Activities

In both traditional (classical) and quantum computation, bit-flip operations, also known as NOT gates, are fundamental. They act as the basic switch that flips “0” to “1” or vice-versa, and such a simple operation is essential to building more complex logic gates.

Since any state that can represent a "1" or a "0" can be used to store information, we started wondering if the pair of "symmetry-broken" states found in parametric oscillators (e.g., LC circuit with capacitor plates that periodically move) and discrete time crystals could also encode these bits. If so, could we then design protocols to perform a bit-flip, or NOT gate, on them?

In our paper, we have theoretically tested how well a specific bit-flip protocol can withstand the disruptive behaviour of noise from thermal and quantum processes. Our simulations showed some exciting predictions: a protocol based on the sudden increase in the driving frequency for bits encoded in the resonant states of a parametric oscillator and discrete time crystals in the open Dicke model are robust against thermal and quantum noise, respectively. The discrete time crystal has an extra benefit: in the Dicke model, its superradiant state can “protect” the system from quantum disruptions. Our work represents an important step towards “taming” time crystals, which we hope will open doors for potential future applications

arXiv:2504.04900

Physical Review B

Critical transitions, such as a stock market crash and an abrupt climate change, can be understood using a mathematical framework called bifurcation theory. Typical examples of bifurcation include the pitchfork bifurcation, wherein the system goes from one fixed point to another, and the Hopf bifurcation, wherein a stable fixed point turns into an oscillating solution known as a limit cycle. An extremely rare type of transition is the Neimark-Sacker or torus bifurcation. 

Using a quantum gas experiment, we demonstrate, for the first time, a torus bifurcation as a continuous time crystal becomes unstable and starts "beating". That is, the continuous time crystal, characterised by a single well-defined frequency of oscillations, turns into a quasiperiodic dynamical state with an additional frequency incommensurate with respect to the original one. In contrast to the appearance of a limit cycle as a two-dimensional closed loop in phase, this quasiperiodic or beating dynamics manifests as a torus, a limit torus. We show in this work that the nature of transitions involving time crystals at the thermodynamic or mean-field level can be understood using bifurcation theory, commonly used in complex dynamical systems. Our work also provides an elementary platform for observing quasiperiodic dynamical phases.

arXiv:2411.00155

Physical Review Letters

Press release

In recent years, interest in phase transitions involving static and dynamical states has increased. An example of this is a transition involving a stationary superradiant phase and a time crystalline phase, which can be understood as a limit cycle solution, in an atom-cavity system (see our related work published in Science). For transitions involving static or equilibrium phases, it has been known that quantum noise smoothens the transition making it appear crossover-like. In our work, we predicted a similar smoothening of the transition but now between stationary and dynamical phases. This is the first time that the fundamental effects of quantum noise, inherent in microscopic and mesoscopic systems, are investigated and revealed in the context of phase transitions involving dynamical phases, particularly time crystals and limit cycles. A consequence of this quantum-induced smoothing behaviour is the unexpected emergence of limit cycles in parameter regimes, in which mean-field or thermodynamic predictions suggest otherwise. We also found that quantum fluctuations cause the oscillation frequencies of these limit cycles to spread out. This has important ramifications in synchronisation phenomena, such as entrainment, as the driving frequency must match an integer multiple of the limit cycle frequency for these to occur.

arXiv:2407.21390

Physical Review A

The Kibble-Zurek mechanism applies to various critical phenomena, wherein a system undergoes a continuous phase transition. To realise a phase transition, a tuning parameter that controls the phase of the system is typically varied, and according to this mechanism, the number of defects that will form in the system is related to the speed at which the critical point is crossed - the faster the transition is crossed, the larger the number of defects. While the idea was originally formulated for cosmological phase transition in the early universe, it eventually found applications in condensed matter. 

In our work published in Physical Review B (Editors' Suggestion), we demonstrate that the Kibble-Zurek mechanism also applies to open systems - systems that interact with their environment. Our key result is that for intermediate traversal speeds of a phase transition, dissipation may lead to an apparent delay in the Kibble-Zurek mechanism. This results in a lag between the actual time the system has entered a new phase and the time inferred from a threshold-based criterion for observable quantities, as done in most experiments. Our predictions apply to a general class of systems, including the Dicke model and its lattice version.

arXiv:2407.13424

Physical Review B (Editors' Suggestion)

Press release

A blinking firefly can be made to synchronise with a blinking LED, a phenomenon called entrainment. Entrainment essentially means that an intrinsically oscillating signal, such as the blinking fireflies, can synchronise with an external signal, such as the blinking LED. 

In our work, a Bose-Einstein condensate and the photons trapped between two highly reflecting mirrors can combine to form a quasiparticle dubbed as a polariton. These hybrid light-matter quantum objects can oscillate in time at a well-defined frequency, signalling that the system has entered a limit cycle phase, also known as a continuous time crystal (Science). By periodically driving the intensity of an external laser beam at twice the observed frequency of the limit cycle, we demonstrate that the polaritons will still oscillate but at a rate exactly twice as slow as the applied laser. Thus, we observe a subharmonic entrainment of the limit cycle or, equivalently, a transformation of a continuous time crystal into a discrete time crystal, breaking the symmetry of the periodically varying laser.

