Non-equilibrium quantum systems host a plethora of topological phenomena. A topological property of quantum dynamics can be related to the effective dimensional extension of the system by time-periodic drives. Following this line of reasoning, it has been shown that a two-level system coupled to two circularly polarized drives can mediate a frequency conversion between the two fields that happens at a topologically quantized rate [1]. In this talk, we will address two types of questions that naturally arise for this kind of quantum system.

The first is whether interaction can change the topological features in the dynamically-induced synthetic dimension. We positively answer this question by adding spin-spin interactions to the prototypical model of the topological frequency converter [2]. We demonstrate that the interplay of interaction and synthetic dimension gives rise to striking topological phenomena that have no counterpart in the non-interacting regime. Remarkably, these features already appear for the minimal case of two interacting spins, and can result into an enhancement of frequency conversion as a direct manifestation of the correlated topological response.

Given a realization of the topological frequency converter by an externally driven spin qubit, the second question that arises is how environmental effects may affect the dynamical topological response. By studying a quasiperiodically driven central spin model, we demonstrate that the coupling to the surrounding (nuclear) spin bath can lead to an amplification of the frequency conversion that is proportional to the number of (nuclear) spins of the host material.

[1] I. Martin, G. Refael, and B. Halperin, Phys. Rev. X 7, 041008 (2017).

[2] S. Körber, L. Privitera, J. C. Budich, and B. Trauzettel, Phys. Rev. Research 2, 022023(R) (2020).