Discrete Time-Crystals Achieve Coexistence of Distinct Orders in Driven Systems

The quest to create materials that break time-translation symmetry has led scientists to explore exotic states of matter known as discrete time crystals. Shashank Mishra and Sayan Choudhury, both from the Harish-Chandra Research Institute, now demonstrate a pathway to engineer multiple, distinct time-crystalline orders within a single system. Their work reveals that carefully controlling the way a system is driven allows for the coexistence of these different temporal phases in spatially separated regions, resulting in a material that responds with varying frequencies depending on location. This achievement establishes spatially structured driving as a powerful technique for creating and controlling novel forms of time-crystalline order, potentially opening doors to new technologies based on precise temporal control at the quantum level.

A drive protocol allows for the realisation of distinct dynamical topological charge (DTC) orders in different spatial regions of the system, resulting in spatially varying sub-harmonic responses with distinct frequencies. The team employs a semi-classical analysis to establish the stability of these co-existing DTC orders in the thermodynamic limit, and further establishes their stability in the presence of quantum fluctuations. The results demonstrate spatially structured driving as a powerful route to engineer novel forms of time-crystalline order.

Discrete Time Crystals Realized and Characterized

The field of discrete time crystals, or DTCs, is rapidly advancing, with research focusing on their realization, properties, and potential applications in quantum systems. DTCs are non-equilibrium phases of matter exhibiting periodic behavior in time, even without continuous external driving, breaking time-translation symmetry. Investigations explore mechanisms to create and stabilize DTCs, including Floquet systems utilizing periodic driving, many-body localization protecting against decay, quantum scars resisting thermalization, and Hilbert space fragmentation creating disconnected regions. The Lipkin-Meshkov-Glick model serves as a widely used theoretical framework for studying many-body quantum systems and investigating DTCs.

Researchers also explore central spin models, Rydberg atom arrays, quantum processors using superconducting qubits, and trapped ions as experimental platforms for realizing and observing DTCs. Related phenomena, such as entanglement steering, many-body localization, quantum scars, fractal time crystals, chimera states, and quasi-discrete time crystals, are also under investigation. Current research demonstrates multiple routes to DTCs and emphasizes the importance of protection mechanisms like many-body localization and quantum scars. Experimental progress has been made using Rydberg atom arrays and superconducting qubits, and connections to other exotic quantum phases are being explored. DTCs hold potential for applications in quantum metrology, quantum information processing, and fundamental studies of non-equilibrium quantum systems.

Coexisting Discrete Time Crystals Demonstrated in Model

Scientists have demonstrated the emergence of distinct discrete time crystals within the Lipkin-Meshkov-Glick model, achieved through spatially nonuniform periodic driving. This breakthrough reveals that carefully tailored drive protocols can realize different time-crystalline orders in separate spatial regions, resulting in sub-harmonic responses with distinct frequencies. This co-existence of time-crystalline phases represents a temporal analog of equilibrium phase coexistence, opening new avenues for exploring symmetry breaking in driven quantum systems. The team established the stability of these co-existing discrete time crystals in the thermodynamic limit and confirmed their resilience to perturbations, even in the presence of quantum fluctuations.

Calculations of the decorrelator and fidelity out-of-time-order correlator validated the approach and confirmed the accuracy of the method. Experiments reveal a complex stability landscape, demonstrating the ability to engineer novel forms of time-crystalline order through spatially structured driving. This work establishes spatially nonuniform driving as a powerful route to engineer novel forms of time-crystalline order and explore the interplay between spatial inhomogeneity and temporal symmetry breaking in driven quantum systems.

Discrete Time Crystals Coexist Spatially

This research demonstrates the emergence of spatially distinct discrete time crystals within a single, globally coupled system subjected to spatially varying periodic driving. Carefully designed driving protocols enable the realization of different time-crystalline orders in separate regions, resulting in sub-harmonic responses with differing frequencies. This represents a new form of nonequilibrium phase coexistence, analogous to the stable coexistence of water and ice, where multiple ordered phases maintain distinct internal structures while in contact. Researchers confirmed that this coexistence is not simply a harmonic component of a single, higher-period phase, but rather reflects genuinely distinct dynamical phases. Beyond coexisting time crystals, the study also identified regions where time-crystalline order coexists with a synchronized, period-T state, creating chimera-like dynamics within the system. The findings highlight spatially structured driving as a powerful method for engineering complex temporal order and expand the understanding of prethermal Floquet systems, with potential applications in platforms such as trapped ions and cavity-mediated spin ensembles.