Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which
2q particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with ${2}^{p}\ensuremath{\ge}{2}^{q}$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.
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.
In the Hong-Ou-Mandel interferometric scheme, two identical photons that illuminate a balanced beam splitter always leave through the same exit port. Similar effects have been predicted and (partially) experimentally confirmed for multiphoton Fock-number states. In the limit of large photon numbers, the output distribution follows a ${(1\ensuremath{-}{x}^{2})}^{\ensuremath{-}1/2}$ law, where
x is the normalized imbalance in the output photon numbers at the two output ports. We derive an analytical formula that is also valid for imbalanced input photon numbers with a large total number of photons, and focus on the extent to which the hypothesis of perfect balanced input can be relaxed, discussing the robustness and universal features of the output distribution.