Avi Pe'er
A Comment on the Letter by G. Scarcelli, V. Berardi and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
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In a recent Phys. Rev. E Rapid Communication, the authors, Silvestrov and Beenakker, introduce a way to lengthen the Ehrenfest time, $τ$, for fully chaotic systems. We disagree with several statements made in their paper, and address the following points essential to their conclusions: 1) it is not true that all semiclassical approximations for chaotic systems fail at a so-called `logtime', $τ\propto - \ln (\hbar)$, differing only by a numerical coefficient; and 2) the limitation of the semiclassical approximation as expressed in the authors' Eq. (8) is not limited by their argument leading to…
In arXiv:1707.02197, the authors considered the Sachdev-Ye-Kitaev model with quadratic perturbation (also known as mass-deformed SYK), and claimed that the quantum Lyapunov exponent would vanish in the regime of low temperature and small quartic coupling. We calculate the exponent exactly in that regime and show that it is nonzero.
The three-wave mixing processes in a second-order nonlinear medium can be used for imaging protocols, in which an object field is injected into the nonlinear medium together with a reference field and an image field is generated. When the reference field is chaotic, the image field is also chaotic and does not carry any information about the object. We show that a clear image of the object be extracted from the chaotic image field by measuring the spatial intensity correlations between this field and one Fourier component of the reference. We experimentally verify this imaging protocol in the …
We present a novel experimental technique that can differentiate unequivocally between chaotic light and coherent light with amplitude fluctuations, and thus permits to characterize unambiguously the output of a laser. This technique consists of measuring the second-order intensity cross-correlation at the outputs of an unbalanced Michelson interferometer. It is applied to a chaotic light source and to the output of a semiconductor nanolaser whose "standard" intensity correlation function above-threshold displays values compatible with a mixture of coherent and chaotic light. Our experimental …
We analyze and realize the recovery, by means of spatial intensity correlations, of the image obtained by a seeded frequency downconversion process in which the seed field is chaotic and an intensity modulation is encoded on the pump field. Although the generated field is as chaotic as the seed field and does not carry any information about the modulation of the pump, an image of the pump can be extracted by measuring the spatial intensity correlations between the generated field and one Fourier component of the seed.
In a recent Letter [PRL 101, 074101 (2008)], Kapulkin and Pattanayak presented evidence that a quantum Duffing oscillator, sufficiently damped so that it is not classically chaotic, becomes chaotic in the transition region between quantum and classical motion. If true, this would be a striking result. However, Kapulkin and Pattanayak did not calculate the Lyapunov exponent for the system, usually regarded as the litmus-test of chaos. Here we perform this calculation, which throws considerable doubt upon their conclusions.
The claim that Kuwahara et al. [1] have reported the observation of a Hanbury Brown-Twiss electron antibunching dip (their Fig. 3) could possibly be explained as an electron source emission rate dependency on the light polarization. Strain on their GaAs/GaAsP sample is uniaxial, and one would expect a linear dichroism in the photoemission possibly as large as 15% [7] - much larger than the 0.1% reported effect. The same concern exist for circular polarized light.
This is a 1-page comment on a wrong paper that recently appeared in PRL (Phys. Rev. Lett. 86 (23), 5393 (2001), also quant-ph/0101004). The authors claim to have shown that using a quantum computer gives an "exponential advantage" for simulating and studying classical chaotic systems.
In a recent Letter (Phys. Rev. Lett. \textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations.
Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the chaotic sea to attenuate the destructive interference generating dynamical localization. This phenomenon is related to the nature of complex orbits describing tunneling between torus and chaotic regions. The tunneling rate is found to obey a perturbative scaling with noise intensity when the noise intensity is sufficiently small and then saturate in a large noise…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system and the decay rate of the resonance state. We numerically support the conjecture by studying the phase-space Husimi function and the position representation of resonance states of the chaotic standard map, the baker map, and a random matrix model, each with partial escape.
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix…
We study the effects of a collective flow and multiple scattering on two-particle correlation measurements in Hanbury-Brown-Twiss intensity interferometry. We find that under a collective flow the effective source distribution in a two-particle correlation measurement depends on the initial source distribution. In addition, it depends on a collective flow phase function which consists of terms that tend to cancel each other. As the detected particles traverse from the source point to the freeze-out point, they are subject to multiple scattering with medium particles. We examine the effects of …
In a setup illuminated by chaotic light, we consider different schemes that enable to perform imaging by measuring second-order intensity correlations. The most relevant feature of the proposed protocols is the ability to perform plenoptic imaging, namely to reconstruct the geometrical path of light propagating in the system, by imaging both the object and the focusing element. This property allows to encode, in a single data acquisition, both multi-perspective images of the scene and light distribution in different planes between the scene and the focusing element. We unveil the plenoptic pro…
Robustness of chaotic-light correlation imaging against turbulence
该研究提出可同时实现关联成像与一阶强度成像的方案，对比发现强湍流下关联成像更具优势，且湍流主导图像分辨率时该优势更突出。
Correlation Plenoptic Imaging (CPI) is a novel imaging technique, that exploits the correlations between the intensity fluctuations of light to perform the typical tasks of plenoptic imaging (namely, refocusing out-of-focus parts of the scene, extending the depth of field, and performing 3D reconstruction), without entailing a loss of spatial resolution. Here, we consider two different CPI schemes based on chaotic light, both employing ghost imaging: the first one to image the object, the second one to image the focusing element. We characterize their noise properties in terms of the signal-to…
Analytical determination of multi-time correlation functions in quantum chaotic systems
本文从随机矩阵理论出发，解析推导了量子混沌系统中多点关联函数（含OTOC）的时间依赖，发现其与粗粒化波函数的傅里叶变换相关，并通过自旋链数值实验验证，探讨了对马尔可夫性和量子回归的启示。
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed for Bell correlations based on non-commutative operations involving polarizers. As in the entanglement model, the Bell correlation is obtained from a probability calculus without explicit use of deterministic hidden variables. The probability calculus used is associated with chaotic light. Joint wave intensity correlations at spatially separated polarization…
By using the nonuniform discrete Fourier transform on the center positions of the symmetric intensity distribution of the output beam, we recover the vibration information of two mirrors, which is lost in the analysis of Danan \emph{et al.} in the work [Phys. Rev. Lett. \textbf{111}, 240402 (2013), arXiv:1304.7469]. We believe a photon always follows continuous trajectories, and a photon has to enter an interferometer at first and then leave it, if this photon has ever been inside the interferometer.
Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bun…
We compare the field-field g(1)(τ), intensity-field g(3/2)(τ), and intensity-intensity g(2)(τ) correlation functions for models that are of relevance in astrophysics. We obtain expressions for the general case of a chaotic radiation, where the amplitude is Rician based on a model with an ensemble of harmonic oscillators in Brownian motion. We obtain the signal to noise ratios for two methods of measurement. The intensity-field correlation function signal to noise ratio scales with the first power of |g(1)(τ)|. This is in contrast with the well-established result of g(2)(τ) which goes as the sq…
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