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arXiv:1705.06677 · Physical Review A

Markovian and non-Markovian dynamics of quantum emitters coupled to two-dimensional structured reservoirs

Alejandro González-Tudela, J. I. Cirac

Published Oct 5, 2017• 130 citations
arXivHTMLPDF

Abstract

The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In A. Gonz\'alez-Tudela and J. I. Cirac, Phys. Rev. Lett. 119, 143602 (2017), we show how exotic quantum dynamics emerges when quantum emitters are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic non-Markovian interactions, and remarkable superradiant and subradiant behavior. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the band.

DOI
10.1103/physreva.96.043811

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The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In A. Gonz'alez-Tudela and J. I. Cirac, Phys. Rev. Lett. 119, 143602 (2017), we show how exotic quantum dynamics emerges when quantum emitters are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic non-Markovian interactions, and remarkable superradiant and subradiant behavior. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the band.
We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which cannot be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band, we predict an exponential relaxation at a rate different from that predicted by Fermi's golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.
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.
The spectral structure of a photonic reservoir shapes radiation phenomena for embedded quantum emitters. We implement an all-optical analog to study such an effect, particularly to observe the non-Markovian radiation dynamics of an emitter coupled to two-dimensional structured reservoirs. Its dynamics is simulated by light propagating through a photonic lattice, acting as a reservoir for an adjacent waveguide that mimics a coupled quantum emitter. We study radiation dynamics in square and Lieb lattices under different coupling regimes and observe how the flat band properties of the Lieb lattice significantly enhances light-matter coupling and non-Markovianity. Our platform opens a path for the experimental exploration of single-photon quantum optical phenomena in structured reservoirs to enhance light-matter interactions.
Waveguide quantum electrodynamics constitutes a modern paradigm for the interaction of light and matter, in which strong coupling, bath structure, and propagation delays can break the radiative conditions that quantum emitters typically encounter in free space. These characteristics intertwine the excitations of quantum emitters and guided radiation modes to form complex multiphoton dynamics. So far, combining the collective decay of the emitters with the non-Markovian effects induced by the modes has escaped a full solution and the detailed physics behind these systems remains unknown. Here we analyze such a collective non-Markovian decay in a minimal system of two excited emitters coupled to a one-dimensional single-band waveguide. We develop an exact solution for this system in terms of elementary functions that unveils hidden symmetries and predicts new forms of spontaneous decay. The collective non-Markovian dynamics, which are strongly dependent on the vacuum coupling and the detuning from the center of the band, show exotic features that can be characterized with a simple and readily available criterion. Our analytic methods shed light on the complexity of collective light-matter interactions and open up a pathway for understanding multiparticle open quantum systems. Published by the American Physical Society 2024
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole–dipole interactions with tunable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state that inherits the anisotropic properties of the original dissipation and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.