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