Quantum Jumps for Time Crystals

Discrete time crystals (DTC) in many-body systems are a prominent example of a many-body non-equilibrium state of matter.

There have been many theoretical proposals on how to achieve a many-body DTC and they were realised in several experiments. An underlying framework for all different types of DTC models is lacking.

My first main goal is to study the DTC phase in many-body systems with a novel framework, namely through their quantum jump behaviour induced by an environment.

My second main goal is to go beyond the Lindblad description required for the first goal and consider also the case where Lindblad rates can go negative.

Usual jump methods do not work in this case and I will rely on a novel jump method that I co-developed specifically for this situation. To deploy its full power, the method requires further development which will be the first objective of the project. I will study three systems with a DTC phase.

The first is a toy model, a driven anharmonic oscillator, a good test case for the method which will provide new insight in the dynamical phase. Next, I study two true many-body systems.

The first is a collection of spins where the DTC phase relies on many-body localisation (MBL), inspired on experimentally implemented protocols. My aim here is to distinguish the DTC phase from the ordinary MBL and ergodic phase by the jump statistics. Beyond this, I will explore how many sites must be monitored to detect and distinguish different phases.

Finally, I will study a large ensemble of spins that can show the DTC phase, like the experiment in Nitrogen-Vacancy centres, which does not rely on MBL realise the DTC phase. It would be extremely elucidating to compare the nature of the phase to the one that does rely on MBL. I will compare the results from both cases in hopes unifying both realisations or finding clear distinctions.