Light reflection on a mirror can be thought as a simple physical effect. However if this happens when the mirror moves a rich scenario opens up. Here we aim at analyzing it from a quantum communication perspective. In particular, we study the kind of quantum channel that arises from (Gaussian) light reflection upon an accelerating mirror. Two competing mechanisms emerge in such a context, namely photons production by the mirror's motion and interference between modes. As consequence we find out a quantum amplifier channel and quantum lossy channel respectively below and above a threshold frequency (that depends on parameters determining mirror's acceleration). Exactly at the threshold frequency the channel behaves like a purely classical additive channel, while it becomes purely erasure for large frequencies. In addition the time behavior of the channel is analyzed by employing wave packets expansion of the light field.
Light reflection on a mirror can be thought as a simple physical effect. However if this happens when the mirror moves a rich scenario opens up. Here we aim at analyzing it from a quantum communication perspective. In particular, we study the kind of quantum channel that arises from (Gaussian) light reflection upon an accelerating mirror. Two competing mechanisms emerge in such a context, namely photons production by the mirror's motion and interference between modes. As consequence we find out a quantum amplifier channel and quantum lossy channel respectively below and above a threshold frequency (that depends on parameters determining mirror's acceleration). Exactly at the threshold frequency the channel behaves like a purely classical additive channel, while it becomes purely erasure for large frequencies. In addition the time behavior of the channel is analyzed by employing wave packets expansion of the light field.
Motivated by the fact that the null shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semitransparency and derive a general implicit expression for the corresponding Bogolyubov coefficients. Then, we turn this into an explicit analytical form by focusing on mirrors that are accelerated via an impulsive force. From the so-obtained Bogolyubov coefficients we derive the particle production. Finally, we realize the field coming from the left-past spacetime region, passing through the semitransparent moving mirror and ending up to the right-future spacetime region as undergoing the action of a Gaussian quantum channel. We study the transmission and noisy generation properties of this channel, relating them to the Bogolyubov coefficients of the mirror's motion, through which we evaluate capacities in transmitting classical and quantum information.
We study the reflection of narrow (in space) quantum wavepackets from nonabsorptive mirrors (totally or partially reflecting). If the initial mean value of the momentum component perpendicular to the mirror surface is less than the momentum uncertainty, then the mean value of this component gradually increases with time at the expense of shrinking the packet in the momentum space. As a consequence, very slow particles moving initially in the direction parallel to the mirror surface will be deflected to appreciable angles, even when they pass at macroscopical distances from the mirror. We give analytical expressions describing the asymptotical behaviour of wavefunctions and density matrices in the coordinate and momentum representations for arbitrary narrow initial packets. We show that the asymptotical mean values and variances do not depend on the phases of the complex reflection and transmission coefficients. Moreover, they are insensitive to the concrete form of the reflective potential in the case of totally reflecting mirrors. For partially reflecting mirrors we introduce the concept of conditional wavefunctions and mean values. The dependences of the asymptotical values of different quantities characterizing the packet (e.g. the `momentum transformation coefficient' and the `invariant uncertainty product') on the parameters of the reflecting potential (the height and width or characteristic length of the transition region) are analysed in the examples of the potentials of Epstein's type and their limit cases (the ideal reflecting wall and the delta potential). A possibility for the verification of the effect of quantum deflection in experiments with ultracold atoms is briefly discussed.
One-photon sources are important elements in quantum optics. The archetypal example is an atom raised to an excited state at time t = 0, then de-exciting with emission of a single photon. The development of this kind of source depends on progress with experimental techniques, e.g. the possibility of isolating a single atom, molecule or quantum well. In this complement, we present the formalism for describing the corresponding radiation, and use it to discuss some spectacular experiments which bring out properties quite incompatible with a classical description of the electromagnetic field. We begin in Section 5B.2 by describing the anti-correlation between detections on either side of a semi-reflecting mirror, establishing the quantitative difference with a classical field. Section 5B.3 discusses a quantum optical effect that was only demonstrated at the beginning of the twenty-first century, namely the quantum coalescence of two one-photon wave packets on a semi-reflecting mirror, which occurs even when the two photons were emitted by independent atoms. An analogous effect, the Hong–Hou–Mandel effect, is discussed in Chapter 7. These effects exemplify quantum interference involving two photons. Finally, Section 5B.4 is concerned with quantum calculations involving quasi-classical states. As we now know, this leads to results that are identical to the predictions of semi-classical theory.
