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arXiv:quant-ph/0703163

Time Asymmetry in Quantum Physics - II. Experimental Demonstration Using a Single Ion

Arno Böhm, Hani Kaldass, Soliman R. Komy, W. P. Schleich

Published Mar 18, 2007• 1 citation
arXivHTMLPDF

Abstract

Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times. This provides the means of demonstrating the beginning of time of a semigroup evolution for a decaying state.

DOI
10.48550/arxiv.quant-ph/0703163

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Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times. This provides the means of demonstrating the beginning of time of a semigroup evolution for a decaying state.
The meaning of time asymmetry in quantum physics is discussed.On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group.Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution.Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)).If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ = Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t 0 ≤ t < ∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system.The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry.From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
We show that it is possible to measure the Schrödinger wave of a single quantum system. This provides a strong argument for associating physical reality with the quantum state of a single system, and challenges the usual assumption that the quantum state has physical meaning only for an ensemble of identical systems. While the Schrödinger wave is a basic element of quantum theory, it is generally believed that one cannot associate physical reality to the wave of a single particle. Rather, the Schrödinger wave is often viewed as a mathematical tool for calculating the probabilities of various outcomes of certain experiments when many such experiments are performed on an ensemble of identical systems, all in the same quantum state. Several arguments seem to support this point of view: i) We have never seen the quantum state of a single particle in a laboratory. Indeed, while a wave is typically spread over a region of space, we never see a particle simultaneously in several distinct locations. ii) If we could see a quantum state, we could presumably distinguish it from any other quantum state, but the unitary time evolution of states in quantum
The status of Time in the Quantum Theory remains even today a largely open question. In particular, the existence of a Quantum Time Operator that would describe the distribution of decay times of an unstable quantum system (in analogy with the Position operator that is associated to the position distribution) remained a polemichal question during several decades. Recently, we conceived experimental proposals involving CP violating processes (of single mesons and entangled pairs of mesons) that can be considered as crucial experiments aimed at testing the existence of a Quantum Time Operator. In the present paper, we shall present a similar proposal that can be realized with a single trapped ion. These proposals aim at bringing fundamental problems related to the status of Time in the Quantum Theory to the realm of experimental physics.
A quantum mechanical theory with time asymmetry intrinsic to states (or observables) features the concept of an initial time of the state and thus a preparation time of the physical system represented by the state. This special time is investigated in the context of scattering theory, where, in standard quantum mechanics, the physical meaning of a preparation time has remained obscure. In an experiment, the preparation time corresponds to an ensemble of times of scattering marking the times in the laboratory when one scattering projectile interacts with one target quantum.