colored laser noise and spurious mechanical modes, we
implement a realistic state-space model. This allows us to obtain the
conditional system state, i.e., conditioned on previous measurements, with
minimal least-square estimation error. We apply this method for estimating the
mechanical state, as well as optomechanical correlations both in the weak and
strong coupling regime. The application of the Kalman filter is an important
next step for achieving real-time optimal (classical and quantum) control of
cavity optomechanical systems.Comment: replaced with published version, 5+12 page
Feedback control of quantum state reduction
Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability
Testing quantum mechanics: a statistical approach
As experiments continue to push the quantum-classical boundary using
increasingly complex dynamical systems, the interpretation of experimental data
becomes more and more challenging: when the observations are noisy, indirect,
and limited, how can we be sure that we are observing quantum behavior? This
tutorial highlights some of the difficulties in such experimental tests of
quantum mechanics, using optomechanics as the central example, and discusses
how the issues can be resolved using techniques from statistics and insights
from quantum information theory.Comment: v1: 2 pages; v2: invited tutorial for Quantum Measurements and
Quantum Metrology, substantial expansion of v1, 19 pages; v3: accepted; v4:
corrected some errors, publishe
Quantum Measurement Theory in Gravitational-Wave Detectors
The fast progress in improving the sensitivity of the gravitational-wave (GW)
detectors, we all have witnessed in the recent years, has propelled the
scientific community to the point, when quantum behaviour of such immense
measurement devices as kilometer-long interferometers starts to matter. The
time, when their sensitivity will be mainly limited by the quantum noise of
light is round the corner, and finding the ways to reduce it will become a
necessity. Therefore, the primary goal we pursued in this review was to
familiarize a broad spectrum of readers with the theory of quantum measurements
in the very form it finds application in the area of gravitational-wave
detection. We focus on how quantum noise arises in gravitational-wave
interferometers and what limitations it imposes on the achievable sensitivity.
We start from the very basic concepts and gradually advance to the general
linear quantum measurement theory and its application to the calculation of
quantum noise in the contemporary and planned interferometric detectors of
gravitational radiation of the first and second generation. Special attention
is paid to the concept of Standard Quantum Limit and the methods of its
surmounting.Comment: 147 pages, 46 figures, 1 table. Published in Living Reviews in
Relativit
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
An important problem in applied science is the continuous nonlinear filtering
problem, i.e., the estimation of a Langevin state that is observed indirectly.
In this paper, it is shown that Euclidean quantum mechanics is closely related
to the continuous nonlinear filtering problem. The key is the configuration
space Feynman path integral representation of the fundamental solution of a
Fokker-Planck type of equation termed the Yau Equation of continuous-continuous
filtering. A corollary is the equivalence between nonlinear filtering problem
and a time-varying Schr\"odinger equation.Comment: 19 pages, LaTeX, interdisciplinar
A discrete invitation to quantum filtering and feedback control
The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph
- …