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AIP conference proceedings

Wave-like behavior of phase-modulated three single-photon states in a six-port Mach-Zehnder Interferometer

Suryadi

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This study investigates three-photon interference dynamics in a six-port Mach-Zehnder Interferometer (6p-MZI), focusing on the quantum interference characteristics of photon state distributions under varying phase conditions. By introducing a phase modulator to manipulate photon distinguishability through phase shifts, we demonstrate significant modulation of output photon state probabilities. The analysis reveals multiple interference patterns, including even photon distribution across output ports, photon coalescence at a single port, and partial photon distributions. The probability amplitudes exhibit distinct phase dependencies, with 100% probability for even distribution at ±2mπ, approximately 30% peak probability for single-port coalescence at (2/3+m)π and (4/3+m)π, and sinusoidal interference fringes for two-photon same-port detection. These findings provide strong evidence of wave-like behavior in three-photon quantum systems and contribute to a deeper understanding of multi-photon interference. The strong phase sensitivity of three-photon interference in the 6p-MZI system highlights its potential applications in quantum metrology and photonic quantum technologies.

DOI
10.1063/5.0338868

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This study investigates three-photon interference dynamics in a six-port Mach-Zehnder Interferometer (6p-MZI), focusing on the quantum interference characteristics of photon state distributions under varying phase conditions. By introducing a phase modulator to manipulate photon distinguishability through phase shifts, we demonstrate significant modulation of output photon state probabilities. The analysis reveals multiple interference patterns, including even photon distribution across output ports, photon coalescence at a single port, and partial photon distributions. The probability amplitudes exhibit distinct phase dependencies, with 100% probability for even distribution at ±2mπ, approximately 30% peak probability for single-port coalescence at (2/3+m)π and (4/3+m)π, and sinusoidal interference fringes for two-photon same-port detection. These findings provide strong evidence of wave-like behavior in three-photon quantum systems and contribute to a deeper understanding of multi-photon interference. The strong phase sensitivity of three-photon interference in the 6p-MZI system highlights its potential applications in quantum metrology and photonic quantum technologies.
This study presents a theoretical analysis of three-photon interference in a six-port Mach-Zehnder Interferometer (6p-MZI) system, which incorporates two identical ideal six-port optical beam splitters (tritters) and phase modulators. We investigate interference patterns produced by hybrid input photon configurations that combine Fock state and coherent states, exploring the effects of both relative phase differences and average number of coherent photon state at the input ports. Our analysis demonstrates that the phase positions of constructive interference peaks systematically shift in response to the average number of coherent photons (∣α∣2)\left(|\alpha|^{2}\right)(∣α∣2) at the input ports. When ∣α∣2|\alpha|^{2}∣α∣2 increases from 0 to 0.5, the constructive interference peaks at output ports 2 and 3 undergo symmetric shifts of up to π/3\pi / 3π/3 radians relative to the extreme interference pattern of output port 3 at 5π/35 \pi / 35π/3. The results highlight the high sensitivity of interference patterns to both relative phase differences and coherent state photon amplitudes. These findings suggest novel approaches for controlling three-photon interference patterns in 6p-MZI systems through precise manipulation of phase and low-amplitude coherent photon states. This work advances our understanding of multi-photon interference in the quantum regime, with potential applications in quantum information processing, metrology, and fundamental quantum optics studies.
We present a unified theoretical analysis of three-photon quantum interference in a Six-Port Mach-Zehnder Interferometer (6p-MZI) constructed from two cascaded tritters, with two independent phase modulators placed between the tritter arms. We analytically derive the transfer matrix of the 6p-MZI and show how they organize into three symmetry classes, governed by the discrete Fourier transform (DFT) structure of the tritter and the conjugate relations. Furthermore, we analyze two input regimes: First, three indistinguishable single photons are injected into the tritter, and the output probability distributions P[111]P_{[111]}P[111]​, P[{300}]P_{[\{300\}]}P[{300}]​, and P[{210}]P_{[\{210\}]}P[{210}]​ are derived as functions of the two relative phases (φ1,φ2)(φ_1, φ_2)(φ1​,φ2​). At φ2=0φ_2 = 0φ2​=0, the single-phase limit is recovered, which confirms 100\% visibility of the even-distribution fringe. Second, a hybrid coherent-Fock input ∣α⟩1∣α⟩2∣1⟩3|α\rangle_1|α\rangle_2|1\rangle_3∣α⟩1​∣α⟩2​∣1⟩3​ is analyzed via the density matrix formalism. The average photon number at each output port exhibits amplitude-dependent phase shifts. Our results establish the 6p-MZI as a programmable platform for tripartite quantum state manipulation and coherent amplitude sensing.
Abstract We present the theoretical study of three-photon interference in the six ports Mach-Zehnder Interferometer (6p-MZI). The 6p-MZI consist of two lossless symmetrically balanced tritters and three independently controllable phase modulators inserted in each photon line path between the tritters. Three photons (Fock state) are injected onto the first tritter input ports and measured in second tritter output ports. By independently varying the phases states of the three photons, one can control the detection probability of photon numbers at final tritter output ports. The calculation results demonstrated that, at the specific combination of phase states, the three photons interference exhibited a coalescence phenomenon, which is the three-photons detected at the same output port. Interestingly, the probability of detecting photons in all combination modes of |0, 0, 3), |0, 3, 0〉, and |3, 0, 0〉 are monotonously in the equal values.
Abstract We present a theoretical study of the interferences between hybrid single-photon state, coherent state, and vacuum state in the designed medium of a six-ports Mach-Zehnder Interferometer (6p-MZI). The hybrid three different quantum states were simultaneously injected into the input ports of the interferometer. The derivation result demonstrated that the output state showed the statistical blend states among a substituted single-photon state, coherent state, and vacuum state. Interestingly, our calculation results attested that the maximum probability of detected photons at the individual interferometer output ports were significantly dependents on the amplitude of the inputted coherent state.
Based on heralded interference on a six-port Mach-Zehnder interferometer, we propose protocols to generate a series of multiphoton states in primary output port, by injecting a coherent state in primary input port and two Fock states in two ancillary input ports, and measuring two Fock states in two ancillary output ports. Only manipulating at the single-photon level (i.e, |0> or |1>) in all ancillary ports, we generate sixteen types (six categories) of multiphoton nonclassical states, whose state vectors are unified as superposition of a new coherent state, a single-photon added coherent state, and a two-photon added coherent state. Indeed, a wide range of nonclassical phenomena can be created by modulating the interaction parameters (including coherent field strength and shift phase). We mainly analyze quadrature-squeezing effects for all our considered states. Of particular interest is maximum squeezing of up to 2.57dB, with success probability 6.7%, at least in our present cases.
We examine the fourth-order interference properties of two photons at a lossless four-port optical device. The photon pair is represented by a joint single-photon wave-packet state with arbitrary spectral composition. We explicitly determine the coincidence probabilities at the output ports of a beam splitter and a Mach-Zehnder interferometer when the incident wave packet is described by a joint Gaussian spectral distribution and the two photons are incident one at each port of the device. For uncorrelated and distinguishable input photons, the fourth-order interference is readily understood in terms of the particle or wave behavior of each photon acting separately. On the other hand, highly correlated photon pairs, such as those generated from spontaneous parametric down-conversion, exhibit fourth-order interference effects at the output of the interferometer that depend expressly on the joint nature of the photon-pair wave packet, and cannot be described by the particle or wave behavior of either photon.