Non-Markovian Quantum Optics with Three-Dimensional State-Dependent Optical Lattices

A. González-Tudela1,2 and J. I. Cirac1

1Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Str. 1. 85748 Garching, Germany
2Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain.

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Quantum emitters coupled to structured photonic reservoirs experience unconventional individual and collective dynamics emerging from the interplay between dimensionality and non-trivial photon energy dispersions. In this work, we systematically study several paradigmatic three dimensional structured baths with qualitative differences in their bath spectral density. We discover non-Markovian individual and collective effects absent in simplified descriptions, such as perfect subradiant states or long-range anisotropic interactions. Furthermore, we show how to implement these models using only cold atoms in state-dependent optical lattices and show how this unconventional dynamics can be observed with these systems.

Quantum optics is the theory which describes the interaction between
quantized light and matter. It captures many relevant phenomena such as the
spontaneous emission of optically excited states. In the simplest scenario,
that is, when the photon timescales are much faster than the emitters ones,
their dynamics can be obtained within a perturbative (Markovian)
description, for example predicting an exponential decay of the emitter

Recent experimental advances in the integration of quantum emitters with
nanophotonic structures, in circuit QED, or in the simulation of quantum
optical phenomena with matter waves provide us with systems where these
perturbative descriptions break and novel non-Markovian phenomena emerge.
In our manuscript, we focus on the implementation of several structured 3D
environments with matter waves and show how new type of dynamics and
interactions emerge from the interplay between the dimensionality and
photon energy dispersion.

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[7] Michael Stewart, Joonhyuk Kwon, Alfonso Lanuza, and Dominik Schneble, "Dynamics of matter-wave quantum emitters in a structured vacuum", Physical Review Research 2 4, 043307 (2020).

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[12] A. Heinz, A. J. Park, N. Šantić, J. Trautmann, S. G. Porsev, M. S. Safronova, I. Bloch, and S. Blatt, "State-Dependent Optical Lattices for the Strontium Optical Qubit", Physical Review Letters 124 20, 203201 (2020).

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[15] T Shi, Y-H Wu, A González-Tudela, and J I Cirac, "Effective many-body Hamiltonians of qubit-photon bound states", New Journal of Physics 20 10, 105005 (2018).

[16] Luca Leonforte, Angelo Carollo, and Francesco Ciccarello, "Vacancy-like Dressed States in Topological Waveguide QED", Physical Review Letters 126 6, 063601 (2021).

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