## Periodic Reporting for period 4 - FoQAL (Frontiers of Quantum Atom-Light Interactions)

Okres sprawozdawczy: 2019-09-01 do 2020-05-31

The key to the success of atomic physics and quantum optics relies on our understanding and ability to control the way that light and matter interact with each other at the level of their constituent particles – single atoms and photons. From fundamental tools such as laser cooling and trapping or cavity quantum electrodynamics come potentially powerful applications ranging from the study of many-body systems (“quantum simulation”) using ultracold atoms to quantum atom-light interfaces for quantum information processing and quantum networks. However, these same techniques have clear limitations or tradeoffs, which preclude many parameter regimes or paradigms for the utilization of cold atoms, and which constitute bottlenecks for further progress.

Separately, in recent years, groups worldwide have succeeded in interfacing cold atoms with micro- and nano-photonic systems, with a primary goal of improving the figures of merit and scalability of their macroscopic counterparts. However, while the direct transfer of paradigms from macroscopic to nanoscopic systems might increase figures of merit, it results in no fundamentally new functionalities. Within this context, FoQAL pursues a dramatic and powerful new vision of what can be achieved with nanophotonic systems. Exploiting unique features such as control over the dimensionality and dispersion of light, complex multiple scattering and interference, the engineering of quantum vacuum forces, and the strong optical fields and forces associated with confining light to the nanoscale, we aim to completely re-define our understanding of the ways in which light and matter can interact at the quantum level. In particular, our objectives were to develop fundamentally new paradigms for atomic trapping, tailoring atomic interactions, and quantum nonlinear optics that are not bound by previous limits, and which cannot be duplicated in macroscopic systems even in principle.

Separately, in recent years, groups worldwide have succeeded in interfacing cold atoms with micro- and nano-photonic systems, with a primary goal of improving the figures of merit and scalability of their macroscopic counterparts. However, while the direct transfer of paradigms from macroscopic to nanoscopic systems might increase figures of merit, it results in no fundamentally new functionalities. Within this context, FoQAL pursues a dramatic and powerful new vision of what can be achieved with nanophotonic systems. Exploiting unique features such as control over the dimensionality and dispersion of light, complex multiple scattering and interference, the engineering of quantum vacuum forces, and the strong optical fields and forces associated with confining light to the nanoscale, we aim to completely re-define our understanding of the ways in which light and matter can interact at the quantum level. In particular, our objectives were to develop fundamentally new paradigms for atomic trapping, tailoring atomic interactions, and quantum nonlinear optics that are not bound by previous limits, and which cannot be duplicated in macroscopic systems even in principle.

One of the main initial challenges in theoretically understanding the emerging atom-nanophotonics interfaces is that many of the systems do not obviously fit into previously established models for quantum atom-light interactions. Within this context, we have developed a novel and universal formalism capable of describing atom-light interactions in complex dielectric settings. On one hand, this so-called quantum “spin model” has been crucial to understanding and modeling the first experiments in the world that observe atomic interactions in photonic crystal waveguides. On the other hand, it has been used to theoretically predict new and exotic phenomena that should be realizable with such systems, such as the formation of molecules of photons, or “quantum crystallization,” in which entanglement between atomic internal degrees of freedom are responsible for the formation and stabilization of spatial order. We have also used this model to develop powerful new numerical techniques, in combination with tensor network methods, to remove exponential inefficiencies from previous techniques to calculate the full quantum dynamics in the interaction between propagating light fields and atomic media.

Furthermore, due to its universal nature, the spin model can even be used to provide new insights into “conventional” atomic systems, such as free-space ensembles. One interesting aspect of this model is that it accounts for multiple scattering and interference of light emission, which are not included in conventional models. We have shown that interference can be a remarkable resource. For example, by exploiting interference, we have developed a new protocol for a quantum memory for light, whose error bound as a function of system resources is exponentially better than previously developed bounds. We have also shown that this model may provide insights on why the refractive index of materials at optical frequencies is universally so small, being always of order unity.

FOQAL has resulted in at least 27 publications in total, including in prominent journals such as PRX (3 publications), Nature Communications (2), Nature, and a review of the new field of atom-nanophotonics interfaces in Review of Modern Physics. These include two collaborative papers with experiments that explore the phenomena that we have proposed. Furthermore, we have reached an audience of over 5000 researchers, through dissemination in workshops, conferences, seminars, and schools.

Furthermore, due to its universal nature, the spin model can even be used to provide new insights into “conventional” atomic systems, such as free-space ensembles. One interesting aspect of this model is that it accounts for multiple scattering and interference of light emission, which are not included in conventional models. We have shown that interference can be a remarkable resource. For example, by exploiting interference, we have developed a new protocol for a quantum memory for light, whose error bound as a function of system resources is exponentially better than previously developed bounds. We have also shown that this model may provide insights on why the refractive index of materials at optical frequencies is universally so small, being always of order unity.

FOQAL has resulted in at least 27 publications in total, including in prominent journals such as PRX (3 publications), Nature Communications (2), Nature, and a review of the new field of atom-nanophotonics interfaces in Review of Modern Physics. These include two collaborative papers with experiments that explore the phenomena that we have proposed. Furthermore, we have reached an audience of over 5000 researchers, through dissemination in workshops, conferences, seminars, and schools.

FOQAL has proposed rich new possibilities for quantum technologies and quantum phenomena in atom-nanophotonics interfaces. These include novel techniques to realize strong photon-photon interactions, such as by exploiting atom-photon bound states in photonic crystal interfaces or atomic motion, proposals for novel effects such as quantum crystallization or photon molecules, and systems that allow for photon number separation via strong photon number-dependent group velocities. Some of these ideas can already be put into practice, as evidenced by direct experimental collaborations in systems ranging from cold atoms coupled to photonic crystals to waveguide QED with superconducting qubits. Furthermore, we have developed a novel “spin model” theoretical formalism to understand atom-light interactions in general circumstances. Beyond the promising future of atom-nanophotonics interfaces, we believe that this model could lead to a broad re-envisioning of atom-light interfaces in general and their true capabilities. For example, it raises the possibility to create protocols for applications with error bounds exponentially better than previously known, due to exploiting interference in light emission. We envision that this model will also form the basis for a more fundamental theory of the ultimate limiting values of refractive index in real materials.