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17 pages, 8787 KiB

Open AccessArticle

Multipole Approach to the Dynamical Casimir Effect with Finite-Size Scatterers

by Lucas Alonso, Guilherme C. Matos, François Impens, Paulo A. Maia Neto and Reinaldo de Melo e Souza

Entropy 2024, 26(3), 251; https://doi.org/10.3390/e26030251 - 12 Mar 2024

Cited by 1 | Viewed by 1262

Abstract

A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size [...] Read more.

A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size and oscillation frequency), this assumption is inadequate and drastically overestimates the DCE radiation. Taking the opposite limit, we use instead the dipolar approximation to obtain a simpler and more realistic treatment of DCE for macroscopic bodies. Our approach is inspired by a microscopic theory of DCE, which is extended to the macroscopic realm by a suitable effective Hamiltonian description of moving anisotropic scatterers. We illustrate the benefits of our approach by considering the DCE from macroscopic bodies of different geometries. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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21 pages, 877 KiB

Open AccessArticle

Partial Bell-State Measurement with Type-II Parametric Down Conversion: Extracting Phase Information from the Zeropoint Field (I)

by Alberto Casado and Santiago Guerra

Entropy 2023, 25(3), 393; https://doi.org/10.3390/e25030393 - 21 Feb 2023

Cited by 1 | Viewed by 1952

Abstract

In this paper, the nexus between the Bell-state measurement and extracting phase information from the zeropoint field is investigated. For this purpose, the Wigner representation in the Heisenberg picture is applied in a Bell-type experiment in which the polarisation-entangled photon pairs generated in [...] Read more.

In this paper, the nexus between the Bell-state measurement and extracting phase information from the zeropoint field is investigated. For this purpose, the Wigner representation in the Heisenberg picture is applied in a Bell-type experiment in which the polarisation-entangled photon pairs generated in a type-II parametric down-conversion do not overlap. The signal intensities at the detectors are calculated in a four-mode approximation, being expressed as functions of the modules and phases of the four zeropoint amplitudes entering the crystal. A general criterion for identifying the correlated detectors is proposed based on the equality of the signal intensities, and without involving the calculation of the joint detection probabilities. In addition, from the analyses in the rectilinear and diagonal basis, it is shown that the distinguishability of the polarisation Bell states, which is in direct correspondence with the joint detection events in each experiment, can be related to the knowledge of the phases of the vacuum field entering the entanglement source, and giving rise to correlated detections. To this purpose, it is conjectured that a detection event is associated with a maximum value of the signal intensity averaged in the modules of the zeropoint amplitudes, as a function of the vacuum phases. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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14 pages, 298 KiB

Open AccessFeature PaperArticle

Quantum Oscillator at Temperature T and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics

by Margarita A. Man’ko and Vladimir I. Man’ko

Entropy 2023, 25(2), 213; https://doi.org/10.3390/e25020213 - 22 Jan 2023

Cited by 5 | Viewed by 1501

Abstract

A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle moving in the electric field of [...] Read more.

A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

16 pages, 334 KiB

Open AccessArticle

Stochastic Particle Creation: From the Dynamical Casimir Effect to Cosmology

by Matías Mantiñan, Francisco D. Mazzitelli and Leonardo G. Trombetta

Entropy 2023, 25(1), 151; https://doi.org/10.3390/e25010151 - 11 Jan 2023

Cited by 3 | Viewed by 1422

Abstract

We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic [...] Read more.

We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic counterpart. Then, we go beyond the perturbative evaluation using a stochastic version of the multiple scale analysis, that takes into account stochastic parametric resonance. We stress the relevance of the coupling between the different modes induced by the stochastic motion. In the single-mode approximation, the equations are formally analogous to those that describe the stochastic particle creation in a cosmological context, that we rederive using multiple scale analysis. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

17 pages, 354 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

by Hiromichi Nakazato, Alessandro Sergi, Agostino Migliore and Antonino Messina

Entropy 2023, 25(1), 96; https://doi.org/10.3390/e25010096 - 3 Jan 2023

Cited by 6 | Viewed by 1867

Abstract

We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator

U (t)

of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach [...] Read more.

We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator

U (t)

of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of

S U (2)

by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any

S U (2)

model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

13 pages, 2195 KiB

Open AccessFeature PaperArticle

Superior Resilience of Non-Gaussian Entanglement against Local Gaussian Noises

by Sergey Filippov and Alena Termanova

Entropy 2023, 25(1), 75; https://doi.org/10.3390/e25010075 - 30 Dec 2022

Viewed by 1569

Abstract

Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to [...] Read more.

Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain

κ_{i}

and the noise parameter

μ_{i}

for modes

i = 1, 2

) whenever

κ_{1} μ_{2}^{2} + κ_{2} μ_{1}^{2} < \frac{1}{4} (κ_{1} + κ_{2}) (1 + κ_{1} κ_{2})

, which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the “Gaussian world” paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at Gaussian states). Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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20 pages, 783 KiB

Open AccessArticle

Adiabatic Amplification of the Harmonic Oscillator Energy When the Frequency Passes through Zero

by Viktor V. Dodonov and Alexandre V. Dodonov

Entropy 2023, 25(1), 2; https://doi.org/10.3390/e25010002 - 20 Dec 2022

Cited by 1 | Viewed by 1504

Abstract

We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through a zero value. We consider both the classical and quantum descriptions of the system. We show that after a single frequency passage [...] Read more.

We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through a zero value. We consider both the classical and quantum descriptions of the system. We show that after a single frequency passage through a zero value, the famous adiabatic invariant ratio of energy to frequency (which does not hold for a zero frequency) is reestablished again, but with the proportionality coefficient dependent on the initial state. The dependence on the initial state disappears after averaging over the phases of initial states with the same energy (in particular, for the initial vacuum, the Fock and thermal quantum states). In this case, the mean proportionality coefficient is always greater than unity. The concrete value of the mean proportionality coefficient depends on the power index of the frequency dependence on a time near the zero point. In particular, the mean energy triplicates if the frequency tends to zero linearly. If the frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of time intervals between zero points, so that the mean energy behavior becomes quasi-stochastic after many passages through a zero value. The original Born–Fock theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many Fock states, whose weights do not depend on time in the new adiabatic regime. When the mean energy triplicates, the initial Nth Fock state becomes a superposition of, roughly speaking, 6N states, distributed nonuniformly. The initial vacuum and low-order Fock states become squeezed, as well as the initial thermal states with low values of the mean energy. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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19 pages, 984 KiB

Open AccessArticle

Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method

by Stanley S. Coelho, Lucas Queiroz and Danilo T. Alves

Entropy 2022, 24(12), 1851; https://doi.org/10.3390/e24121851 - 19 Dec 2022

Cited by 8 | Viewed by 4159

Abstract

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency

ω_{0}

, which undergoes a sudden jump to a frequency [...] Read more.

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency

ω_{0}

, which undergoes a sudden jump to a frequency

ω_{1}

and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis–Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when

ω_{1} < ω_{0}

. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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14 pages, 1381 KiB

Open AccessArticle

Extreme Electron Acceleration with Fixed Radiation Energy

by Michael R. R. Good, Chiranjeeb Singha and Vasilios Zarikas

Entropy 2022, 24(11), 1570; https://doi.org/10.3390/e24111570 - 31 Oct 2022

Cited by 7 | Viewed by 1648

Abstract

We examine the extreme situation of radiation from an electron that is asymptotically accelerated to the speed of light, resulting in finite emission energy. The analytic solution explicitly demonstrates the difference between radiation power loss and kinetic power loss (null). Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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Review

Jump to: Research

17 pages, 366 KiB

Open AccessReview

Nonlocal Static and Dynamical Vacuum Field Correlations and Casimir–Polder Interactions

by Roberto Passante and Lucia Rizzuto

Entropy 2023, 25(10), 1424; https://doi.org/10.3390/e25101424 - 8 Oct 2023

Viewed by 870

Abstract

In this review, we investigate several aspects and features of spatial field correlations for the massless scalar field and the electromagnetic field, both in stationary and nonstationary conditions, and show how they manifest in two- and many-body static and dynamic dispersion interactions (van [...] Read more.

In this review, we investigate several aspects and features of spatial field correlations for the massless scalar field and the electromagnetic field, both in stationary and nonstationary conditions, and show how they manifest in two- and many-body static and dynamic dispersion interactions (van der Waals and Casimir–Polder). We initially analyze the spatial field correlations for noninteracting fields, stressing their nonlocal behavior, and their relation to two-body dispersion interactions. We then consider how field correlations are modified by the presence of a field source, such as an atom or in general a polarizable body, firstly in a stationary condition and then in a dynamical condition, starting from a nonstationary state. We first evaluate the spatial field correlation for the electric field in the stationary case, in the presence of a ground-state or excited-state atom, and then we consider its time evolution in the case of an initially nonstationary state. We discuss in detail their nonlocal features, in both stationary and nonstationary conditions. We then explicitly show how the nonlocality of field correlations can manifest itself in van der Waals and Casimir–Polder interactions between atoms, both in static and dynamic situations. We discuss how this can allow us to indirectly probe the existence and the properties of nonlocal vacuum field correlations of the electromagnetic field, a research subject of strong actual interest, also in consequence of recent measurements of spatial field correlations exploiting electro-optical sampling techniques. The subtle and intriguing relation between nonlocality and causality is also discussed. Full article

(This article belongs to the Special Issue Quantum Nonstationary Systems)

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