This study presents a theoretical investigation into the interference properties of three photons in a six-port optical beam splitter, commonly referred to as a tritter. We examine various configurations of the relative phase differences among the input photons. Our findings reveal that fully constructive interference periodically occurs at a single output port for specific constant phase differences, while fully destructive interference simultaneously manifests at the remaining two output ports. These distinctive interference patterns arise across a wide range of specific phase difference combinations among the input photons. We suggest that these unique interference characteristics provide new insights into the potential implementation of a three-party quantum key distribution protocol. Such three-photon interference phenomena are crucial for facilitating symmetric secure key distribution among three parties.
This study presents a theoretical investigation into the interference properties of three photons in a six-port optical beam splitter, commonly referred to as a tritter. We examine various configurations of the relative phase differences among the input photons. Our findings reveal that fully constructive interference periodically occurs at a single output port for specific constant phase differences, while fully destructive interference simultaneously manifests at the remaining two output ports. These distinctive interference patterns arise across a wide range of specific phase difference combinations among the input photons. We suggest that these unique interference characteristics provide new insights into the potential implementation of a three-party quantum key distribution protocol. Such three-photon interference phenomena are crucial for facilitating symmetric secure key distribution among three parties.
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) at the input ports. When ∣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 radians relative to the extreme interference pattern of output port 3 at 5π/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.
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.
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[{300}], and P[{210}] are derived as functions of the two relative phases (φ1,φ2). At φ2=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 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.
The main features of quantum mechanics reside in interference deriving from the superposition of different quantum states. While current quantum optical technology enables two-photon interference both in bulk and integrated systems, simultaneous interference of more than two particles, leading to richer quantum phenomena, is still a challenging task. Here we report the experimental observation of three-photon interference in an integrated three-port directional coupler realized by ultrafast laser writing. By exploiting the capability of this technique to produce three-dimensional structures, we realized and tested in the quantum regime a three-port beam splitter, namely a tritter, which allowed us to observe bosonic coalescence of three photons. These results open new important perspectives in many areas of quantum information, such as fundamental tests of quantum mechanics with increasing number of photons, quantum state engineering, quantum sensing and quantum simulation. For the development and application of quantum technologies, devices capable of implementing more than two-photon processes are vital. Towards this aim, Spagnolo et al.build a three-port beam splitter and demonstrate mutual interference between the three photons.
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.
Summary form only given. The main features of quantum mechanics reside into interference deriving from the superposition of different quantum objects. The Hong-Ou-Mandel effect is a purely quantum phenomenon deriving from the interference of two photons. It is a consequence of the bosonic nature of light and can be observed when two identical photons impinge simultaneously on a two-port balanced beam splitter and, as a result, both are forced to exit from the same port. While current quantum optical technology enables two-photon interference both in bulk and integrated systems, simultaneous interference of more than two particles, leading to richer quantum phenomena, is still a challenging task.The emergence of integrated quantum photonics have opened exciting perspectives for the realization of scalable, miniaturized and intrinsically stable optical setups. In particular, the ultrafast laser-writing technique has proved to be a powerful tool for demonstrating new quantum integrated-optics devices, able to perform quantum logic operations as well as two-photon quantum walks. Here we report the experimental observation of threephoton interference in an integrated three-port directional coupler realized by ultrafast laser-writing. By exploiting the capability of this technique to produce three-dimensional structures, we realized and tested in the quantum regime a three-photon beam splitter, namely a tritter, which allowed us to observe bosonic coalescence of three photons [1]. Such a system can be exploited as a building block to implement a generalized class of multi-arm interferometers. We introduce the concept of 3D multi-photon interferometry [2], and we discuss their application in the context of quantum interferometry and quantum phase estimation. We propose novel geometries for integrated multi-arm interferometers based on three-port (tritter) and four-port (quarter) devices, and we discuss possible measurement protocols, based on the injection of multi-photon Fock states in this kind of multi-port devices, demonstrating relevant metrological advantages in phase-estimation tasks. Furthermore, we provide a first insight on the application of this technology in the still unexplored field of multiparameter estimation.Several other contexts may benefit from the adoption of 3-dimensional integrated interferometers realized by femtosecond laser-writing. For instance, they can be adopted for the realization of “proof-of-principle” quantum simulators [3], and, combined in a modular structure, they can be used to realize full-scale quantum simulators for large size quantum systems. The adoption of multiphoton-multimode platforms may indeed disclose the “hardto-simulate” scenario by adopting linear optics to implement a computational power beyond the one of a classical computer.