Synthesizing a structured environment in a parametrically driven resonator

We present and analyze a straightforward method to realize the dynamics of a quantum system in contact with a structured environment (having an adjustable spectral density). Interesting effects can arise for a nontrivial structured environment, including partial decays, revivals, and engineered steady-states. These effects may be especially important for systems where topological robustness can be compromised depending on the character of the structured environment [1]. Our approach takes advantage of methods for band-structure engineering in a parametrically driven resonator, leading to an effective model with a near-arbitrary energy-momentum relation [2, 3]. This allows a single resonator to realize a modular element that emulates an environment having a near-arbitrary density of states. In the quantum limit, this method can be used to create an effective environment coupled to qubits for applications in quantum simulation or bath engineering. We will show how to implement this method in optical fiber-loop resonators, which are especially well suited for this application as the salient effects can already be observed with classical light, emulating the effective quantum dynamics.

[1] A. Ricottone, et al., Topological transition of a non-Markovian dissipative quantum walk Phys. Rev. A 102, 012215 (2020).

[2] A. Dutt, et al. Experimental band structure spectroscopy along a synthetic dimension Nat. Commun. 10, 3122 (2019).

[3] F. Pellerin, et al., Wave-Function Tomography of Topological Dimer Chains Phys. Rev. Lett. 132, 183802 (2024).