Nonlinear Optics

Simulations of Time Asymmetric Quantum Mechanics by Nonlocal Nonlinear Optics

Giulia Marcucci, Maria Chiara Braidotti, Silvia Gentilini, Claudio Conti

Published Jan 1, 2017• 1 citation

Abstract

Time-reversal symmetry in quantum mechanics has been debated by many authors, like Gamow, Prigogine and others. We show that intrinsically irreversible quantum theories can be simulated by nonlinear optical shock waves in nonlocal media.

DOI: 10.1364/nlo.2017.nth2a.4

Related papers

Time Asymmetric Quantum Mechanics and Shock Waves: Exploring the Irreversibility in Nonlinear Optics

Giulia Marcucci, Maria Chiara Braidotti, Silvia Gentilini +1 more

Abstract The description of irreversible phenomena is a still debated topic in quantum mechanics. Still nowadays, there is no clear procedure to distinguish the coupling with external baths from the intrinsic irreversibility in isolated systems. In 1928 Gamow introduced states with exponentially decaying observables not belonging to the conventional Hilbert space. These states are named Gamow vectors, and they belong to rigged Hilbert spaces. This review summarizes the contemporary approach using Gamow vectors and rigged Hilbert space formalism as foundations of a generalized “time asymmetric” quantum mechanics. We study the irreversible propagation of specific wave packets and show that the topic is surprisingly related to the problem of irreversibility of shock waves in classical nonlinear evolution. We specifically consider the applications in the field of nonlinear optics. We show that it is possible to emulate irreversible quantum mechanical process by the nonlinear evolution of a laser beam and we provide experimental tests by the generation of dispersive shock waves in highly nonlocal regimes. We demonstrate experimentally the quantization of decay rates predicted by the time‐asymmetric quantum mechanics. This work furnishes support to the idea of intrinsically irreversible wave propagation, and to novel tests of the foundations of quantum mechanics.

Annalen der PhysikJul 11, 201710 citations

Generalized uncertainty principle and squeezing in nonlinear nonlocal photon fluids

Maria Chiara Braidotti, Antonio Mecozzi, Claudio Conti

We theoretically predict classical squeezing of nonlinear photon fluids. Techniques of time-asymmetric quantum mechanics allow showing that Gaussian states develop squeezing spontaneously in nonlocal nonlinear media. These results open new opportunities for quantum nonlinear optics.

Nonlinear OpticsJan 1, 20170 citations

Nonlinear, deformed and irreversible quantum systems : proceedings of the International Symposium on Mathematical Physics, Arnold Sommerfeld Institute 15-19 August 1994, Clausthat, Germany

Heinz Dietrich Doebner, V. K. Dobrev, P. Nattermann

Intrinsically irreversible representations of unstable quantum systems, I. Antoniou quantum mechanical arrows of time, A. Bohm isotropic harmonic oscillator on the quantum euclidean space, G. Fiore relevant and irrelevant nonlinear schrodinger equation, N. Gisin diffeomorphism groups and nonlinear quantum mechanics, G.A. Goldin from Hamiltonian mechanics to nonlinear Schrodinger equations, J.-D. Hennig nonlinear Schrodinger dynamics and nonlinear observables, W. Lucke nonlinear gauge transformations and the Doebner-Goldin equation, P. Nattermann chaos and the limit of classical and quantum mechanics, T. Petrosky why irreversibility? the formulation of classical and quantum mechanics for unstable dynamical systems, I. Prigogine harmonic oscillators on quantum space, S. Watamura. (Part Contents).

WORLD SCIENTIFIC eBooksJan 1, 19954 citations

Time-Reversal and Irreversibility

Arno Böhm, Piotr Kielanowski

The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert space case admits a new kind of irreversibility which does not appear in the conventional case. The origin of this irreversibility can be traced back to different initial-boundary conditions for the states and observables. It is shown that this irreversibility does not contradict the experimentally tested consequences of the time-reversal invariance of the conventional case but instead we have to introduce a new time reversal operator.

arXiv:quant-ph/9512014Dec 12, 19950 citations

Resonances, Gamow Vectors and Time Asymmetric Quantum Theory

Arno Böhm, Raymond Scurek, Sujeewa Wikramasekara

Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical theory.

arXiv:nucl-th/9902076Revista Mexicana de FísicaFeb 26, 19995 citations

Time-reversal invariance and irreversibility in time-asymmetric quantum mechanics

Mario Castagnino, Manuel Gadella, Olímpia Lombardi

The aim of this paper is to analyze the concepts of time-reversal invariance and irreversibility in the so-called ’time-asymmetric quan-tum mechanics’. We begin with pointing out the difference between these two concepts. On this basis, we show that irreversibility is not as tightly linked to the semigroup evolution laws of the theory-which lead to its non time-reversal invariance- as usually suggested. In turn, we argue that the irreversible evolutions described by the theory are coarse-grained processes. 1 1

Sep 1, 20050 citations