Non-Hermitian dynamics in a driven-dissipative and spatially correlated light-matter system
Pure quantum states, as described in quantum mechanics textbooks, are ideal representations inevitably deteriorated in real systems by any dissipative connection to the environment. In this work we derive a unified theoretical frame to study the non-Hermitian dynamics of a driven-dissipative quantum system and validate it by comparison to experimental data of matter-wave diffraction. To highlight the role of dissipation, we perform the comparison in a near-resonant regime of light-matter interaction, where perturbative approaches fail. Here, we show that the developed formalism enables both exact simulations and an intuitive interpretation based on modal analysis. The theoretical analysis is based on the general master equation description of driven-dissipative systems, from which we derive an effective complex potential $V_\mathrm{eff}(\Omega,\Delta)$ that depends on control parameters such as the amplitude and detuning of the light matter interaction. Experimentally, we drive a $^{87}$Rb BEC near resonance using periodic excited-state engineering, mapping the spatially modulated $V_{\rm eff}[\Omega,\Delta(x)]$ into momentum space for precise quantification. The experimental results agree with numerical simulations of the master equation and demonstrate the interplay between coherent drive and dissipation, with an exceptional signature: a reduced decay rate with increasing drive. Such dynamics is then interpreted by a modal analysis of the non-Hermitian Hamiltonian $H_\mathrm{eff}=p^2/2m+V_\mathrm{eff}$ which provide an intuitive and qualitative explanation for such driven-dissipative system.