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arXiv:1107.2883 · Physical Review A

Amplitude control of quantum interference

William J. Mullin, Franck Laloë

Published Feb 2, 2012• 4 citations
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Abstract

Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam-splitter transmittivity. We then consider a Bell-type experiment with two independent sources and find strong violations of local realism for arbitrarily large source number $N$; for small $N$, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.

DOI
10.1103/physreva.85.023602

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Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam-splitter transmittivity. We then consider a Bell-type experiment with two independent sources and find strong violations of local realism for arbitrarily large source number NNN; for small NNN, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection R=1/2R = 1/2R=1/2 and transmission $ T = 1/2 $. In this work, the general mechanism of the interaction of two photons in a beam splitter is considered using an analytical solution, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only $ R = 1/2 $ and $ T = 1/2 $, but also their root-mean-square fluctuations $ ΔR ^ 2, ΔT ^ 2 $, which arise due to the dependence of $R = R(ω_1, ω_2) $ and $ T = T (ω_1, ω_2) $ on the frequencies where ω1,ω2ω_1, ω_2ω1​,ω2​ are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations $ ΔR^2 $ and $ ΔT^2 $ can be neglected and $ R=T=1/2 $ is chosen, the developed theory coincides with previously known results.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
The interference of two Bose-Einstein condensates, initially in Fock states, can be described in terms of their relative phase, treated as a random unknown variable. This phase can be understood either as emerging from the measurements or pre-existing to them; in the latter case, the originating states could be phase states with unknown phases, so an average over all their possible values is taken. Both points of view lead to a description of probabilities of results of experiments in terms of a phase angle, which plays the role of a classical variable. Nevertheless, in some situations, this description is not sufficient: another variable, which we call the ``quantum angle,'' emerges from the theory. This article studies various manifestations of the quantum angle. We first introduce the quantum angle by expressing two Fock states crossing a beam splitter in terms of phase states and relate the quantum angle to off-diagonal matrix elements in the phase representation. Then we consider an experiment with two beam splitters, where two experimenters make dichotomic measurements with two interferometers and detectors that are far apart; the results lead to violations of the Bell-Clauser-Horne-Shimony-Holt inequality (valid for local-realistic theories, including classical descriptions of the phase). Finally, we discuss an experiment where particles from each of two sources are either deviated via a beam splitter to a side collector or proceed to the point of interference. For a given interference result, we find ``population oscillations'' in the distributions of the deviated particles, which are entirely controlled by the quantum angle. Various versions of population oscillation experiments are discussed, with two or three independent condensates.
We analyze the interference of individual photons in two overlapping Mach–Zehnder interferometers joined via a common beam splitter. We show how two kinds of interference effects—single-photon Mach–Zehnder interference and two-photon Hong–Ou–Mandel interference—interfere with one another, partially canceling each other out. This configuration illustrates how quantum effects can combine nontrivially and, moreover, emphasizes that quantum interference happens at measurement. This work can serve as a bridge to more advanced quantum mechanical concepts, such as testing the predictions of quantum mechanics vs local realism.
In the context of Fock states, demonstrating multiphoton quantum interference, e.g., the generalized Hong-Ou-Mandel (HOM) interference, is at the core of many applications of quantum technologies. However, it is difficult to demonstrate high-visibility quantum interference for a large number of photons. Here, we introduce an experimentally feasible proposal to achieve this goal using phase-randomized weak coherent states and practical photon-number-resolving detectors. Our method can be used to obtain analytically tight bounds of the generalized HOM dip in a beam splitter, and it is robust against practical errors. The simulation shows that for an ideal detector that can resolve any number of photons without an upper bound, the proposed method can bound the generalize HOM interference for a large number of photons, e.g., 100 photons; for a practical detector that can resolve up to 29 photons, the proposed method can bound the generalized HOM interference for 56 photons with visibility 99.499.4%99.4. Our proposal is a general approach for multiphoton quantum interference in optical networks with multiple inputs and outputs.
When two indistinguishable bosons interfere at a beam splitter, they exit through the same output port. This quantum effect, known as Hong-Ou-Mandel interference, underpins many protocols in quantum information. It also generalizes to larger numbers of identical particles, for which interference produces characteristic many-body patterns. So far, experiments have observed the many-particle regime mainly in photonic platforms with unavoidable loss, and atomic realizations have remained challenging. Here we demonstrate Hong-Ou-Mandel interference with up to 12 indistinguishable neutral atoms in a system with negligible loss. Single-particle counting reveals parity oscillations, a bunching envelope and genuine multipartite entanglement, which are defining features of the multiparticle Hong-Ou-Mandel effect. Using the generated quantum states, we demonstrate metrological sensitivities that scale with the number of particles according to the Heisenberg limit. Our technique can be extended to larger ensembles, with wide-ranging applications from high-precision atom interferometry to multiparticle Bell tests.