Floquet Recurrences in Double Kicked Tops Demonstrate Periodicity for and Values, Revealing Dynamical Phase Transitions

The behaviour of driven quantum systems presents a fundamental challenge in physics, and recent work by Avadhut V. Purohit and Udaysinh T. Bhosale, both from Visvesvaraya National Institute of Technology, Nagpur, sheds new light on this area through the study of the double kicked top. This research investigates how precisely controlled, repetitive ‘kicks’ influence the system’s evolution, revealing exact periodicities in its behaviour that depend on the strength of these driving forces. The team demonstrates that these recurrences, independent of system size, allow for a smooth transition between predictable and chaotic dynamics, offering a novel method for controlling quantum systems. This ability to tune between regular and chaotic regimes makes the double kicked top a potentially valuable platform for developing advanced technologies in quantum control and information processing.

Robust Quantum Recurrences in Driven Tops

Scientists have investigated exact quantum recurrences within the double kicked top, a driven spin model extending the well-studied quantum kicked top. By reformulating the system’s dynamics using effective parameters, they analytically demonstrate that the double kicked top exhibits robust recurrences at specific times, even with strong driving forces. These recurrences arise from the interplay between the two kicks and the fundamental quantum nature of the system, resulting in a predictable return to the initial state. This analysis reveals that recurrence times are sensitive to the driving parameters, offering a means to control and manipulate the system’s behaviour.

The research shows that the Floquet operator, which describes the system’s time evolution, exhibits exact periodicity for specific parameter values. These recurrences occur when the driving parameter equals integer or half-odd integer multiples of π/2 or π/4, independent of a phase parameter. Analysis of the system’s energy levels demonstrates a smooth transition from predictable, integrable behaviour to chaotic, non-integrable dynamics as the driving parameters are adjusted. This work establishes that regular and chaotic regimes can be controlled in systems of any size by tuning the driving parameters, characterizing the behaviour of the driven kicked top.

Floquet Periodicity in Double-Kicked Quantum Tops

Researchers have thoroughly investigated the periodicity of the Floquet operator in the double-kicked top, a quantum system with rotational symmetry subjected to repeated driving forces. The Floquet operator describes how the quantum state of the top evolves over time with each driving force, or ‘kick’. Scientists explored how many kicks it takes for the system to return to its initial state, or a state equivalent under rotation, analysing this behaviour for different kick strengths and initial conditions. The key finding is that the system exhibits predictable periodicity, with the number of kicks required for periodicity dependent on the system’s angular momentum and the kick strength.

The research demonstrates that the system returns to its initial state after a specific number of kicks, exhibiting periodicity in its evolution. This periodicity occurs when the driving parameter equals integer or half-odd integer multiples of π/2 or π/4, with the system returning to its initial state after 6 or 12 kicks respectively. Importantly, this periodicity is independent of the phase of the kick, indicating a robust behaviour unaffected by small changes in initial conditions.

Recurrence, Entanglement and Quantum Phase Transitions

Scientists have conducted a comprehensive investigation of the double kicked top, a spin model exhibiting exact recurrences in its dynamics. Through analytical calculations, they demonstrate that the Floquet operator, which governs the system’s time evolution, displays precise periodicity for specific parameter values, independent of a symmetry-breaking parameter. These recurrences, observed for both integer and half-odd integer spin values, reveal a predictable return to initial conditions regardless of the symmetry-breaking strength. The study further explores entanglement dynamics and identifies dynamical quantum phase transitions, exhibiting distinct behaviour depending on the system’s time-reversal symmetry.

Importantly, the researchers demonstrate that the double kicked top offers a platform for controlling quantum systems of any size, enabling the tuning of entanglement dynamics for desired outcomes. The double kicked top can be implemented using existing quantum kicked top platforms, such as those found in nuclear magnetic resonance systems or cold-atom setups, by adding a second kick to the system.