# Photonic Loschmidt echo in binary waveguide lattices

## TL;DR

This paper demonstrates that a photonic Loschmidt echo can be observed in binary waveguide lattices by exchanging sublattices, avoiding the need to reverse the Hamiltonian, thus providing a new way to study time reversal in optical systems.

## Contribution

It introduces a method to observe Loschmidt echo in photonic systems through sublattice exchange, bypassing Hamiltonian reversal, which is novel in optical waveguide research.

## Key findings

- Loschmidt echo observed in binary waveguide lattices.
- Exchange of sublattices induces time reversal effects.
- Applicable to single photon and NOON states in 1D and 2D lattices.

## Abstract

Time reversal is one of the most intriguing yet elusive wave phenomenon of major interest in different areas of classical and quantum physics. Time reversal requires in principle to flip the sign of the Hamiltonian of the system, leading to a revival of the initial state (Loschmidt echo). Here it is shown that Loschmidt echo of photons can be observed in an optical setting without resorting to reversal of the Hamiltonian. We consider photonic propagation in a binary waveguide lattice and show that, by exchanging the two sublattices after some propagation distance, a Loschmidt echo can be observed. Examples of Loschmidt echoes for single photon and NOON states are given in one- and two-dimensional waveguide lattices.