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arXiv:1604.05125 · New Journal of Physics

Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons

Przemysław Bienias, Hans Peter Büchler

Published Dec 22, 2016• 21 citations
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Abstract

We study the propagation of Rydberg slow light polaritons through an atomic medium in the regime where the dispersion relation for the polaritons is well described by the slow light velocity alone. In this regime, the quantum many-body problem can be solved analytically for arbitrary shape of the atomic cloud. We demonstrate the connection of Rydberg polaritons to the behavior of a conventional Kerr nonlinearity for weak interactions and determine the leading quantum corrections for increasing interactions. We propose an experimental setup which allows one to measure the effective two-body interaction potential between Rydberg polaritons as well as higher-body interactions. Our work shows that the locality and causality based no-go theorems for quantum gates do not apply to setups based on Rydberg polaritons.

DOI
10.1088/1367-2630/aa50c3

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We study the propagation of Rydberg slow light polaritons through an atomic medium in the regime where the dispersion relation for the polaritons is well described by the slow light velocity alone. In this regime, the quantum many-body problem can be solved analytically for arbitrary shape of the atomic cloud. We demonstrate the connection of Rydberg polaritons to the behavior of a conventional Kerr nonlinearity for weak interactions and determine the leading quantum corrections for increasing interactions. We propose an experimental setup which allows one to measure the effective two-body interaction potential between Rydberg polaritons as well as higher-body interactions. Our work shows that the locality and causality based no-go theorems for quantum gates do not apply to setups based on Rydberg polaritons.
We study a system of three photons in an atomic medium coupled to Rydberg states near the conditions of electromagnetically induced transparency. Based on the analytical analysis of the microscopic set of equations in the far-detuned regime, the effective three-body interaction for these Rydberg polaritons is derived. For slow light polaritons, we find a strong three-body repulsion with the remarkable property that three polaritons can become essentially noninteracting at short distances. This analysis allows us to derive the influence of the three-body repulsion on bound states and correlation functions of photons propagating through a one-dimensional atomic cloud.
We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. The method allows us to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.
The combination of electromagnetically induced transparency with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this Letter, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to 0. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a nonlinear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.
The combination of electromagnetically induced transparency with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this Letter, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to 0. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a nonlinear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of photons.