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Journal of the Optical Society of America B

Quantum analysis of a Mach–Zehnder interferometer with propagating a single photon Gaussian wave packet

Siddharth Singh, Rohan Katti

Published Jan 2, 2024• 3 citations
Publisher

Abstract

In this paper, a Mach–Zehnder interferometer is analyzed with a single photon Gaussian wave packet at one of its input ports and vacuum state at the other input port. Various noises arising in the Mach–Zehnder interferometer such as photon flux noise and quadrature noise are mathematically analyzed. The effect of variation in device parameters on the power spectral density at the output ports of the Mach–Zehnder interferometer is studied. It is observed that the power spectral density of photon flux noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of phase shift, whereas the power spectral density of quadrature noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of frequency of a single photon wave packet and the phase shift. The analysis carried out in this paper will be helpful in understanding the quantum fluctuations in the design of quantum logic devices and circuits where the Mach–Zehnder interferometer is a core building block.

DOI
10.1364/josab.498566

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In this paper, a Mach–Zehnder interferometer is analyzed with a single photon Gaussian wave packet at one of its input ports and vacuum state at the other input port. Various noises arising in the Mach–Zehnder interferometer such as photon flux noise and quadrature noise are mathematically analyzed. The effect of variation in device parameters on the power spectral density at the output ports of the Mach–Zehnder interferometer is studied. It is observed that the power spectral density of photon flux noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of phase shift, whereas the power spectral density of quadrature noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of frequency of a single photon wave packet and the phase shift. The analysis carried out in this paper will be helpful in understanding the quantum fluctuations in the design of quantum logic devices and circuits where the Mach–Zehnder interferometer is a core building block.
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.
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.
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.
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.
Photon statistics effects are analyzed for Mach-Zehnder and Michelson interferometers in which a strong coherent state is inserted into one input port and a squeezed vacuum is inserted in the other input port. We study the effects related to entanglement, for the general case, by using Zassenhaus's perturbation theory as a function of the squeezing parameter. For the special case in which the strong coherent state exits fully through one output port while the squeezed vacuum exits through the other “dark” output port, the Lie group disentangling method is used. For this case we show that the signal can be amplified with sub-Poissonian photon statistics.