Discrete-Time Crystals

Time Crystals, a novel phase of matter formed through the spontaneous breaking of temporal symmetry, exhibit robust subharmonic oscillations that persist despite imperfections. These unique properties, arising from many-body interactions, collective synchronization, and broken ergodicity, challenge our fundamental understanding of physics and offer promising applications in quantum computing, sensing, and, potentially, energy storage.

Among the different types of time crystals, Discrete Time Crystals (DTCs) arise in periodically driven systems, characterized by subharmonic frequency oscillations. While dissipation can stabilize DTCs in some regimes, incoherent noise can disrupt their long-term temporal order. This dual role of environmental interactions necessitates a deeper understanding of how DTCs respond to decoherence and how their crystalline order can be preserved.

This project focuses on evaluating the fragility of DTCs to a wide range of noise profiles and developing strategies to mitigate the effects of decoherence. Key objectives include:

• Fragility Analysis: Assessing the susceptibility of DTCs to various decoherence mechanisms and noise profiles.
• Mitigation Strategies: Designing and testing innovative protocols to enhance the robustness of DTCs against environmental perturbations.

To achieve these goals, the project employs state-of-the-art computational methodologies, including exact diagonalization for characterizing small systems, tensor networks and density matrix renormalization group (DMRG) techniques for simulating one-dimensional many-body systems, time-dependent variational principle (TDVP) techniques for real-time dynamics, and quantum trajectory methods for modeling open quantum systems under stochastic noise.

By addressing the challenges of decoherence and stabilizing DTCs, this research aims to unlock their potential for practical quantum technological applications, advancing our understanding of non-equilibrium quantum systems.