Two-dimensional exciton-polariton interactions beyond the Born approximation

We provide a many-body theory for the interactions of two-dimensional excitons and polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the two-body interaction strength in two-dimensions has an inverse logarithmic dependence on the scattering length and ground state energy. This leads to a vanishing exciton interaction strength in the zero-momentum limit but a finite polariton interaction strength due to strong light-matter coupling. We also derive the exact Tan relations for exciton-polaritons and calculate Tan's contact coefficient. We show the polariton interaction strength and Tan's contact both exhibit an anomalous enhancement at red photon-exciton detuning when the scattering length is large. Our predictions may provide a qualitatively correct guide for studies of exciton and polariton nonlinearities, and suggest a route to achieving strongly nonlinear polariton gases.Comment: 6 pages, 3 figures + 8 pages of Supplemental Material; many-body calculations (Bogoliubov theory) using a bosonic model Hamiltonia

A Compact Orbital Angular Momentum Spectrometer Using Quantum Zeno Interrogation

We present a scheme to measure the orbital angular momentum spectrum of light using a precisely timed optical loop and quantum non-demolition measurements. We also discuss the influence of imperfect optical components.Comment: 8 pages, 6 figure

Beyond Gaussian Approximation: Bootstrap for Maxima of Sums of Independent Random Vectors

The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous inference in some general settings when $n \gg (\log p)^7$, where $p$ is the multiplicity of the inference problem and $n$ is the sample size. The thrust of this theory is the validity of the Gaussian approximation for maxima of sums of independent random vectors in high-dimension. In this paper, we reduce the sample size requirement to $n \gg (\log p)^5$ for the consistency of the empirical bootstrap and the multiplier/wild bootstrap in the Kolmogorov-Smirnov distance, possibly in the regime where the Gaussian approximation is not available. New comparison and anti-concentration theorems, which are of considerable interest in and of themselves, are developed as existing ones interweaved with Gaussian approximation are no longer applicable

Theory of Ideal Four-Wave Mixing in Bose-Einstein Condensates

Starting from a second-quantized Hamiltonian of many-particle systems, we derive the Gross-Pitaevskii (GP) equation in momentum space, which is suitable for studying the multi-wave mixing processes of coherent matter waves. The coupling equations are then applied to study ideal four-wave mixing (4WM), in which only four waves with definite wavevectors are involved. Some interesting problems of 4WM, such as the phase-matching condition, the collapse and revival behaviour, the effects of relative phase difference, and the conversion efficiency are discussed in detail. We also show that the main characters of recent 4WM experiment [Deng et al, Nature 398, 218 (1999)] can be undersood in the present simplified model.Comment: 5 Pages and 4 EPS figure

What is the best planar cavity for maximizing coherent exciton-photon coupling

We compare alternative planar cavity structures for strong exciton$-$photon coupling, where the conventional distributed Bragg reflector (DBR) and three unconventional types of cavity mirrors$-$ air/GaAs DBR, Tamm $-$ plasmon mirror and sub$-$wavelength grating mirror. We design and optimize the planar cavities built with each type of mirror at one side or both sides for maximum vacuum field strength. We discuss the trade$-$off between performance and fabrication difficulty for each cavity structure. We show that cavities with sub$-$wavelength grating mirrors allow simultaneously strongest field and high cavity quality. The optimization principles and techniques developed in this work will guide the cavity design for research and applications of matter$-$light coupled semiconductors, especially new material systems that require greater flexibility in the choice of cavity materials and cavity fabrication procedures

On Midrange Periodicities in Solar Radio Flux and Sunspot Areas

Using the Hilbert-Huang transform technique, we investigate the midrange periodicities in solar radio flux at 2800 MHz (F10.7) and sunspot areas (SAs) from February 1, 1947 to September 30, 2016. The following prominent results are found: (1) The quasi-periodic oscillations of both data sets are not identical, such as the rotational cycle, the midrange periodicities, and the Schwabe cycle. In particular, the midrange periodicities ranging from 37.9 days to 297.3 days are related to the magnetic Rossby-type waves; 2) The 1.3-year and 1.7-year fluctuations in solar activity indicators are surface manifestations (from photosphere to corona) of magnetic flux changes generated deep inside the Sun; 3) At the timescale of the Schwabe cycle, \textbf{the complicated phase relationships} in the three intervals (1947-1958, 1959-1988, and 1989-2016) agree with the produced periodicities of the magnetic Rossby-type waves. \textbf{The findings indicate that the magnetic Rossby-type waves are the possible physical mechanism behind the midrange periodicities of solar activity indicators. Moreover, the significant change in the relationship between photospheric and coronal activity took place after the maximum of solar cycle 22 could be interpreted by the magnetic Rossby-type waves

