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Physics of Atomic Nuclei

Interference in time

ANDRZEJ GÓŹDŹ, M. DȨBICKI, K. Stefańska

Published May 1, 2008• 6 citations
Publisher

Abstract

A series of experiments has shown the possibility of existence of interference in time, a phenomenon similar to interference in space. A possible description of this phenomenon based on the hypothesis of the quantum projection evolution is presented.
DOI
10.1134/s1063778808050189

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In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat space and time on an equal footing and there are many approaches to the problem how to introduce time operator. In order to support these approaches we propose the experiment that will clearly expose the equivalence of space and time regarding the relation towards quantum interference. The proposed experiment can show that it is possible to have superposition of being created in two different moments in time, and by measuring standard interference pattern, it will be shown that there is interference in time. It is similar to the case of verification of the possibility of single quantum system to be in the state that is superposition of two different positions in space. If so, this would mean that there should be exactly the same formal approach to the space coordinates and time in quantum mechanics since they are all quantum in their nature.
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the temporal structure of the evolution of quantum systems is ill-defined. We present an extension to the model, in which the time evolution is based on the projection postulate rather than the unitary operator. This approach is in agreement with all other aspects of quantum mechanics and allows to discuss time as an observable. Using this framework we present a description of the temporal double-slit experiment in which a~single particle interferes with itself from a different instant of time. Such behaviour has already been observed experimentally but lacked a consistent theoretical explanation.
Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.
The wave aspect of light is observed experimentally through interference phenomena, and in a certain sense such observations always require a division of the given (initial) light field into two or more space-time parts. The division can only be done by introducing matter (massive particles) in the field region, and the light-matter interaction inevitably changes the initial state of the field. Not least when one is dealing with single and few-photon interference, it is good to remember again a central point of Niels Bohr, namely that no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon. It turns out that it is possible to observe interference with a quantized electromagnetic field which contains only one photon. Since the irreversible final detection destroys the photon, it is in practice necessary to repeat the experiment starting from the same initial (given) conditions. Below we shall discuss the basics of single-photon interference in the simplest terms.
The interference of two photons in the optical gating Michelson interferometer is investigated. The phenomenon is studied using two different representations of photons: the space-time domain and a step-by-step two photon state evolution. Both representations lead to an equivalent description of the two-photon states which is the interference of four cases of two-photon traveling states, as implied by the evolution analysis. Additionally, the space-time domain analysis reveals that the classical interference of high-intensity light source is identical to the two-photon interference in the quantum regime except for a multiplicative factor of (n 2), where n is the number of photons.