We examine multiphoton interference with a symmetric $SU(N)$ beam splitter $S_N$ , 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 $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$ , where $n=\sum_{i=1}^N n_i$ , 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) $|1\rangle^{\otimes N}\overset{S_N}{\to}|1\rangle^{\otimes N}$ , 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) $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$ involving a zero amplitude governed by Perm( $Λ$ )=0, for an appropriately constructed matrix $Λ(S_N)$ built from the matrix elements of $S_N$ . 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 $N'\in odd$ .We examine multiphoton interference with a symmetric $SU(N)$ beam splitter $S_N$, 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 $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$, where $n=\sum_{i=1}^N n_i$, 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) $|1\rangle^{\otimes N}\overset{S_N}{\to}|1\rangle^{\otimes N}$, 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) $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$ involving a zero amplitude governed by Perm($Λ$)=0, for an appropriately constructed matrix $Λ(S_N)$ built from the matrix elements of $S_N$. 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 $N'\in odd$.

quant-pharXiv:2601.03395Jan 8, 20260 citations

Explaining the Hong-Ou-Mandel (HOM) experiment

Oyvind Alv Liberg

Jan 1, 20260 citations

Enhanced Hong-Ou-Mandel manifolds and figures of merit for linear chains of identical microring resonators

Peter L. Kaulfuss, Paul M. Alsing, A. Matthew Smith +2 more

We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value ${\ensuremath{\tau}}_{c}$, the curvature of the one-dimensional HOMM ${\overline{\ensuremath{\xi}}}_{N}$, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM $\ensuremath{\delta}{\ensuremath{\tau}}_{N}$. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value ${\ensuremath{\tau}}_{c}$, the curvature of the one-dimensional HOMM ${\overline{\ensuremath{\xi}}}_{N}$, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM $\ensuremath{\delta}{\ensuremath{\tau}}_{N}$. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.

arXiv:2209.14837Physical Review ResearchMay 12, 20232 citations

Hong-Ou-Mandel Comb and Switch using parallel chains of non-identical Micro-Ring Resonators

Peter L. Kaulfuss, Paul M. Alsing, Richard J. Birrittella +3 more

Micro-Ring Resonators (MRRs) allow us to access the Hong-Ou-Mandel (HOM) effect at a variety of tunable parameter combinations along exact analytic solutions. This higher-dimensional space of parameters for which the HOM effect occurs constitutes what is known as a Hong-Ou-Mandel manifold (HOMM). Using a parallel series of non-identical MRRs and changing relative round-trip phase shifts between MRRs allows for the manipulation of the wavelength locations of the HOM effect. Through clever design and fabrication, we can mold the HOMM to place multiple HOM effects, or lack thereof, precisely at desired locations in wavelength. In this paper we discuss how to adjust non-identical MRR parameters to change the resulting HOMM. We also promote example designs that exhibit advantageous HOMM structures, and highlight some of the diverse possibilities that can be accessed with different circuit design. Our main examples are: 1) a wavelength division multiplexer example that matches the HOM effect locations with the already established channels to integrate with a classical communication network and 2) a HOM-based entanglement switch that allows for the rapid switching between 2-photon NOON state outputs and completely separable single photon outputs.Micro-Ring Resonators (MRRs) allow us to access the Hong-Ou-Mandel (HOM) effect at a variety of tunable parameter combinations along exact analytic solutions. This higher-dimensional space of parameters for which the HOM effect occurs constitutes what is known as a Hong-Ou-Mandel manifold (HOMM). Using a parallel series of non-identical MRRs and changing relative round-trip phase shifts between MRRs allows for the manipulation of the wavelength locations of the HOM effect. Through clever design and fabrication, we can mold the HOMM to place multiple HOM effects, or lack thereof, precisely at desired locations in wavelength. In this paper we discuss how to adjust non-identical MRR parameters to change the resulting HOMM. We also promote example designs that exhibit advantageous HOMM structures, and highlight some of the diverse possibilities that can be accessed with different circuit design. Our main examples are: 1) a wavelength division multiplexer example that matches the HOM effect locations with the already established channels to integrate with a classical communication network and 2) a HOM-based entanglement switch that allows for the rapid switching between 2-photon NOON state outputs and completely separable single photon outputs.

arXiv:2401.14491Jan 25, 20240 citations

Interacting Particle Effects

George D. J. Phillies

Graduate texts in contemporary physicsJan 1, 20000 citations

We examine multiphoton interference with a symmetric

SU(N)

beam splitter

S_N

, 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

|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}

, where

n=\sum_{i=1}^N n_i

, 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\rangle^{\otimes N}\overset{S_N}{\to}|1\rangle^{\otimes 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)

|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}

involving a zero amplitude governed by Perm(

Λ

)=0, for an appropriately constructed matrix

Λ(S_N)

built from the matrix elements of

S_N

. 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'\in odd