Multiphoton synthetic lattices in multiport waveguide arrays: synthetic atoms and Fock graphs

Abstract

Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems’ apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multiphoton states through multiport waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multiphoton interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multiphoton states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of N photons propagating through M nearest-neighbor coupled waveguides. In the regime where N ≥ 2 and M ≥ 3 , nonlocal coupling in Fock space gives rise to hitherto unknown all-optical dark states that display intriguing nontrivial dynamics.

A new concept for design of photonic integrated circuits with the ultimate density and low loss

“…In all cases of bunching, the non-classical correlations were confirmed by observing the violation of the Bell-like inequality [38]. Further scaling in the number of undistinguishable photons at the input leads to the parallelisation of quantum random walks, representable by synthetic lattices in the photon-number space [39].…”

Branching high-order exceptional points in non-hermitian optical systems

“…To illustrate the photon dynamics in the projected N -photon subspace, in Fig. (4) we depict the effective N -photon Hamiltonians as Fock graphs [39], where the nodes represent the Fock states |n 1 , . .…”

“…(4-a) there are three Fock states, |1, 1, 0 , |0, 2, 0 and |0, 1, 1 , which are subjected to dissipation and |0, 2, 0 experiences twice the losses, since both photons reside in the dissipative waveguide. Further, since the photons do not interact, the eigenvalues λ (N ) n1,...,nM = M m=1 n m λ m of the Hamiltonian in the Nphoton subspace are given by sums of the single-photon eigenvalues λ m [39]. This leads to an enhanced degeneracy of the N -photon eigenvalues and a large number of coalescent N -photon eigenmodes, which ultimately gives rise to higher order exceptional points as illustrated in the bottom panels of Fig.…”

“…(4-b,c) where the arising Fock graphs are non-planar, i.e., they cannot be drawn in 2D without intersecting edges, and it is thus truly impossible to implement them for single photons in real space via coupled waveguides. Rather, they can only be realized in synthetic space via multiphoton excitations [39]. Additionally, these synthetic structures feature a highly non-trivial distribution of high-and low-loss sites, which are nevertheless perfectly tuned to obtain the higher-order EPs.…”

Multiphoton processes via conditional measurements in the two-field interaction

“…In this technique, the heralded subtraction of photons from two-mode squeezed vacuum states (TMSVS) gives rise to the generation of a family of correlated photon-subtracted TMSVS with a broad range of mean photon numbers and degrees of correlation [19,20]. Remarkably, this type of photon sources have shown to play an important role in the development of novel multiphoton integrated-optics protocols [21,22], as well as in quantum-enhanced spectroscopy [23], and metrology applications [24,25,26].…”