Limit cycles are interesting mathematical objects, some examples of which include the beating of a heart and the firing of neurons in our brain. We identified the minimal number of quantum modes and the type of interaction between them to create limit cycles in bosonic quantum systems interacting with an external environment. We show that the underlying mechanism that leads to so-called continuous time crystals  (Science) in an atom-cavity system is an effective Kerr nonlinearity or self-interaction between the photons induced by the inclusion of a third level in the atoms, which is typically neglected in the standard theoretical treatment of light-matter systems.

We also experimentally observe limit cycles using an atom-cavity platform operating in a regime that was previously thought incapable of hosting limit cycles. This confirms our theoretical prediction regarding the actual mechanism for limit cycles to emerge in this type of system. Our work thus provides a blueprint for generating limit cycles in the quantum world, opening the possibility of exploring their quantum nature in future studies.

arXiv (free): https://arxiv.org/pdf/2401.05332

Published: https://journals.aps.org/.../10.1103/PhysRevA.109.063317

arXiv:2401.05332

Physical Review A

A novel phase of matter called discrete time crystals has been predicted and later on experimentally observed in a dissipative atom-cavity system. Time crystals are known for exhibiting emergent patterns in time and those observed in the atom-cavity platform exhibit what is known as a period-doubling behaviour, which means it takes two cycles of the external periodic drive for the system to return to its original configuration. For this type of time crystal and, in general, for spin systems with all-to-all interactions, we proposed a theory based on parametric resonance to understand the origin of this curious phase of matter. It turns out that fundamentally, the slow response of the time crystal shares the same phenomenology with a child moving up and down on a swing. However, in the case of a time crystal, we found that interaction with the environment and an additional symmetry breaking are both required for the symmetry-breaking period-doubling response to be stable.

arXiv:2402.03729v2

Physical Review A

Superconductivity and its defining feature of dissipationless or resistanceless flow of charged currents are expected to vanish when a material's temperature exceeds the critical temperature for superconductivity. In our work, we predict that some version of the dissipationless current survives even above the critical temperature. However, the currents flow in opposite directions in each superconducting layer of a bilayer superconductor. Our work is consistent with one of the proposed scenarios in the less understood "pseudogap phase" in high-temperature superconductors.

arXiv:2309.04531

Physical Review Letters

Time crystals are a phase of matter known for their formation of patterns in time. They can be created by periodic driving or “shaking”, and their unique signature is a response slower than the rate of the shaking. It has been observed that time crystals can be created using cold atoms interacting via light that could escape or “dissipate” into the environment in a controlled way. However, it remains a mystery what the precise role of the dissipating light plays in the formation of this type of time crystal. In our work published in Physical Review B, we shed light on this by using extensive numerical simulations to show how dissipation could make the time crystals more robust against noise and imperfections. It does so by increasing the number of combinations of parameters that could form a time crystal. We find that there is a “Goldilocks zone” for the dissipation strength – too weak or too strong could make a time crystal less robust. We also identify the fundamental mechanism for the creation of such a time crystal to be a “parametric resonance” – the same process that leads to larger swinging of a pendulum that is periodically shifted up and down.

arXiv:2303.13334

Physical Review B

Our work was recently published in Physical Review Letters and was chosen to be on the cover of that issue. In this work, we have predicted and experimentally observed that a Bose-Einstein condensate may form in a dark state of a periodically shaken atom-cavity system. We have shown that the photon-mediated interactions can lead to the occupation of a dark state, which demonstrates a mechanism for efficiently preparing complex many-body states in open quantum systems.

arXiv:2209.03342

Physical Review Letters