Spectrum and electromagnetic transitions of bottomonium

Stimulated by the exciting progress in the observation of new bottomonium states, we study the bottomonium spectrum. To calculate the mass spectrum, we adopt a nonrelativistic screened potential model. The radial Schr\"{o}dinger equation is solved with the three-point difference central method, where the spin-dependent potentials are dealt with non-perturbatively. With this treatment, the corrections of the spin-dependent potentials to the wave functions can be included successfully. Furthermore, we calculate the electromagnetic transitions of the $nS$ ($n\leq 4$), $nP$ ($n\leq 3$), and $nD$ ($n\leq 2$) bottomonium states with a nonrelativistic electromagnetic transition operator widely applied to meson photoproduction reactions. Our predicted masses, hyperfine and fine splittings, electromagnetic transition widths and branching ratios of the bottomonium states are in good agreement with the available experimental data. Especially, the EM transitions of $\Upsilon(3S)\to \chi_{b1,2}(1P)\gamma$, which were not well understood in previous studies, can be reasonably explained by considering the corrections of the spin-dependent interactions to the wave functions. We also discuss the observations of the missing bottomonium states by using radiative transitions. Some important radiative decay chains involving the missing bottomonium states are suggested to be observed. We hope our study can provide some useful references to observe and measure the properties of bottomonium mesons in forthcoming experiments.Comment: 14 pages, 1 figure, revised version. To appear in PR

A Subpixel Registration Algorithm for Low PSNR Images

This paper presents a fast algorithm for obtaining high-accuracy subpixel translation of low PSNR images. Instead of locating the maximum point on the upsampled images or fitting the peak of correlation surface, the proposed algorithm is based on the measurement of centroid on the cross correlation surface by Modified Moment method. Synthetic images, real solar images and standard testing images with white Gaussian noise added were tested, and the results show that the accuracies of our algorithm are comparable with other subpixel registration techniques and the processing speed is higher. The drawback is also discussed at the end of this paper.Comment: in 2012 IEEE 5th Int. Conf. on Advanced Computational Intelligence (ICACI) (New York: IEEE), 62

Improving Anti-Eavesdropping Ability without Eavesdropper's CSI: A Practical Secure Transmission Design Perspective

This letter studies the practical design of secure transmissions without knowing eavesdropper's channel state information (ECSI). An ECSI-irrelevant metric is introduced to quantize the intrinsic anti-eavesdropping ability (AEA) that the transmitter has on confronting the eavesdropper via secrecy encoding together with artificial-noise-aided signaling. Non-adaptive and adaptive transmission schemes are proposed to maximize the AEA with the optimal encoding rates and power allocation presented in closed-form expressions. Analyses and numerical results show that maximizing the AEA is equivalent to minimizing the secrecy outage probability (SOP) for the worst case by ignoring eavesdropper's receiver noise. Therefore, the AEA is a useful alternative to the SOP for assessing and designing secure transmissions when the ECSI cannot be prior known.Comment: 4 pages, 2 figures, to be published on IEEE Wireless Communications Letters (WCL

High Fidelity Detection of the Orbital Angular Momentum of Light by Time Mapping

We demonstrate high-fidelity detection of the orbital angular momentum (OAM) of light using a compact and practical OAM spectrometer that maps the OAM spectrum to time. The spectrometer consists of a single optical delay loop to achieve timing mapping, a vortex phase plate that iteratively decreases the OAM value, and a single mode fibre to distinguish zero from non-zero OAM states. Light with arbitrarily OAM compositions can be measured. For light with OAM up to 4hbar, we measured an average crosstalk of -21.3 dB, which is mainly limited by the purity of the input states and optical alignment.Comment: 14 pages, 5 figure