C7N: Dynamical signatures of topological states in photon condensates

Julian Schmitt & David Luitz

New since July 2024

In the joint experimental and theoretical project C7N we study the dynamics of bosons in 1D lattices with topological properties induced by a coupling to the environment. Our main goal is to find dynamical signatures of topological states, which we prepare by spatially-controlled gain and loss in the system, as well as of exceptional points of the corresponding non-Hermitian Hamiltonian. We will pursue this goal by studying the dynamics of coupled Bose-Einstein condensates of photons in 1D chains of dye-filled microcavities, see Fig. 1. The project addresses central questions of the CRC-TR 185 concerning the generation, protection and measurement of topological states by coupling to reservoirs.
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We will search for signatures of the topological invariant in the open system by measuring coherent Bloch oscillations of wave packets, which are injected into the optical quantum gas system by a pulsed perturbation of the dye reservoir. We expect the experiments to reveal a geometric phase between topologically distinct lattices, equivalent to the Zak phase, that allows sampling the topological invariant of the bands. This approach will be complemented by measurements of the ensemble geometric phase for mixed states by investigating the counting statistics in the lattice.

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Using optical spectroscopy, in tandem with numerical solutions of simple theoretical models of the experimental setup by non-Hermitian Hamiltonians, we will search for experimental signatures of exceptional points in the complex-valued energy band structure and investigate their interplay with lattice disorder as well as their role for topological steady-state phases in the system, see Fig. 2. On the theory side, we will go one step beyond and also investigate the role of interactions for exceptional points in non-Hermitian systems. For this, we will focus on the mapping of the Lindbladian of bosonic models with gain, loss and dephasing to interacting non-Hermitian ladder Hamiltonians. The goal is to search for many-body exceptional points and their experimental signature. We will furthermore investigate the role of symmetries for the abundance and stability of many-body exceptional points.