Quantum dephasing and decay of classical correlation functions in chaotic systems

We discuss the dephasing induced by the internal classical chaotic motion in the absence of any external environment. To this end we consider a suitable extension of fidelity for mixed states which is measurable in a Ramsey interferometry experiment. We then relate the dephasing to the decay of this quantity which, in the semiclassical limit, is expressed in terms of an appropriate classical correlation function. Our results are derived analytically for the example of a nonlinear driven oscillator and then numerically confirmed for the kicked rotor model.Comment: 14 pages, 1 figur

Complexity of Quantum States and Reversibility of Quantum Motion

We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number ${\cal M}(t)$ of harmonics of the (initially isotropic, i.e. ${\cal M}(0)=0$) Wigner function, which are generated during quantum evolution for the time $t$. We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment $T$ immediately after applying at this moment an instant perturbation governed by a strength parameter $\xi$. It follows that there exists a critical perturbation strength, $\xi_c\approx \sqrt{2}/{\cal M}(T)$, below which the initial state is well recovered, whereas reversibility disappears when $\xi\gtrsim \xi_c(T)$. In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.Comment: 15 pages, 13 figures; the list of references is update

Correlation plenoptic imaging

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in classical imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this paper, we demonstrate that the momentum/position correlation of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.Comment: 6 pages, 3 figure

The observed chemical structure of L1544

Prior to star formation, pre-stellar cores accumulate matter towards the centre. As a consequence, their central density increases while the temperature decreases. Understanding the evolution of the chemistry and physics in this early phase is crucial to study the processes governing the formation of a star. We aim at studying the chemical differentiation of a prototypical pre-stellar core, L1544, by detailed molecular maps. In contrast with single pointing observations, we performed a deep study on the dependencies of chemistry on physical and external conditions. We present the emission maps of 39 different molecular transitions belonging to 22 different molecules in the central 6.25 arcmin$^2$ of L1544. We classified our sample in five families, depending on the location of their emission peaks within the core. Furthermore, to systematically study the correlations among different molecules, we have performed the principal component analysis (PCA) on the integrated emission maps. The PCA allows us to reduce the amount of variables in our dataset. Finally, we compare the maps of the first three principal components with the H$_2$ column density map, and the T$_{dust}$ map of the core. The results of our qualitative analysis is the classification of the molecules in our dataset in the following groups: (i) the $c$-C$_3$H$_2$ family (carbon chain molecules), (ii) the dust peak family (nitrogen-bearing species), (iii) the methanol peak family (oxygen-bearing molecules), (iv) the HNCO peak family (HNCO, propyne and its deuterated isotopologues). Only HC$^{18}$O$^+$ and $^{13}$CS do not belong to any of the above mentioned groups. The principal component maps allow us to confirm the (anti-)correlations among different families that were described in a first qualitative analysis, but also points out the correlation that could not be inferred before.Comment: 29 pages, 19 figures, 2 appendices, accepted for publication in A&A, arXiv abstract has been slightly modifie

Exploring plenoptic properties of correlation imaging with chaotic light

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 property of three different setups, explore their refocusing potentialities and discuss their practical applications.Comment: 9 pages, 4 figure

Correlation Plenoptic Imaging With Entangled Photons

Plenoptic imaging is a novel optical technique for three-dimensional imaging in a single shot. It is enabled by the simultaneous measurement of both the location and the propagation direction of light in a given scene. In the standard approach, the maximum spatial and angular resolutions are inversely proportional, and so are the resolution and the maximum achievable depth of focus of the 3D image. We have recently proposed a method to overcome such fundamental limits by combining plenoptic imaging with an intriguing correlation remote-imaging technique: ghost imaging. Here, we theoretically demonstrate that correlation plenoptic imaging can be effectively achieved by exploiting the position-momentum entanglement characterizing spontaneous parametric down-conversion (SPDC) photon pairs. As a proof-of-principle demonstration, we shall show that correlation plenoptic imaging with entangled photons may enable the refocusing of an out-of-focus image at the same depth of focus of a standard plenoptic device, but without sacrificing diffraction-limited image resolution.Comment: 12 pages, 5 figure

Dynamics of entanglement in quantum computers with imperfections

The dynamics of the pairwise entanglement in a qubit lattice in the presence of static imperfections exhibits different regimes. We show that there is a transition from a perturbative region, where the entanglement is stable against imperfections, to the ergodic regime, in which a pair of qubits becomes entangled with the rest of the lattice and the pairwise entanglement drops to zero. The transition is almost independent of the size of the quantum computer. We consider both the case of an initial maximally entangled and separable state. In this last case there is a broad crossover region in which the computer imperfections can be used to create a significant amount of pairwise entanglement.Comment: 4 pages, 4 figure

Diffraction-limited plenoptic imaging with correlated light

Traditional optical imaging faces an unavoidable trade-off between resolution and depth of field (DOF). To increase resolution, high numerical apertures (NA) are needed, but the associated large angular uncertainty results in a limited range of depths that can be put in sharp focus. Plenoptic imaging was introduced a few years ago to remedy this trade off. To this aim, plenoptic imaging reconstructs the path of light rays from the lens to the sensor. However, the improvement offered by standard plenoptic imaging is practical and not fundamental: the increased DOF leads to a proportional reduction of the resolution well above the diffraction limit imposed by the lens NA. In this paper, we demonstrate that correlation measurements enable pushing plenoptic imaging to its fundamental limits of both resolution and DOF. Namely, we demonstrate to maintain the imaging resolution at the diffraction limit while increasing the depth of field by a factor of 7. Our results represent the theoretical and experimental basis for the effective development of the promising applications of plenoptic imaging.Comment: 10 pages, 10 figure

Values we learn from our parents influence our trust in others with money and business

New research sheds light on what determines trust, a key element of economic activity, write Jeffrey V. Butler, Paola Giuliano and Luigi Guis