419 research outputs found
Collective processes of an ensemble of spin-1/2 particles
When the dynamics of a spin ensemble are expressible solely in terms of
symmetric processes and collective spin operators, the symmetric collective
states of the ensemble are preserved. These many-body states, which are
invariant under particle relabeling, can be efficiently simulated since they
span a subspace whose dimension is linear in the number of spins. However, many
open system dynamics break this symmetry, most notably when ensemble members
undergo identical, but local, decoherence. In this paper, we extend the
definition of symmetric collective states of an ensemble of spin-1/2 particles
in order to efficiently describe these more general collective processes. The
corresponding collective states span a subspace which grows quadratically with
the number of spins. We also derive explicit formulae for expressing arbitrary
identical, local decoherence in terms of these states.Comment: 12 pages, see 0805.2910 for simulations using these method
Efficient feedback controllers for continuous-time quantum error correction
We present an efficient approach to continuous-time quantum error correction
that extends the low-dimensional quantum filtering methodology developed by van
Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery
operations in the form of real-time quantum feedback. We expect this paradigm
to be useful for systems in which error recovery operations cannot be applied
instantaneously. While we could not find an exact low-dimensional filter that
combined both continuous syndrome measurement and a feedback Hamiltonian
appropriate for error recovery, we developed an approximate reduced-dimensional
model to do so. Simulations of the five-qubit code subjected to the symmetric
depolarizing channel suggests that error correction based on our approximate
filter performs essentially identically to correction based on an exact quantum
dynamical model
Tensor polarizability and dispersive quantum measurement of multilevel atoms
Optimally extracting information from measurements performed on a physical
system requires an accurate model of the measurement interaction. Continuously
probing the collective spin of an Alkali atom cloud via its interaction with an
off-resonant optical probe is an important example of such a measurement where
realistic modeling at the quantum level is possible using standard techniques
from atomic physics. Typically, however, tutorial descriptions of this
technique have neglected the multilevel structure of realistic atoms for the
sake of simplification. In this paper we account for the full multilevel
structure of Alkali atoms and derive the irreducible form of the polarizability
Hamiltonian describing a typical dispersive quantum measurement. For a specific
set of parameters, we then show that semiclassical predictions of the theory
are consistent with our experimental observations of polarization scattering by
a polarized cloud of laser-cooled Cesium atoms. We also derive the
signal-to-noise ratio under a single measurement trial and use this to predict
the rate of spin-squeezing with multilevel Alkali atoms for arbitrary detuning
of the probe beam.Comment: Significant corrections to theory and data. Full quality figures and
other information available from http://minty.caltech.edu/papers.ph
Single shot parameter estimation via continuous quantum measurement
We present filtering equations for single shot parameter estimation using
continuous quantum measurement. By embedding parameter estimation in the
standard quantum filtering formalism, we derive the optimal Bayesian filter for
cases when the parameter takes on a finite range of values. Leveraging recent
convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition
which determines the asymptotic convergence of the estimator. For cases when
the parameter is continuous valued, we develop quantum particle filters as a
practical computational method for quantum parameter estimation.Comment: 9 pages, 5 image
An Inverse-Problem Approach to Designing Photonic Crystals for Cavity QED Experiments
Photonic band gap (PBG) materials are attractive for cavity QED experiments
because they provide extremely small mode volumes and are monolithic,
integratable structures. As such, PBG cavities are a promising alternative to
Fabry-Perot resonators. However, the cavity requirements imposed by QED
experiments, such as the need for high Q (low cavity damping) and small mode
volumes, present significant design challenges for photonic band gap materials.
Here, we pose the PBG design problem as a mathematical inversion and provide an
analytical solution for a two-dimensional crystal. We then address a planar (2D
crystal with finite thickness) structure using numerical techniques.Comment: 12 pages, 8 figures, preprint available from
http://minty.caltech.edu/MabuchiLa
Ditopic Receptors Based on Dihomooxacalix[4]arenes Bearing Phenylurea Moieties With Electron-Withdrawing Groups for Anions and Organic Ion Pairs
Two bidentate dihomooxacalix[4]arene receptors bearing phenylurea moieties substituted with electron-withdrawing groups at the lower rim via a butyl spacer (CF3-Phurea 5b and NO2 Phurea 5c) were obtained in the cone conformation in solution, as shown by NMR. The X-ray crystal structure of 5b is reported. The binding affinity of these receptors toward several relevant anions was investigated by 1H NMR, UV-Vis absorption in different solvents, and fluorescence titrations. Compounds 5b and 5c were also tested as ditopic receptors for organic ion pairs, namely monoamine neurotransmitters and trace amine hydrochlorides by 1H NMR studies. The data showed that both receptors follow the same trend and, in comparison with the unsubstituted phenylurea 5a, they exhibit a significant enhancement on their host-guest properties, owing to the increased acidity of their urea NH protons. NO2-Phurea 5c is the best anion receptor, displaying the strongest complexation for F 12, closely followed by the oxoanions BzO 12, AcO 12, and HSO4-. Concerning ion pair recognition, both ditopic receptors presented an outstanding efficiency for the amine hydrochlorides, mainly 5c, with association constants higher than 109 M 122 in the case of phenylethylamine and tyramine
Magnetometry via a double-pass continuous quantum measurement of atomic spin
We argue that it is possible in principle to reduce the uncertainty of an
atomic magnetometer by double-passing a far-detuned laser field through the
atomic sample as it undergoes Larmor precession. Numerical simulations of the
quantum Fisher information suggest that, despite the lack of explicit
multi-body coupling terms in the system's magnetic Hamiltonian, the parameter
estimation uncertainty in such a physical setup scales better than the
conventional Heisenberg uncertainty limit over a specified but arbitrary range
of particle number N. Using the methods of quantum stochastic calculus and
filtering theory, we demonstrate numerically an explicit parameter estimator
(called a quantum particle filter) whose observed scaling follows that of our
calculated quantum Fisher information. Moreover, the quantum particle filter
quantitatively surpasses the uncertainty limit calculated from the quantum
Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only
single-body operators. We also show that a quantum Kalman filter is
insufficient to obtain super-Heisenberg scaling, and present evidence that such
scaling necessitates going beyond the manifold of Gaussian atomic states.Comment: 17 pages, updated to match print versio
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