Dynamical Phase Transitions Speed up Pontus-Mpemba Effects in Open Systems

The seemingly counterintuitive Pontus-Mpemba effect, where warmer water can sometimes freeze faster than cooler water, continues to fascinate scientists, and a new study sheds light on how to dramatically speed up this process. Andrea Nava, Reinhold Egger, Bidyut Dey, and Domenico Giuliano, researchers from Heinrich-Heine-Universität Düsseldorf, I. N. F. N. Cosenza, and Universitá della Calabria, demonstrate that systems undergoing specific dynamical phase transitions offer highly efficient pathways to achieve this effect. Their work reveals that the speed-up in reaching a desired frozen state is linked to a prolonged period of stability before the transition occurs, offering a potential method for optimising freezing protocols and broadening applications beyond simple water cooling. This discovery provides a fundamental understanding of how to manipulate the conditions for rapid freezing, potentially impacting fields from cryopreservation to materials science.

The acceleration of relaxation toward a designated target state is linked to the existence of a prolonged metastable period preceding the transition, establishing a connection between non-equilibrium relaxation and the underlying dynamics of these systems. Manipulating the system’s environment can significantly accelerate relaxation, offering potential applications in quantum technologies and control, specifically faster state preparation and manipulation.

Dynamical phase transitions (DPTs) can be systematically exploited to optimise quantum protocols. As an example, the team studies one-dimensional interacting lattice fermions undergoing a Peierls transition, illustrating the connection between DPTs and quantum Mpemba effects. Classical and quantum Mpemba effects are counterintuitive, non-equilibrium relaxation phenomena occurring after rapid changes in system parameters, attracting considerable attention due to their potential for speeding up relaxation processes and optimising quantum protocols like state preparation and cooling schemes.

Quantum Speedup via Environmental Interactions

This research investigates how open quantum systems interact with their environment and how this impacts the quantum Mpemba effect, where a system reaches equilibrium faster under specific conditions. Employing the Gross-Neveu model and the Lindblad master equation, the team explored how dissipation affects relaxation dynamics and can be harnessed to achieve faster relaxation rates. The research reveals that dissipation can induce dynamical phase transitions and identifies conditions under which the quantum Mpemba effect occurs. The team found that the effect is related to the system’s ability to bypass energy barriers due to dissipation, offering a pathway to faster relaxation. They highlight that conventional Mpemba effects, relying on initial distance from equilibrium, are often limited by the system becoming trapped during phase transitions. The study proposes that a ‘polarised Mpemba effect’, leveraging efficient navigation of phase transitions, is a more promising approach for achieving faster relaxation.

Shortcut to Quantum State Relaxation via DPTs

This research demonstrates that dynamical phase transitions (DPTs) in open quantum systems can be harnessed to create efficient protocols for achieving a quantum version of the Mpemba effect, where a system relaxes to a target state more quickly under specific conditions. While DPTs can initially slow down relaxation due to extended metastable regions, carefully designed two-step protocols can circumvent these regions and significantly accelerate the process. This is achieved by guiding the system through an intermediate state that avoids direct traversal of the DPT, effectively creating a shortcut to the target state. The findings are supported by analysis of a one-dimensional interacting fermion model undergoing a Peierls transition, suggesting the principle applies broadly to other open quantum systems exhibiting DPTs. The authors acknowledge that extended metastable regions associated with DPTs can hinder simple, single-step Mpemba protocols, and future work could explore the optimization of multi-step protocols and their applicability to a wider range of physical systems.