Quantum effects in the interference of photon number states

Abstract

Multi-photon interference results in modulations of output probabilities with phase shift periods that are much shorter than 2 Pi. Here, we investigate the physics behind these statistical patterns in the case of well-defined photon numbers in the input and output modes of a two-path interferometer. We show that the periodicity of the multi-photon interference is related to the weak value of the unobserved intensity difference between the two arms of the interferometer. This means that the operator relations between the photon number differences in input, path, and output can be used to determine the periodicity of the experimentally observed quantum interference, establishing an important link between the classical causality of random phase interference and quantum effects that depend on the superposition of classically distinct possibilities.Comment: 15 pages, including 6 figures; clarifications of approximation and assumptions added in section IV. Final version for publication in Phys. Rev.

Derivation of the statistics of quantum measurements from the action of unitary dynamics

“…This situation has changed, in particular in quantum optics, where the ability to generate a wide variety of non-classical states combines with the large coherent amplitudes of laser light to close the gap between the seemingly classical aspects of continuous quantum dynamics and the fully quantized statistics of photon number distributions. As a result, phase space methods have been particularly successful in quantum optics [1][2][3][4][5][6][7]19], and the present work could be seen as an attempt to explain the fundamental reasons for this success in more general terms. The main new insight presented here is that the mathematical structure of classical theory can be obtained directly from a quantum theoretical explanation of the empirical evidence, without the use of classical models.…”

“…The analysis presented in the following indicates that quantum interference effects can always be mapped onto a specific transformation generated by the observable defining either the initial or the final state. It is therefore possible to develop a more immediate understanding of the physics of quantum coherence by considering that the inner products of Hilbert space actually express a relation between the two different dynamical processes that result in state preparation and in measurements [17][18][19][20]. In this relation, the modulations of probability associated with quantum interferences can be understood in terms of propagation time differences between two intersections of the orbits represented by the quantum states.…”

Contextuality, coherences, and quantum Cheshire cats

“…By having the state prohibited by preselection as its 'ket' , and the state prohibited by postselection as its 'bra' , the coherence is allowed by both the pre-and postselection, despite the two states it is formed of both individually being prohibited. As discussed in [44], these coherences between prohibited states form necessary components of the quantum descriptions of contextual systems, despite not being describable classically.…”

Contextuality and inequality violations in a three-path interferometer

“…To illustrate contextuality in a three path interferometer, it is therefore necessary to construct an interferometer that relates at least three contexts to each other. 11,12 Here, we explain how such an interferometer can be constructed by starting from a graph of the contextuality relations and mapping it onto a specific sequence of paths interfering at beam splitters. We then use the interferometer to examine the relation of quantum contextuality with possible photon paths through the interferometer.…”

“…The most reasonable alternative seems to be the introduction of negative path presence, as discussed in previous work. [11][12][13][14]…”