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.
Multi-photon interference is the foundation of many applications regarding quantum technologies. Notably, the interference of multiple photons, registered using resolved measurements, is related to the permanent of a matrix, a problem known to be a #P-hard task. Traditionally, achieving high-visibility interference requires a high degree of indistinguishability between the interfering photons. However, this restriction can be circumvented by observing interference in the conjugate variables. This method has been successfully demonstrated using resolved measurements in the temporal and frequency domain. In this work, we extend these approaches to the spatial degrees of freedom of light. Theoretically, we demonstrate that the joint probability of detecting two photons at different positions in the output ports (3 and 4) of a beam-splitter is indeed determined by the permanent of a matrix related to the unitary transformation described by the interferometer. From an experimental perspective, we present experimental results for spatially-resolved interference in position for photons that are distinguishable in transverse momentum. We employ a setup to perform spatially-resolved measurements on photons with an adjustable distinguishability in both the central transverse momentum variable and the lateral displacement from the optical axis. This setup provides full simultaneous tunability over the distinguishability in the spatial variables. Additionally, by varying the lateral displacement, we observe how distinguishability in the position impacts the interference pattern. Overall, our results align well with the theoretical model, reinforcing the validity of our approach. Thus, this work offers new insights into the available degrees of freedom for studying of multi-photonic interference and its applications.
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary
nsnp×nsnp unitary matrix on the state of light in
ns spatial and
np internal modes. I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations. I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU
(n) basis states, which reduce the canonical subgroup chain, for arbitrary
n. The boson realizations are employed to construct
D-functions, which are the matrix elements of arbitrary irreducible representations, of SU
(n) in the canonical basis. I show that immanants of principal submatrices of a unitary matrix
T are a sum of the diagonal
D(Ω)-functions of group element
Ω over
t determined by the choice of submatrix and over the irrep
(λ) determined by the immanant under consideration. The algorithm for
SU(n) D-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.
Multiphoton interference is crucial to many photonic quantum technologies. In particular, interference forms the basis of optical quantum information processing platforms and can lead to significant computational advantages. It is therefore interesting to study the interference arising from various states of light in large interferometric networks. Here, we implement a quantum walk in a highly stable, low-loss, multiport interferometer with up to 24 ultrafast time bins. This time-bin interferometer comprises a sequence of birefringent crystals which produce pulses separated by 4.3\,ps, all along a single optical axis. Ultrafast Kerr gating in an optical fiber is employed to time-demultiplex the output from the quantum walk. We measure one-, two-, and three-photon interference arising from various input state combinations, including a heralded single-photon state, a thermal state, and an attenuated coherent state at one or more input ports. Our results demonstrate that ultrafast time bins are a promising platform to observe large-scale multiphoton interference.
Multiphoton interference is crucial to many photonic quantum technologies. In particular, interference forms the basis of optical quantum information processing platforms and can lead to significant computational advantages. It is therefore interesting to study the interference arising from various states of light in large interferometric networks. Here, we implement a quantum walk in a highly stable, low-loss, multiport interferometer with up to 12 ultrafast time bins. This time-bin interferometer comprises a sequence of birefringent crystals that produce pulses separated by 4.3 ps, all along a single optical axis. Ultrafast Kerr gating in an optical fiber is employed to time-demultiplex the output from the quantum walk. We measure one-, two-, and three-photon output states arising from various input state combinations, including a heralded single-photon state, a thermal state, and an attenuated coherent state at one or more input ports. Our results demonstrate that ultrafast time bins are a promising platform to observe large-scale multiphoton interference.