We report the possibility of completely destructive interference of three indistinguishable photons on a three port device providing a generalisation of the well known Hong-Ou-Mandel interference of two indistinguishable photons on a two port device. Our analysis is based on the underlying mathematical framework of SU(3) transformations rather than SU(2) transformations. We show the completely destructive three photon interference for a large range of parameters of the three port device and point out the physical origin of such interference in terms of the contributions from different quantum paths. As each output port can deliver zero to three photons the device generates higher dimensional entanglement. In particular, different forms of entangled states of qudits can be generated depending on the device parameters. Our system is different from a symmetric three port beam splitter which does not exhibit a three photon Hong-Ou-Mandel interference.
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.
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.
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.