Quantum Typicality and Initial Conditions

If the state of a quantum system is sampled out of a suitable ensemble, the measurement of some observables will yield (almost) always the same result. This leads us to the notion of quantum typicality: for some quantities the initial conditions are immaterial. We discuss this problem in the framework of Bose-Einstein condensates.Comment: 8 page

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

Huygens' principle and Dirac-Weyl equation

We investigate the validity of Huygens' principle for forward propagation in the massless Dirac-Weyl equation. The principle holds for odd space dimension n, while it is invalid for even n. We explicitly solve the cases n=1,2 and 3 and discuss generic $n$. We compare with the massless Klein-Gordon equation and comment on possible generalizations and applications.Comment: 7 pages, 1 figur

Long-lived entanglement of two multilevel atoms in a waveguide

We study the presence of nontrivial bound states of two multilevel quantum emitters and the photons propagating in a linear waveguide. We characterize the conditions for the existence of such states and determine their general properties, focusing in particular on the entanglement between the two emitters, that increases with the number of excitations. We discuss the relevance of the results for entanglement preservation and generation by spontaneous relaxation processes.Comment: 6 pages, 1 figur

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

Typical observables in a two-mode Bose system

A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always the same result. We investigate the general features of typical observables, the criteria to determine typicality and finally focus on the case of density correlation functions, which are related to spatial distribution of particles and interference.Comment: 8 pages, 1 figur

Resolution Limit of Correlation Plenoptic Imaging between Arbitrary Planes

Correlation plenoptic imaging (CPI) is an optical imaging technique based on intensity correlation measurement, which enables detecting, within fundamental physical limits, both the spatial distribution and the direction of light in a scene. This provides the possibility to perform tasks such as three-dimensional reconstruction and refocusing of different planes. Compared with standard plenoptic imaging devices, based on direct intensity measurement, CPI overcomes the problem of the strong trade-off between spatial and directional resolution. Here, we study the resolution limit in a recent development of the technique, called correlation plenoptic imaging between arbitrary planes (CPI-AP). The analysis, based on Gaussian test objects, highlights the main properties of the technique, as compared with standard imaging, and provides an analytical guideline to identify the limits at which an object can be considered resolved

Phase Transitions in ZnZ_{n} Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED

We study the ground-state properties of a class of $\mathbb{Z}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the $\mathrm{U}(1)$ group, preserve the unitary character of the minimal coupling, and have therefore the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper we study the cases $n = 2 \div 8$ by means of a DMRG code that exactly implements Gauss' law. We perform a careful scaling analysis, and show that, in absence of a background field, all $\mathbb{Z}_n$ models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the $CP$ symmetry. We then perform the large-$n$ limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition the zero-charge sector of the massive Schwinger model, which occurs at negative mass.Comment: 15 pages, 18 figure

Signal-to-noise properties of correlation plenoptic imaging with chaotic light

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-noise ratio (SNR) and compare their performances. We find that the SNR can be significantly higher and easier to control in the second CPI scheme, involving standard imaging of the object; under adequate conditions, this scheme enables reducing by one order of magnitude the number of frames for achieving the same SNR.Comment: 12 pages, 3 figure