Nonlinear systems are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last century. Recently our developments in quantum technologies has given us the ability to engineer systems through with no natural analog. We are now at the stage where we can explore nonlinear effect in quantum hybrid systems. In this presentation, we illustrate how these nonlinear effects allow the exploration of novel effects such as superradiance induced negative temperature relaxation.
Nonlinear systems are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last century. Recently our developments in quantum technologies has given us the ability to engineer systems through with no natural analog. We are now at the stage where we can explore nonlinear effect in quantum hybrid systems. In this presentation, we illustrate how these nonlinear effects allow the exploration of novel effects such as superradiance induced negative temperature relaxation.
The efficient generation, coherent control, manipulation and measurement of quantum states of light and matter is at the core of quantum technologies. Hybrid quantum systems, where one combines the best parts of multiple individual quantum systems together without their weaknesses, are now seen as a way to engineer composite quantum systems with the properties one requires. This would in principle allow one to probe new physical regimes. However, the issue until recently has been that hybridization has not resulted in systems with superior properties. Recently however we [Nature Photonics 11, 3639 (2016)] have shown an increased coherence times in hybrid system is of composed nitrogen-vacancy centers strongly coupled to a superconducting microwave resonator. This demonstration has enabled this kind of hybrid system to enter the regime where quantum nonlinearities are present. We discuss several types of nonlinearity effects that can be naturally explored (bistability and superradiance). Our work paves the way for the creation of spin squeezed states, novel metamaterials, long-lived quantum multimode memories and solid-state microwave frequency combs. Further in the longer term it may enable the exploration of many-body phenomena in new cavity quantum electrodynamics experiments.
Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds-a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.
Quantum mechanics is fundamentally governed by the Schrödinger equation, which is linear in the wave function. Nevertheless, quantum systems can exhibit highly nonlinear behavior in their observable dynamics. Such nonlinearities can emerge from many-body interactions, nonlinear coupling mechanisms, or the interplay between coherent evolution and dissipation. In the collective limit, microscopic quantum interactions can give rise to qualitatively new macroscopic behavior. Open quantum systems provide a rich setting for such phenomena, as environmental coupling introduces dissipation and fluctuations that compete with coherent dynamics and can alter the steady states and dynamical phases of a system. Combined with nonlinear interactions, this competition can produce behavior with no direct counterpart in conventional linear light--matter systems. In this thesis, I investigate such collective phenomena through nonlinear two-photon light--matter interactions and engineered quantum reservoirs. I first investigate the driven--dissipative two-photon Dicke model and demonstrate the emergence of a dissipative superradiant phase transition. The quadratic light--matter interaction introduces distinct stability requirements in the presence of dissipation. In particular, two-photon loss stabilizes the superradiant phase, allowing its steady states and critical behavior to be characterized. I next investigate photon blockade and transient quadrature-squeezed radiation in the two-photon Tavis--Cummings model. I show that two-photon interactions collectively enhance photon blockade and squeezing, in contrast to the conventional one-photon model, where the effective nonlinearity diminishes in the collective limit. Finally, I consider collective behavior induced by reservoir engineering. Two spatially separated open quantum systems without direct coherent interaction can undergo a nonlocal quantum phase transition when coupled to correlated quantum reservoirs. Remarkably, the transition is hidden from local observables and emerges only through nonlocal correlations and collective observables. Together, these results demonstrate how nonlinear interactions and engineered dissipation can reshape collective behavior in open quantum systems.
Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to show that many nonlinear collective phenomena can be successfully treated by a recently developed method called the Scale Separation Approach whose name is due to the idea of separating different characteristic space-time scales existing in nonequilibrium statistical systems. This approach is rather general and can be applied to various nonequilibrium physical problems, several of which are discussed here. The problems considered not only serve as illustrations of the method but are quite important by themselves presenting interesting physical effects, such as Collective Liberation of Light, Turbulent Photon Filamentation, Superradiant Spin Relaxation, Negative Electric Current, and Magnetic Semiconfinement of Atoms.
Many interesting physical systems, e.g. condensed matter systems, are hard to study. From the experimental point of view, in such systems most parameters are ''frozen" for a given sample. From the theoretical point of view, they often cannot be simply modelled from first principles. In contrast, laser-matter interactions are very well known theoretically, and a very high degree of control of laser beams is available for the experimentalist. In the last years, one learned to ''engineer" quantum hamiltonians using ultracold atoms interacting with electromagnetic fields. For example, laser beams may form an interference pattern that is ''seen" by the atoms as a periodic potential, thus creating an analog of a crystal. However, the analog has great advantages over the original system, as one has a larger control of its properties: One can vary the parameters of the potential by changing the properties of the laser beams, one can make a ''mesoscopic" quantum system by using a Bose-Einstein condensate, one can change it to a degenerate Fermi gas by using a fermionic isotope, one can control atom-atom interactions by using the so-called . Building on seminal ideas of Feynman, the notion of ''quantum simulator" -- a ''simpler" system able to mimic the physics of a complicate one -- recently became a reality. In a variety of situations of experimental interest, weakly interacting degenerate boson gases (Bose-Einstein condensates) are very well described by the Nonlinear Schödinger Equation with a cubic nonlinearity (called, in the present context, the {\it Gross-Pitaevskii equation}), which is much simpler than the underlying many-body problem. This opened a new field for both theoretical and experimental studies: The {\it nonlinear} quantum mechanics, where the familiar techniques like the spectral analysis in terms of eigenvalues and eigenvectors, which derive from the linearity of the usual Schödinger equation, cannot be used. The mathematical framework of this new quantum mechanics is still largely to be invented. Meanwhile, one can resort to numerical simulations -- and to experiments. In this talk, I will discuss two simple yet important examples illustrating these ideas. First, I will show how one can ''quantum simulate" with ultracold atoms the celebrated Anderson model, which describes quantum disordered systems. One can even enrich this system by adding particle-particle interactions in a controlled way. Second, I will show a simple model displaying ''quasiclassical" chaos, that is, chaotic behavior related to sensitivity to the initial conditions, which cannot exist in {\it linear} quantum mechanics. I will show that the observed behavior, although intrinsically quantum, can be described by the KAM theorem.