Tomographic reconstruction of quantum states in N spatial dimensions

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the procedure is that the angular frequencies of the N harmonic potentials are incommensurable. We discuss what kind of information can be found if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite time measurements. As a further example of quantum state reconstruction in N dimensions we consider the two related cases of an N-dimensional free particle with periodic boundary conditions and a particle in an N-dimensional box, where we find a similar condition of incommensurability and finite recurrence time for the one-dimensional system.Comment: 8 pages, 1 figur

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures, in direct analogy to the position and momentum correlations originally considered by EPR.Comment: Final published version (corrections in Ref. [32], updated references

Direct probing of the Wigner function by time-multiplexed detection of photon statistics

We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon parity measurements and displacement operations, replacing the conventional homodyne tomography. Our emphasis lies on reconstructing the Wigner function of non-Gaussian Fock states with highly negative values in a scheme that is based on a realistic experimental setup. In order to establish the concept of loss-tolerance for state characterization we show how losses can be decoupled from the impact of other experimental imperfections, i.e. the non-unity transmittance of the displacement beamsplitter and non-ideal mode overlap. We relate the experimentally accessible parameters to effective ones that are needed for an optimised state reconstruction. The feasibility of our approach is tested by Monte Carlo simulations, which provide bounds resulting from statistical errors that are due to limited data sets. Our results clearly show that high losses can be accepted for a defined parameter range, and moreover, that (in contrast to homodyne detection) mode mismatch results in a distinct signature, which can be evaluated by analysing the photon number oscillations of the displaced Fock states.Comment: 22 pages, 13 figures, published versio

Modematching an optical quantum memory

We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.Comment: 17 pages, 4 figures. Brief section added treating the transverse spatial structure of the memory interaction. Some references added. A few typos fixe

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three- wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second- order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singular- value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.Comment: 24 pages, 20 figure

Aircraft control via variable cant-angle winglets

Copyright @ 2008 American Institute of Aeronautics and AstronauticsThis paper investigates a novel method for the control of "morphing" aircraft. The concept consists of a pair of winglets; with adjustable cant angle, independently actuated and mounted at the tips of a baseline flying wing. The general philosophy behind the concept was that for specific flight conditions such as a coordinated turn, the use of two control devices would be sufficient for adequate control. Computations with a vortex lattice model and subsequent wind-tunnel tests demonstrate the viability of the concept, with individual and/or dual winglet deflection producing multi-axis coupled control moments. Comparisons between the experimental and computational results showed reasonable to good agreement, with the major discrepancies thought to be due to wind-tunnel model aeroelastic effects.This work has been supported by a Marie Curie excellence research grant funded by the European Commission

REGULATION OF LIPOLYSIS BY [BETA]-ADRENERGIC ACTIVATION AND EXERCISE IN OBESE AFRICAN-AMERICAN AND CAUCASIAN WOMEN

African-American women (AAW) are twice as likely to be obese as Caucasian women (CW); however, previous in-vitro studies have shown that AAW have higher densities of beta-adrenergic receptors (B-AR) in the subcutaneous (SC) adipose tissue and an increased lipolytic response to B-AR stimulation when compared to CW. There are no in-vivo studies to help resolve this apparent contradiction between in-vitro lipolytic response and the incidence of obesity. The purpose of this study is therefore to determine if AAW, as compared to CW, have a larger lipolytic response to pharmacological (isoproterenol) and physiological (exercise) stimulation. Methods: 33 obese women (16 AAW; 17 CW) participated in the microdialysis (MD) study. MD consisted of two probes placed in SC abdominal adipose tissue and perfused with either isoproterenol (ISO) or a control solution. Dialysate glycerol (index of lipolysis) was measured from probes at rest and, from the control probe, during exercise. Results: Dialysate glycerol increased 384.9% in AAW and 191.2% in CW in response to ISO (p=0.046 AAW vs CW). Dialysate glycerol increased 66 [mu]mol/L in AAW and 84 [mu]mol/L in CW in response to exercise (p=0.94 AAW vs CW). Conclusion: AAW have a higher lipolytic response to pharmacological B-AR stimulation, but have a similar lipolytic response to exercise, as compared to CW. These findings suggest that lipolytic response to B-AR stimulation and exercise are likely not contributing factors to the higher incidence of obesity in AAW as compared to CW.M.S

Reconstruction of photon statistics using low performance photon counters

The output of a photodetector consists of a current pulse whose charge has the statistical distribution of the actual photon numbers convolved with a Bernoulli distribution. Photodetectors are characterized by a nonunit quantum efficiency, i.e. not all the photons lead to a charge, and by a finite resolution, i.e. a different number of detected photons leads to a discriminable values of the charge only up to a maximum value. We present a detailed comparison, based on Monte Carlo simulated experiments and real data, among the performances of detectors with different upper limits of counting capability. In our scheme the inversion of Bernoulli convolution is performed by maximum-likelihood methods assisted by measurements taken at different quantum efficiencies. We show that detectors that are only able to discriminate between zero, one and more than one detected photons are generally enough to provide a reliable reconstruction of the photon statistics for single-peaked distributions, while detectors with higher resolution limits do not lead to further improvements. In addition, we demonstrate that, for semiclassical states, even on/off detectors are enough to provide a good reconstruction. Finally, we show that a reliable reconstruction of multi-peaked distributions requires either higher quantum efficiency or better capability in discriminating high number of detected photons.Comment: 8 pages, 3 figure