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Optical lattices around a nanofiber waveguide

Periodic Reporting for period 1 - NanoArray (Optical lattices around a nanofiber waveguide)

Reporting period: 2016-09-01 to 2018-08-31

The NanoArray project realized at Laboratoire Kastler Brossel in Paris aimed at developing a theoretical framework for light scattering in arrays of cold multi-level atoms trapped in the vicinity of an optical nanofiber, in parallel with ongoing experiments at the host.

Three overall objectives were pursed and obtained. The first one was the development of an ab-initio microscopic description of light interaction with one-dimensional arrays of atoms trapped in the vicinity of an optical nanofiber, where not only the atom-atom interactions through the nanofiber and free-space modes were taken into account but also the complex vector structure of light and the multi-level structure of the atoms. Using the developed formalism it was then possible to explain experimental results on atomic Bragg scattering and highly-efficient quantum memory implementation. The developed formalism finally allowed to study the emergence of subradiance in a periodic lattice with a specific period close to a quarter of the resonant atomic wavelength.
The objectives of the project were the development of a theoretical framework for light scattering in arrays of atoms trapped in the vicinity of an optical nanofiber, the control of light propagation in such a system and the study of subradiance effects emerging from special organization of the atoms.

Ab-initio microscopic theory of light scattering.
The first step of the project was devoted to the development of an ab-initio microscopic description of light interaction with one-dimensional arrays of multi-level atoms trapped in the vicinity of a waveguide. This formalism relied on modifying Green function and atomic decay rate due to the presence of the nanofiber and introducing the S-matrix of scattering and the Resolvent operator, which can be linked to the transmission and reflection coefficients characterizing the forward and backward propagation of the guided photon through the trapped atomic arrays. This development allowed us to make comparison with experimental results on strong Bragg reflection in this system. The consideration of degeneracy of the atomic ground state allowed us to study the scattering process in presence of both Rayleigh and Raman scattering channels by considering the full vector model of light and keeping the complete angular momentum structure of the guided light. Moreover, the dipole-dipole interaction was taken into account. This interaction plays a very important role when the distance between atoms becomes smaller than the resonant wavelength. This model finally allowed us to study the effect of order and disorder in the arrays. These results have been published in Phys. Rev. A 97, 023827 (2018).

High-efficient quantum memory.
The developed formalism was extended by including interaction of the system with an external control field in order to study slow-light effect and control of the light propagation. Variation of the control field power and spatial organization of atoms in the chain allowed us to find optimal conditions for the largest time delay of the light in the system under electromagnetically induced transparency conditions.

Moreover, the developed formalism taking into account multi-level atoms was applied to explain the experimental results obtained in a free-space quantum memory for flying optical qubits. We showed theoretically and experimentally that the multilevel atomic structure results in an effective ground state decoherence and leads to a reduction of the storage-and-retrieval efficiency at high optical depth. The results have been published in Nat. Commun. 9, 363 (2018).

Subradiance effect.
Based on the developed formalism, we have also studied subradiance effects in a periodic lattice of atoms. We have shown that the organization of atoms in 1D array with subdifractional period close to a quarter of the resonant wavelength leads to strong subradiance. We have studied this effect as a function of light polarization and number of atoms. These results pave the way to new experimental investigations of subradiance and superradiance effects in an optical lattice in the vicinity of a nanoscale structure.

The different results obtained during the fellowship have been presented in various international conferences in the field of atomic physics, quantum optics and quantum information, such as:

• Quantum Information and Measurement IV (QIM 2017, Paris, France).
• Х-th seminar on Quantum Optics and Quantum Information dedicated to the memory of D.N. Klyshko (2017, Moscow, Russia)
• Workshop on Quantum Light-Matter Interaction in Low Dimensions (2017, Barcelona, Spain).
• Optical Nanofiber Applications (ONNA 2017, Okinawa, Japan).
• International Conference on Metamaterials and Nanophotonics (METANANO 2017, Vladivostok, Russia)
• GDR Colloquium on Quantum Engineering, from Fundamental Aspects to Applications (2017, Nice, France)
• International Conference on Quantum Optics (2018, Obergurgl, Austria)
• International Conference on Laser Optics (2018, Saint-Petersburg, Russia)
• International Conference on Atomic Physics (2018, Barcelona, Spain)
The NanoArray project explored theoretically different quantum optical effects resulting from the combination of nanophotonics and cold-atom physics. This original combination represents a new paradigm for quantum light-matter interaction and has the potential to lead to functional quantum optics circuits. Moreover, this paradigm gives rise to novel phenomenon due to long-range photon-mediated interactions between the atoms.

Alexandra Sheremet has developed an ab-initio microscopic theory of light scattering in such a hybrid system. The results obtained during the fellowship (microscopic theory of light scattering, influence of ordering and disordering of the atoms, influence of multi-level atomic structure, emergence of superradiance and subradiance effects in this context) represent pioneer outcomes in the field of waveguide-QED, quantum communications and quantum information.