It is well known that the Hong–Ou–Mandel (HOM) effect can be realized on beam splitters (BSs) in the form of coupled waveguides. It is believed that in this case, the theory is similar to HOM interference on conventional BSs. In this work, it is shown that if a BS is used in the form of a coupled waveguide, the theory of HOM interference can differ significantly from the known one. It is shown that even in the case of completely identical photons, the visibility of V can essentially differ from unity. The developed theory must be taken into account in quantum optical schemes, where BSs are represented mainly as coupled waveguides.
Indistinguishable and/or entangled photons propagating in waveguide arrays (WAs) represent a promising platform whose utility ranges from research on fundamental aspects of quantum mechanics all the way to applications in quantum sensing and quantum information processing. Quantum simulators of decoherence reveal that while decoherence processes inevitably destroy single-particle coherence and any form of multiparticle entanglement, quantum correlations based on particle indistinguishability do endure. Further, by judiciously combining multi-photon states with the idea of synthetic dimensions in WAs yields the notion of a synthetic atom and in turn this provides entirely novel perspectives on the dynamics of such multi-photon states. Similarly, simple beam splitters fed with indistinguishable photons, can be used to perform discrete fractional Fourier transforms or can be tuned to realize exceptional points of any order. The latter setup facilitates efficient quantum-enhanced sensors.
We propose a new interferometric setup which displays a completely destructive generalized N-photon Hong–Ou–Mandel interference. The key property of this scheme is that it does not require any optical elements like beam splitters or integrated waveguide structures. The interference is intrinsically produced by the evolution of N photons in free space when emitted by N identical single photon sources and measured by N detectors in the far field. In this sense, the setup is a most simple and natural implementation of the Hong–Ou–Mandel interference effect, i.e. of a completely destructive multi-photon interference produced by independent incoherent sources.
We examine multiphoton interference with a symmetric
SU(N) beam splitter
SN, an extension of features of the
SU(2) 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons
n/N in each output port), when a total number
n of photons impinges on the
N-port device. These are transitions of the form
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N, where
n=∑i=1Nni, which generalize the Hong-Ou-Mandel (HOM) effect $|1,1\rangle \overset{S_2}{\to}|1,1\rangle $, the eHOM effect $|n_1,n_2\rangle \overset{S_2}{\to}|\tfrac{n_1+n_2}{2},\tfrac{n_1+n_2}{2}\rangle $, and the generalized HOM effect (gHOM)
∣1⟩⊗N→SN∣1⟩⊗N, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of sub-amplitudes of the total zero amplitude. We develop symmetry properties for the generalized eHOM effect (geHOM)
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N involving a zero amplitude governed by Perm(
Λ)=0, for an appropriately constructed matrix
Λ(SN) built from the matrix elements of
SN. We develop an analytical constraint equation for Perm
(Λ) for arbitrary
N that allows us to determine when it is zero. We generalize the SU(2) beam splitter feature of central nodal line (CNL), which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of
N=2∗N′ where
N′∈odd.