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Physical Review A

Interference, recoil, and uncontrollable interaction

Ole Ulfbeck

Published Jul 30, 2014• 0 citations
Publisher

Abstract

When the initial state in a collision involves indeterminate momenta, the conservation law for momentum no longer applies to the individual event with a sharpness beyond the indeterminacy. As a consequence, there are collisions that are recoilless in the sense that the state of one of the quanta is unchanged by the collision while the other quantum emerges in a superposition of momenta. Recoilless collisions that avoid entanglement are basic for experiments studying coherence effects for individual quanta involving interactions of the quantum with reflectors or diaphragms. The idea that in interference experiments there is an inevitable recoil that can be made unobservable by firmly bolting the reflector or diaphragm to a solid support is false since in interference with individual quanta there $\mathit{is}$ no recoil to control. The highly quantal character of the reflector or diaphragm in the interference experiment apparently went unnoticed in the conception of complementarity.

DOI
10.1103/physreva.90.012117

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When the initial state in a collision involves indeterminate momenta, the conservation law for momentum no longer applies to the individual event with a sharpness beyond the indeterminacy. As a consequence, there are collisions that are recoilless in the sense that the state of one of the quanta is unchanged by the collision while the other quantum emerges in a superposition of momenta. Recoilless collisions that avoid entanglement are basic for experiments studying coherence effects for individual quanta involving interactions of the quantum with reflectors or diaphragms. The idea that in interference experiments there is an inevitable recoil that can be made unobservable by firmly bolting the reflector or diaphragm to a solid support is false since in interference with individual quanta there is\mathit{is}is no recoil to control. The highly quantal character of the reflector or diaphragm in the interference experiment apparently went unnoticed in the conception of complementarity.
Joint atom-photon states can become nonseparably entangled by momentum conservation in scattering events. The consequences are open for observation in interference experiments in which one particle is used to monitor the evolution of the other. We have previously quantified the degree of available recoil entanglement in spontaneous emission, and present here the extensions to Rayleigh scattering and Raman scattering, with an emphasis on the similarity among the three cases. It is found that such scattering processes have the potential to create a higher degree of entanglement between the scattered photon and the recoiled atom than any reported to date.
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]
In 1924, Bohr, Kramers and Slater tried to introduce into microphysics conservation principles that hold only on the average. This attempt was abandoned in the light of the Compton-Simon experiment (and its later refinements). Since that time, except for a moment of doubt in 1936, it has been thought that the classical conservation laws (for energy and momentum) hold in quantum theory for each individual interaction, in a way that yields the classical exchange-and-balance of momentum (or energy) familiar from the laws of elastic collisions. It has been thought, that is, that in each individual “collision” what one part of the total system loses in linear momentum (say) another part gains, so as to maintain the same total amount afterwards as before. To those familiar with discussions of the interpretation of quantum theory, however, it will be apparent that the very concepts needed to express this idea of an elastic collision are generally not admitted in the theory. For one needs the idea that both before and after collision the total system has a well-defined value for the conserved quantity and, moreover, that the various component parts of the system have well-defined values for those quantities out of which the conserved one is composed. But in the case of spin, for example, it is customary to say that although total spin may be conserved in certain interactions one cannot attribute values to the separate components of spin (in various directions) because the associated operators do not commute. (Thus the whole sum is not even the sum of its parts.) Moreover, one does not generally refer to the values of quantities except in eigenstates. Hence, in general, one would not refer to the value of the conserved quantity before and after interaction, except for interactions initiated in eigenstates.
The two-particle wave function of neutrino and recoil nucleus is found as a solution of an initial-value problem in the far zone for a time longer than the electron capture decay lifetime of a hydrogenlike ion. The neutrino-recoil entanglement arising in such a process is a consequence of the momentum conservation and is closely related to the wave packet structure of the state. Because of neutrino mixing, the joint wave packet involves the coherent superposition of the neutrino mass eigenstate packets. This is the new physical realization of the Einstein-Podolsky-Rosen thought experiment, which has no analogue in quantum optics and quantum informatics. A class of possible experiments for the registration of a neutrino and a recoil nucleus is proposed. It is shown that, due to spatial correlations, neutrino and recoil oscillations can be observed in the coincidence experiment.