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arXiv:1705.09635 · Physical Review A

Creation and detection of photonic molecules in Rydberg gases

Matthias Moos, Razmik G. Unanyan, Michael Fleischhauer

Published Aug 25, 2017• 7 citations
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Abstract

We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency, where they form strongly interacting massive particles, termed Rydberg polaritons. Depending on the strength of the van der Waals-type interactions of the atoms either bunching or antibunching of photons can be observed when driving the atoms off-resonantly. The bunching is associated with the formation of bound states. We employ a Green's function approach and numerical wave-function simulations to analyze the conditions for the creation and the dynamics of these photonic molecules and their interplay with the scattering continuum which can also show photon bunching. Analytic solutions of the pair-propagation problem obtained from a pseudopotential approximation and verified numerically provide a detailed understanding of bound and scattering states. We find that the scattering contributions acquire asymptotically a robust relative phase which can be employed to separate bound state and scattering contributions by a homodyne detection scheme.

DOI
10.1103/physreva.96.023853

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We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency, where they form strongly interacting massive particles, termed Rydberg polaritons. Depending on the strength of the van der Waals-type interactions of the atoms either bunching or antibunching of photons can be observed when driving the atoms off-resonantly. The bunching is associated with the formation of bound states. We employ a Green's function approach and numerical wave-function simulations to analyze the conditions for the creation and the dynamics of these photonic molecules and their interplay with the scattering continuum which can also show photon bunching. Analytic solutions of the pair-propagation problem obtained from a pseudopotential approximation and verified numerically provide a detailed understanding of bound and scattering states. We find that the scattering contributions acquire asymptotically a robust relative phase which can be employed to separate bound state and scattering contributions by a homodyne detection scheme.
Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.
We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasibound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wave function resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms.
We study the photon blockade of two-photon scattering in a one-dimensional waveguide, which contains two atoms coupled via the Rydberg interaction. We obtain the analytic scattering solution of photonic wave packets with the Laplace transform method. We examine the photon correlation by addressing the two-photon relative wave function and the second-order correlation function in the single- and two-photon resonance cases. It is found that, under the single-photon resonance condition, photon bunching and antibunching can be observed in the two-photon transmission and reflection, respectively. In particular, the bunching and antibunching effects become stronger with the increasing of the Rydberg coupling strength. In addition, we find a phenomenon of bunching-antibunching transition caused by the two-photon resonance.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.
The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van der Waals interaction that is present between alkali metal atoms which are laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.
Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of interacting quasiparticles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions. Specifically, we obtain a master equation governing the dynamics of Rydberg polaritons and identify conditions when it can essentially be described by an effective Hamiltonian of a single-species polariton. We verify this Hamiltonian by numerical two-excitation simulations. Under typical stationary EIT conditions it is impossible to reach the strongly interacting regime where long-range density-density correlations emerge. In contrast, by employing the time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasicrystalline order. We provide a physical explanation for the differences between stationary and time-dependent schemes.