Abstract
What is the role of topology in the propagation of quantum light in photonic lattices? We address this question by studying the propagation of squeezed states in a topological one-dimensional waveguide array, benchmarking our results with those for a topologically trivial localized state, and studying their robustness against disorder. Specifically, we study photon statistics, one-mode and two-mode squeezing, and entanglement generation when the localized state is excited with squeezed light. These quantum properties inherit the shape of the localized state but, more interestingly, and unlike in the topologically trivial case, we find that propagation of squeezed light in a topologically protected state robustly preserves the phase of the squeezed quadrature as the system evolves. We show how this latter topological advantage can be harnessed for quantum information protocols.
Highlights
During the last decades, a series of discoveries illuminated a way where topological arguments allowed to explain or envision the behavior of electrons in materials [1,2,3,4,5]
Topology has been found to provide robustness in lasers [32, 33] and amplifiers [34, 35], while coupling between quantum states of light and topological degrees of freedom allows for topological protection of photon statistics and quantum correlation [36]
We present a thorough report on the propagation of squeezed light in a topological photonic lattice, and the effects of topology on quantum features of light1
Summary
The SSH system consists of a one dimensional dimerized chain of identical modes, with a uniform onsite term β across the entire lattice and alternating hopping amplitudes u and v, described by the hamiltonian. The system presents a bulk bandgap of |u − v|, exponentially localized states with a propagation constant equal to that of the bare waveguides and perfect sublattice polarization appear at the edge of a finite lattice terminated in a weak coupling. These states are topologically protected by chiral symmetry [63], which is broken by onsite terms differing on each sublattice or couplings between sites of the same sublattice for example. In contrast to the topological edge state, the impurity induced one does not present any symmetry protected properties, so its propagation constant and spatial distribution will vary upon any type of disorder present in the lattice
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