Zero-Transmission Law for Multiport Beam Splitters

Abstract

The Hong-Ou-Mandel effect is generalized to a configuration of n bosons prepared in the n input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.PACS numbers: 03.67. Lx, 05.30.Jp, The Hong-Ou-Mandel (HOM) effect [1] is an impressive manifestation of the bosonic quantum nature of photons. In the original experiment, two identical photons are sent simultaneously (within their coherence time) through the two input ports of a balanced beam splitter. Since no interaction between the photons takes place, one would intuitively expect the photons to propagate independently and not presume any correlations in the number of photons measured at both output ports. Surprisingly, the photons always leave the setup together, but never exit at different ports. Such coincident events at both output ports are completely suppressed.This effect is used in many applications: The visibility of the dip in the coincident detection rate provides a characterization for the indistinguishability of two photons [2,3], and therewith for the quality of photon sources. HOM setups are used to project photons onto the maximally entangled |Ψ − Bell-state, and consequently to, both, create and detect such states [4]. This is used for example in entanglement swapping protocols [5] and quantum metrology [6]. Furthermore, the nondeterministic gate operations in linear optics quantum computation [7] are based on the HOM effect.It is suggestive to generalize the HOM setup for more than two photons and more than two input or output ports. Indeed, the enhancement of events with all particles in one port -bunching events -has been observed experimentally when several photons enter each of the two modes of an unbiased (i.e., balanced) two-port beam splitter [8,9]. For a specially designed biased setup of three particles and three input ports, the suppression of coincident events was shown [10]. In the case of a Bell multiport beam splitter [11,12] which redistributes n incoming particles to n ports in an unbiased way, it is known that coincident events are suppressed when n is even [13].All these results imply important applications, from the creation and detection of multipartite quditentangled states [14,15], over the implementation of entanglement swapping protocols for many particles and the design of efficient quantum gates for qudits [16], to the experimentally controlled transition from indistinguishability to distinguishability for many identical particles [17]. However, we still lack a comprehensive understanding of the n-particle, n-port generalization of the HOM effect, since the complexity of such a scattering problem scales very unfavorably with n: The number of interfering amplitudes as well as that of possible output events grow faster than exponentially. Hence, a detailed analysis of individual output events is prohibitive, and needs to be substituted by statistical considerations. This is the purpose of the ...

Nonmonotonic quantum-to-classical transition in multiparticle interference

“…The theoretical prediction fits the experimental data perfectly well, without adjustable parameters besides the overall count rate. Note that bunching signals, as the (4, 0) event observed here, always exhibit a monotonic transition, as a consequence of the bosonic enhancement (28) of the associated, unique many-particle path, which induces the strict hierarchy p Table 1. We stress that the encountered nonmonotonicity in the (2, 2) event is fundamentally distinct from oscillating signals originating from singlephoton interference in refs.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…, respectively, see (151), as a function of the backscattering angle θ. Negative and positive θ correspond to an optical thickness of b = 25 and b = 5, respectively.…”

“…In total, we get the same result as if the particles were distinguishable. This equivalence is generally valid if all particles are prepared in the same initial state, and if the Hamiltonian is symmetric under exchange of particles [151].…”

Suppression laws for multiparticle interference in Sylvester interferometers

“…The simplest case is the Hong-Ou-Mandel (HOM) effect when two particles impinge on distinct ports of a balanced beam splitter: quantum interference suppresses the coincident output (one particle per each output) in the case of bosons and the single-port output (both particles in either output) in case of fermions. In the multi-particle case, a sort of generalised HOM effect occurs for symmetric multiport beam splitters [5][6][7][8]. In particular, Tichy et al [7] showed that for a particular class of multiports, namely Bell or Fourier multiports, and input states with cyclic symmetry, a full suppression of most of the output combinations is observed; a * andrea.crespi@polimi.it simple analytical law gives a sufficient criterion for such suppression.…”

“…It has to be noted that the existence of a sharp suppression law directly comes from the symmetry characteristics of the matrix. While it has been conjectured that other suppression laws could exist for other class of symmetric unitaries, only the class of Fourier matrices has been investigated extensively up to now [7,20,21].…”