Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics

• URL: http://arxiv.org/abs/2408.04987v2
• Date: Wed, 12 Feb 2025 22:52:15 GMT
• Title: Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Authors: A. A. Lyublinskaya, P. A. Nosov, I. S. Burmistrov,
• Abstract summary: Correlated quantum many-body states can be created and controlled by the dissipative protocols. Number-conserving protocols are particularly appealing due to their ability to stabilize topologically nontrivial phases. We show that number-conserving protocols may not be a reliable universal tool for stabilizing dark states.
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• Abstract: Correlated quantum many-body states can be created and controlled by the dissipative protocols. Among these, particle number-conserving protocols are particularly appealing due to their ability to stabilize topologically nontrivial phases. Is there any fundamental limitation to their performance? We address this question by examining a general class of models involving a two-band fermion system subjected to dissipation designed to transfer fermions from the upper band to the lower band. By construction, these models have a guaranteed steady state - a dark state - with a completely filled lower band and an empty upper band. In the limit of weak dissipation, we derive equations governing the long-wavelength and long-time dynamics of the fermion densities and analyze them numerically. These equations belong to the Fisher-Kolmogorov-Petrovsky-Piskunov reaction-diffusion universality class. Our analysis reveals that the engineered dark state is generically unstable, giving way to a new steady state with a finite density of particles in the upper band. We also estimate the minimum system sizes required to observe this instability in finite systems. Our results suggest that number-conserving dissipative protocols may not be a reliable universal tool for stabilizing dark states.

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