We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to identify and resolve manifolds in phase space that contribute to the form factor. They can be associated to classical invariant manifolds such as periodic orbits, but also to non-classical structures like sets of midpoints between periodic points. By contrast to scars in wavefunctions, these features are not subject to the uncertainty relation and therefore need not show any smearing. They constitute important exceptions from a continuous convergence in the classical limit of the Wigner towards the Liouville propagator. We support our theory with numerical results for the quantum cat map and the harmonically driven quartic oscillator.
Boson-sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson-sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson-sampling with photons of arbitrary spectral structure and relate the sampling statistics of the device to matrix permanents. This sheds light on the computational complexity of different regimes of the photons' spectral …
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical system, therefore causing significant deviations of the spectral density from RMT expectations. In this work, the problem is considered of both RMT-ruled and scarred chaotic systems coupled to an opening. In particular, predictions are derived for the spectral density of a chaotic Hamiltonian scattering into a single- or multiple channels. The results are tested o…
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number re…
We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They distinguish from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom ex…
We demonstrate a single-photon sensitive spectrometer in the visible range, which allows us to perform time-resolved and multi-photon spectral correlation measurements. It is based on a monochromator composed of two gratings, collimation optics and an array of single photon avalanche diodes. The time resolution can reach $110$ ps and the spectral resolution is $2$ nm/pixel, limited by the design of the monochromator. This technique can easily be combined with commercial monochromators, and can be useful for joint spectrum measurements of two photons emitted in the process of parametric down co…
We develop a semi-classical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhoo…
We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to…
The ladder configuration of atomic levels provides a source for telecom photons (signal) from the upper atomic transition. \ For rubidium and cesium atoms, the signal field has the range around 1.3-1.5 $μ$m that can be coupled to an optical fiber and transmitted to a remote location. \ Cascade emission may result in pairs of photons, the signal entangled with the subsequently emitted infrared photon (idler) from the lower atomic transition.\ This correlated two-photon source is potentially useful in the (Duan-Lukin-Cirac-Zoller) DLCZ protocol for the quantum repeater.\ We implement the cascade…
Optimized Tensor-Network Renormalization for Quantum Dynamics: Resolving the Spectral Function of $\mathrm{K_2Co(SeO_3)_2}$
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所，北京凝聚态物理国家研究中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院化学与化工系）；PSI Center for Scientific Computing, Theory and Data, Paul Scherrer Institute（保罗谢尔研究所科学计算、理论与数据中心）
Generating quantum error correcting codes from topological pre-thermal scars
Collège de France（法兰西学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of New Mexico（新墨西哥大学）；International Solvay Institutes（国际索尔维研究所）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Center for Nonlinear Phenomena and Complex Systems（非线性现象与复杂系统中心）；Sandia National Laboratories（桑迪亚国家实验室）
A trajectory segment in an energy shell, which combines to form a closed curve with a segment in another canonically driven energy shell, adds an oscillatory semiclassical contribution to the smooth classical background of the quantum probability density for a transition between their energies. If either segment is part of a Bohr-quantized periodic orbit of either shell, the centre of its endpoints lies on a scar disk of the spectral Wigner function for single static energy shell and the contribution to the transition is reinforced by phase coherence. The exact representation of the transition…
