Speaker
Description
The non-equilibrium response of many-body quantum systems to time-dependent driving remains a central frontier in modern physics, with profound implications for quantum simulator architectures such as superconducting circuits. A primary challenge in these platforms is the preparation of highly correlated states through quantum phase transitions (QPTs), where the unavoidable critical slowing down forces a breakdown of the adiabatic regime. The Kibble-Zurek mechanism (KZM) provides a cornerstone framework for predicting defect formation in such dynamics. While Markovian dissipation typically compromises universal scaling due to the competition between extrinsic noise, internal relaxation, and quench dynamics, the impact of non-Markovian memory remains largely unexplored.
In this work, we investigate the validity of the KZM in the Open Quantum Rabi Model (OQRM) coupled to a non-Markovian Ohmic bath. Notably, this model has been simulated in the deep strong coupling regime using a quantum circuit with flux qubits. The dynamics is governed by the Hamiltonian $H = H_{\text{Q-O}} + H_I$, with $H_{\text{Q-O}} = -\frac{\Delta}{2}\sigma_{x} + \omega_{0} a^{\dagger}a + g\sigma_{z}(a^{\dagger}+a)$. The term $H_I = \sum_{i} \left[ \frac{p_i^2}{2M_i} + \frac{k_i(x-x_i)^2}{2} \right]$ accounts for a bath of harmonic oscillators coupled to the resonator coordinate $x = \sqrt{1/2m\omega_0}(a+a^\dagger)$.
Using advanced Matrix Product State simulations (DMRG and TDVP), we demonstrate that environmental memory induces a Berezinskii-Kosterlitz-Thouless (BKT) transition. This criticality is dynamically witnessed by the equilibrium relaxation time $\tau$, which follows the scaling behavior $\tau(g) \propto \exp\left(\frac{B}{\sqrt{|g-g_{c}|}}\right)$. By implementing linear quenches across the critical point, we show that the excitation energy $E_{\text{exc}}$ evaluated at the exact freeze-out time $t_{f}$ reveals a robust universal power-law scaling $E_{\text{exc}} \propto t_f^{-\mu}$.
Crucially, since the non-Markovian bath redefines the underlying universality class, dissipation does not inherently compete with adiabatic dynamics. The non-equilibrium response is accurately captured by a renormalized two-level framework, establishing the KZM as a reliable probe of criticality in open quantum systems.