Quantum counterfactual communication applies to information transmission that is free from particles commuting in-between; it is at the forefront of the present computing technology. Here, we consider a perfect mirror that reflects any incident photon with 100% probability. By the existing literature, the reflected photon loses a certain amount of energy because a portion of its wave nevertheless gets transmitted. That is, there exist separated photon-less waves that carry energies. We thus consider sending a photon to a perfect mirror and transmitting its wave to a receiver, which by gaining energy obtains the sought information.
The idea of wave packet, that clarified many conceptual difficulties, has more recently been revisited to address interferometric and dynamical issues.Present work focuses on the spatio-temporal dynamics of the quantum wave packets in the Fermi-Ulam Accelerator Model.The specific system considered here is a one-dimensional box under periodic oscillations at one boundary. Such a seemingly simple system can be mapped to non-trivial problems like BEC trapped in an oscillating cavity or dynamics of atomic wave packet in different potential in presence or absence of gravitational field.The system is shown to display rich dynamical features including transitions from regular to stochastic and further to chaotic domain in classical phase space. We have obtained the approximated eigen-value solutions of the problem through time dependent Schrodinger’s equation under rescaling transformations that effectively replace moving boundary with a static one. Consequently the running time becomes a nonlinear function of the continuously changing boundary.Based on these solutions, revivals or the resurrection of the original wave packet, in the driven and un-driven Fermi-Ulam model are presented. Such revivals correspond to the constructive interference whereas the wave packet’s collapse owes to destructive interference. Furthermore, interplay of constructive and destructive interferences also readily mimics the fractional revivals.It is further demonstrated that initial position and momentum play a highly crucial role in the emergent revival and fractional revival patterns.It is shown that the symmetries exhibited by such structures in un-driven systems are usually lost under driven conditions and the revival/fractional revival times can only be predicted through a transcendental equation whose solution mainly depends on the strength of the external driving force.In present thesis we have proposed a comprehensive mathematical technique to calculate these hitherto unpredictable times.In addition, a graphical method is also suggested to observe these asymmetric revival/fractional revival times.This apparent asymmetry, do display an overall periodicity over a comparatively long span covering many times of revivals.It is found that whenever the ratio between the period of wall oscillation and quantum revival time `α/β' is a rational number then the revivals time shows a periodicity after β number of revival times over α wall oscillation. Standard tools of autocorrelation and quantum carpets, a consequence of quantum interference, have been employed for visual manifestation of these revivals.These carpets amply demonstrate the explicit asymmetric shifting of revival times for the driven case.These micro changes exhibited in quantum carpet morphologies consequently yield amended phase velocities associated with the canals and ridges in the driven framework.Furthermore, to grasp the quantum phase space dynamics in its entirety, we have also utilized the more sophisticated techniques of the Wigner function and information entropy.It is demonstrated mathematically that revivals not apparent via autocorrelation become prominent in the Wigner phase space description along with the appearance of smooth mini wave packets in the fractional revivals.These interference patterns emerge due to the state vector formed through the linear combination of Gaussians with different positions and momenta having pure Gaussian as well as oscillatory terms. Moreover, the information entropy, like the Wigner function also predicts the revivals when and where they happen.Thus a rich pattern of fractional revivals, including some altogether new ones, are observed through this tool in both driven and un-driven situations.Finally we have elucidated various scenarios including cold atoms in magneto-optical traps where such a system can be experimentally realized along with the suggestions for future work in this specific domain
When a stationary reflecting wall acting as a perfect mirror for an atomic beam with well-defined incident velocity is suddenly removed, the density profile develops during the time evolution an oscillatory pattern known as diffraction in time. The interference fringes are suppressed or their visibility is diminished by several effects such as averaging over a distribution of incident velocities, apodization of the aperture function, atom-atom interactions, imperfect reflection, or environmental noise. However, when the mirror moves with finite velocity along the direction of propagation of the beam, the visibility of the fringes is enhanced. For mirror velocities below beam velocity, as used for slowing down the beam, the matter wave splits into three regions separated by space-time points with classical analogs. For mirror velocities above beam velocity a visibility enhancement occurs without a classical counterpart. When the velocity of the beam approaches that of the mirror the density oscillations rise by a factor 1.8 over the stationary value.