Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields

In the previous paper [M. Tsang, Phys. Rev. A 81, 063837 (2010), e-print arXiv:1003.0116], I proposed a quantum model of a cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable novel quantum operations on the two modes, including laser cooling of the microwave mode, electro-optic entanglement, and backaction-evading optical measurement of a microwave quadrature. In this sequel, I focus on the quantum input-output relations between traveling optical and microwave fields coupled to a cavity electro-optic modulator. With red-sideband optical pumping, the relations are shown to resemble those of a beam splitter for the traveling fields, so that in the ideal case of zero parasitic loss and critical coupling, microwave photons can be coherently up-converted to "flying" optical photons with unit efficiency, and vice versa. With blue-sideband pumping, the modulator acts as a nondegenerate parametric amplifier, which can generate two-mode squeezing and hybrid entangled photon pairs at optical and microwave frequencies. These fundamental operations provide a potential bridge between circuit quantum electrodynamics and quantum optics.Comment: 12 pages, 10 figures, v2: updated and submitte

Multifractality and scale invariance in human heartbeat dynamics

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be manifested as a dependence on scale or beat number of the probability density functions (PDFs) of the heart rate increments. On the other hand, scale invariance has been recently reported in a detrended analysis of healthy heart rate increments [Kiyono et al., Phys. Rev. Lett. {\bf 93}, 178103 (2004)]. In this paper, we resolve this paradox by clarifying that the scale invariance reported is actually exhibited by the PDFs of the sum of detrended healthy heartbeat intervals taken over different number of beats, and demonstrating that the PDFs of detrended healthy heart rate increments are scale dependent. Our work also establishes that this scale invariance is a general feature of human heartbeat dynamics, which is shared by heart rate fluctuations in both healthy and pathological states

Resonant Shattering of Neutron Star Crusts

The resonant excitation of neutron star (NS) modes by tides is investigated as a source of short gamma-ray burst (sGRB) precursors. We find that the driving of a crust-core interface mode can lead to shattering of the NS crust, liberating ~10^46-10^47 erg of energy seconds before the merger of a NS-NS or NS-black hole binary. Such properties are consistent with Swift/BAT detections of sGRB precursors, and we use the timing of the observed precursors to place weak constraints on the crust equation of state. We describe how a larger sample of precursor detections could be used alongside coincident gravitational wave detections of the inspiral by Advanced LIGO class detectors to probe the NS structure. These two types of observations nicely complement one another, since the former constrains the equation of state and structure near the crust-core boundary, while the latter is more sensitive to the core equation of state.Comment: 5 pages, 2 figures. Accepted to PR

Ziv-Zakai Error Bounds for Quantum Parameter Estimation

I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that scales with the average energy and a limit similar to the quantum Cram\'er-Rao bound that scales with the energy variance. These results are further illustrated by applying the bound to a few examples of optical phase estimation, which show that a quantum Ziv-Zakai bound can be much higher and thus tighter than a quantum Cram\'er-Rao bound for states with highly non-Gaussian photon-number statistics in certain regimes and also stay close to the latter where the latter is expected to be tight.Comment: v1: preliminary result, 3 pages; v2: major update, 4 pages + supplementary calculations, v3: another major update, added proof of "Heisenberg" limit, v4: accepted by PR

On the Relationship between Resolution Enhancement and Multiphoton Absorption Rate in Quantum Lithography

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a ``NOON'' quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated, in order to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.Comment: 14 pages, 7 figures, submitted, v2: rewritten in response to referees' comments, v3: rewritten and extended, v4: accepted by Physical Review

Proximity Effects in Radiative Transfer

Though the dependence of near-field radiative transfer on the gap between two planar objects is well understood, that between curved objects is still unclear. We show, based on the analysis of the surface polariton mediated radiative transfer between two spheres of equal radii $R$ and minimum gap $d$, that the near--field radiative transfer scales as $R/d$ as $d/R \rightarrow 0$ and as $\ln(R/d)$ for larger values of $d/R$ up to the far--field limit. We propose a modified form of the proximity approximation to predict near--field radiative transfer between curved objects from simulations of radiative transfer between planar surfaces.Comment: 5 journal pages, 4 figure

Quantum temporal correlations and entanglement via adiabatic control of vector solitons

It is shown that optical pulses with a mean position accuracy beyond the standard quantum limit can be produced by adiabatically expanding an optical vector soliton followed by classical dispersion management. The proposed scheme is also capable of entangling positions of optical pulses and can potentially be used for general continuous-variable quantum information processing.Comment: 5 pages, 1 figure, v2: accepted by Physical Review Letters, v3: minor editing and shortening, v4: included the submitted erratu

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media

We derive exact strong-contrast expansions for the effective dielectric tensor \epeff of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for \epeff to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing $n$-point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the {\it coarseness} of the composite, i.e., local volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure

The Discovery of an X-ray/UV Stellar Flare from the Late-K/Early-M Dwarf LMC 335

We report the discovery of an X-ray/UV stellar flare from the source LMC 335, captured by XMM-Newton in the field of the Large Magellanic Cloud. The flare event was recorded continuously in X-ray for its first 10 hours from the precursor to the late decay phases. The observed fluxes increased by more than two orders of magnitude at its peak in X-ray and at least one in the UV as compared to quiescence. The peak 0.1-7.0 keV X-ray flux is derived from the two-temperature APEC model to be ~(8.4 +/- 0.6) x 10^-12 erg cm-2 s-1. Combining astrometric information from multiple X-ray observations in the quiescent and flare states, we identify the NIR counterpart of LMC 335 as the 2MASS source J05414534-6921512. The NIR color relations and spectroscopic parallax characterize the source as a Galactic K7-M4 dwarf at a foreground distance of (100 - 264) pc, implying a total energy output of the entire event of ~(0.4 - 2.9) x 10^35 erg. This report comprises detailed analyses of this late-K / early-M dwarf flare event that has the longest time coverage yet reported in the literature. The flare decay can be modeled with two exponential components with timescales of ~28 min and ~4 hours, with a single component decay firmly ruled out. The X-ray spectra during flare can be described by two components, a dominant high temperature component of ~40-60MK and a low temperature component of ~10MK, with a flare loop length of about 1.1-1.3 stellar radius.Comment: 35 pages, 6 figures, 5 tables, accepted for publication in Ap