Reports on Progress in Physics

Research highlight:

Physics Worlds: Progress In series

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: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

In our work published in Science chosen for "First Release", we demonstrate the first observation of a continuous time crystal in a lab. This time crystal is very close to the original time crystal proposed by Nobel laureate, Frank Wilczek, in his seminal work in 2012. A continuous time crystal is similar to a standard crystal, like ice, where we know that there is a periodic pattern in space but we can not pinpoint the exact location of the molecules. In a continuous time crystal, the time when the system starts to oscillate is random. 

We specifically use a Bose-Einstein condensate inside an optical cavity to demonstrate that limit cycles, marked by oscillating photon occupation in the cavity,  may emerge in the system under the right conditions. We showed that these limit cycles exhibit the robustness and spontaneous symmetry breaking expected of a continuous time crystal. 

arXiv:2202.06980

Science

News articles and interviews:

"Researchers observe continuous time crystal" (Phys.org)

"A new kind of time crystal has been created and lasts 10 milliseconds" (NewScientist)

While the dissipative time crystal (DTC) that we have recently observed (Physical Review Letter) has been shown to be qualitatively consistent with a theoretical description in the ideal limit, the question remains if this new phase of matter can remain stable beyond the idealised scenario. In our work published in Physical Review A, we have investigated the stability of DTCs in the presence of an inhomogeneous trap and competing short- and long-range interactions, which push the system beyond the ideal case. 

By mapping the phase diagram for various conditions, we show that the DTC can indeed remain stable and robust despite the presence of imperfections or mean-field breaking components. Moreover, we discover a new type of DTC, which we call prethermal dissipative time crystals. A prethermal DTC is characterised by increasing lifetime as the system is effectively driven faster. Our study demonstrates a general strategy to determine the influence of inevitable imperfections on any many-body state that is created in atom-cavity systems.

arXiv:2202.11952

Physical Review A

The Dicke model is one of the fundamental models in understanding the interaction between light and matter. The standard Dicke model involves two-level atoms interacting with a single quantum mode of light. In our joint publications appearing back-to-back in Physical Review A and Physical Review Letters, we have shown that a shaken atom-cavity system can emulate a driven three-level generalisation of the Dicke model.

We have theoretically predicted that the periodically driven three-level Dicke model has three dynamical signatures: (1) light-induced superradiance, (2) light-enhanced superradiance, and (3) incommensurate time crystalline phase. In our experiment, we have observed the emergence of an incommensurate time crytal, which also serves as a smoking gun for the quantum simulation of the three-level Dicke model.

Theory:

arXiv:2108.10877

Physical Review A

Experiment:

arXiv:2108.11113

Physical Review Letter

Together with collaborators from the University of Hamburg, we were able to create a time crystal that is exposed to the environment in a controlled way. Using a Bose-Einstein condensate inside an optical cavity, we demonstrate that periodic modulation of the light-mater coupling may lead to a periodic switching of the spatial configuration of the atoms between two sublattices of a chequerboard pattern. More interestingly, the complete cycle requires two driving periods suggesting that time-translation symmetry is broken - a hallmark of time crystals. 

Our work represents a crucial step in potentially making this phase of matter useful since almost all time crystals require isolation from the environment. On a more fundamental level, we provide a prototypical example of interesting phases arising from the complex interplay between many-body interaction, driving, and dissipation.

arXiv:2012.08885

Physical Review Letter (Editors' Suggestion)

Viewpoint Article by Z. Gong and M. Ueda

The famous Higgs boson in particle physics has an analogue in condensed matter, which is aptly called the Higgs mode. Beyond fundamental and theoretical interests, can we possibly use this elusive mode for practical purposes? 

In our recently published work, the answer appears to be "yes". In particular, we predict that the transport property of cuprate superconductors can be enhanced by essentially shining them with light at a frequency slightly above the Higgs frequency. The resulting oscillation of the Higgs mode then leads to a parametric amplification of the superconducting response.

arXiv:2011.08094

Physical Review B

We demonstrate theoretically and experimentally the emergence of a dynamical density wave order by resonant driving in an atom-cavity system. The oscillating density grating, associated with this order, suppresses the scattering of photons into the cavity.  

arXiv:2003.14135

New Journal of Physics

Manipulating equilibrium properties via non-equilibrium dynamics has led to novel phenomena, such as light-induced superconductivity. Recently, a new class of genuine dynamical states was discovered called time crystals. The rigidity of emergent oscillations in a time crystal makes it a promising tool for precision frequency generation. Here, we propose to induce a time crystal in a high-Tc superconductor by driving a sum resonance between two fundamental excitations in systems with broken U(1) symmetry - the Higgs mode and the phase or plasma mode. Our work advances light-assisted dynamical control of solids towards genuine non-equilibrium states, which have no counterpart in equilibrium.

arXiv:2004.13383

Physical Review Research 

Press coverage

We propose to stabilise a dynamical phase - a continuous time crystal - in a driven-dissipative system comprising of an atomic Bose-Einstein condensate inside a high finesse optical cavity by periodically modulating the external pump. In turning on the modulation, we tune the atom-cavity system from a continuous to a discrete time crystal. 

arXiv:2004.14633

New Journal of Physics