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Multi-photon probing of complex open quantum systems

Periodic Reporting for period 1 - MULTIPROB (Multi-photon probing of complex open quantum systems)

Reporting period: 2019-02-01 to 2021-01-31

Photon-based quantum technologies are a promising platform for processing quantum information, because it combines the resilience of the photon with simple and powerful tools for its manipulation. A key requirement towards this goal is building and understanding deterministic light-matter quantum interfaces, where photons and quantum emitters can interact strongly at the level of few quanta. This enables the engineering of strong photon-photon interactions mediated by the emitters and the construction of two- or multi-photon quantum photonic devices for creating quantum superpositions and entanglement between photons.

Modern nanophotonic and nanofabrication techniques allow for the control of these quantum light-matter interactions in many labs around the world, for instance, with quantum dot or atomic emitters coupled to nanophotonic waveguides or ---in the microwave regime---with superconducting qubits coupled to transmission lines. Nevertheless, the characterization of those interactions is typically limited to measure single-photon transmission, second order correlations, or pump-probe experiments, which give only partial information about the generated photon quantum correlations and the effect of the nanophotonic environment.

The overall objective of this project was to develop more sophisticated multi-photon probing protocols to enable a complete characterization of photon-photon correlations induced by complex quantum emitters, including realistic conditions of noise and dissipation due to the nanophotonic environment. In addition, these techniques should be simple enough to be implemented with standard optical control and measurement tools, such as monochromatic coherent input states and homodyne or intensity detection methods. The action concluded with the theoretical development of such a protocol and with its experimental test in collaboration with the group of P. Lodahl at the Niels Bohr Institute, Copenhagen.
The main results of the project are:

1) We developed a practical experimental protocol to completely characterize photon-photon correlations mediated by complex quantum emitters based on a reconstruction of the single- and two-photon scattering matrices of the system. Our procedure is simple as it probes the emitters with one or two weak monochromatic coherent inputs and reconstructs the scattering matrices from standard homodyne or intensity correlations at the output. We showed that the method based on homodyne measurements can be applied to probe many-body quantum systems of emitters with complex level structure, subject to noise and decoherence, and interacting with photons in waveguides, cavities, or free-space. If homodyne detection is not possible, we also designed an alternative method with intensity measurements, which is more restrictive but still useful in many practical nanophotonic settings such as one complex multi-level emitter coupled to a bi-directional nanophotonic waveguide, subjected to decoherence and spectral diffusion.

2) From a theoretical point of view, the protocol we developed establishes a general relation between multi-photon scattering matrices and multi-time homodyne correlations of a quantum scatterer when probed with weak monochromatic coherent fields. This allowed us to develop a powerful new method to numerically calculate single- and two-photon scattering matrices of complex scatterers using a standard quantum optics description of the open quantum system such as input-output formalism, quantum Langevin, and master equations. The generality of this method enables the computation of two-photon scattering matrices and photon correlations in situations inaccessible to standard scattering methods. This includes two-photon scattering on complex many-body open quantum systems subject to decoherence and noise, as it is unavoidable in real nanophotonic platforms, as well as photon scattering under structured nanophotonic environments.

3) An important part of the project was to establish a collaboration with the experimental group of P. Lodahl at the Niels Bohr Institute, Copenhagen, who are experts in building and controlling interactions between quantum dots and photons propagating in photonic crystal waveguides. On the one hand, this allowed us to ensure that the protocol we were designing is simple enough to be implemented with available state-of-art technology. On the other hand, this collaboration lead to the experimental test of the protocol using intensity correlation measurements, which was published in PRL 126, 023603 (2021) (see publication tab). With this we demonstrated the first experimental characterization and isolation of genuine two-photon quantum correlations from a single quantum emitter.

4) The knowledge gained during the project allowed us to develop parallel studies related to probing and characterization of other complex open quantum systems using quantum optics tools. This includes the complete tomographic characterization of QND detectors of superconducting qubits, the design of a synchronized multi-photon source, and the description of quantum noise in driven-dissipative photonic lattices working as topological amplifiers.

The overall work done during the project resulted in 4 published papers, one software uploaded to Zenodo, 4 preprints, and one more to be submitted. We disseminated the results in 7 international conferences (6 contributed talks and 1 poster), as well as with 4 invited seminars of research groups. Many of the contributed talks were online due to the Covid pandemic, and the records of the talks are available in the webpage of the project ( Furthermore, the outreach activity “the power of light” was designed and presented in two instances during the Week of Science 2019 in Madrid. A record of the event is also available on the webpage.
Our research advanced the state-of-the-art of the fields of quantum nonlinear optics and nanophotonics in various aspects. First, the development of a simple two-photon protocol via the scattering matrix enables a complete characterization of photon correlations generated by quantum emitters, in contrast to standard probing techniques such as second-order intensity correlations, which give partial information only. Second, the method is also a powerful calculation tool for obtaining the one- an two-photon scattering matrix of complex many-body open quantum systems subject to realistic noise sources and decoherence. Some of these situations are inaccessible to standard scattering matrix calculation methods such as path integral or diagrammatic methods, which are typically used in more idealized situations. Third, we experimentally tested this new method in collaboration with the group of P. Lodahl and isolated---for the first time---the genuine two-photon correlations generated by a single quantum emitter interacting with light.

This research opens the door to completely characterize and improve the design of nonlinear quantum nanophotonic devices beyond the single-photon regime. Building more robust photon-based quantum techonologies is likely to impact to society in the near future in diverse aspects ranging from communication to sensing, and computation. In addition, our multi-photon probing protocol facilitates and stimulates the study of photon-photon correlations in strongly correlated quantum many-body systems and quantum simulators out-of-equilibrium driven by light.
Representative figure of the multi-photon probing protocol