Non-stationary coherent quantum many-body dynamics through dissipation (1804.06744v2)

Abstract: The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

• The paper demonstrates that non-stationary many-body quantum systems can exhibit sustained oscillations under dissipation using the Lindblad formalism.
• The methodology classifies asymptotic Liouvillian subspaces, bridging multi-block structures with decoherence-free subspaces, and is supported by numerical analysis.
• The findings have practical implications for quantum synchronization and systems design in quantum technologies such as simulators and quantum computers.

Non-Stationary Coherent Quantum Many-Body Dynamics Through Dissipation

The paper "Non-stationary coherent quantum many-body dynamics through dissipation" addresses a significant topic in quantum mechanics, namely the paper of non-stationary dynamics in many-body quantum systems subject to dissipation. The authors investigate such dynamics utilizing the formalism of open quantum systems and employing the Lindblad master equation to encompass both coherent and dissipative processes. A central theme of the work is the exploration of conditions under which quantum many-body systems exhibit sustained oscillatory behaviors rather than relaxing to a stationary state, which is of interest for both theoretical understanding and potential applications in quantum technologies.

The authors begin by revisiting the Lindblad equation, working with cases where the eigenvalues of the Liouvillian are purely imaginary, a scenario indicative of oscillating coherences or limit cycles. This formalism is employed to construct many-body quantum synchronization processes, bridging known results with their new findings. A notable contribution is the classification of asymptotic subspaces of the Liouvillian, drawing parallels between the multi-block structures identified and decoherence-free subspaces known in literature. Unlike decoherence-free subspaces, which remain unaffected by dissipation and evolve deterministically, multi-block structures are influenced by dissipation and generally involve mixed states due to the dynamics.

Further insight is gained by extending the scope beyond the Markovian framework, analyzing systems with total Hamiltonians incorporating system-bath interactions. The authors emphasize the implications of such arrangements for sustained non-equilibrium dynamics and provide novel theorems that enrich the understanding of decoherence-free many-body subspaces and general complex coherent dynamics under dissipation. Notably, they derive conditions under which non-trivial operators can give rise to states with purely imaginary eigenvalues, offering a structured approach to identifying and characterizing these dynamical subspaces.

The implications of this research are manifold. Theoretically, it advances understanding of quantum synchronization and the complex interplay between coherence, dissipation, and many-body interactions. Practically, it has potential consequences for the design and control of quantum systems, such as quantum computers or simulators, that leverage these dynamical properties for enhanced performance or resilience to decoherence.

The paper explores these ideas in several contexts, including decoherence-free subspaces in the XXZ spin chain and multi-block structures in the Hubbard model. Numerical results from exact diagonalization supplement the theoretical insights, reflecting on phenomena like Bethe strings and the incommensurate nature of spectra in thermodynamic limits. The analysis of the XXZ spin chain highlights the impact of system size and interactions, and elucidates conditions under which persistent oscillations arise. The Hubbard model examples extend the discussion to scenarios featuring transport phenomena and spin dephasing, broadening the relevance of their findings.

Future work could explore the robustness of these dynamical features to perturbations such as additional Lindblad operators or deviations from idealized conditions. The pursuit of experimental verifications is a logical subsequent step, with ultracold atoms in optical lattices identified as a promising platform for realizing and testing these theoretical predictions. The paper outlines potential implementations using current experimental setups capable of emulating the Hubbard model and facilitating controlled dissipation, thereby paving the way for experimental validation and further exploration of these complex quantum dynamics.