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arXiv:2003.10463 · Physical Review Letters

Quantum Many-Body Dynamics of Driven-Dissipative Rydberg Polaritons

Tim Pistorius, Javad Kazemi, Hendrik Weimer

Published Dec 30, 2020• 10 citations
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Abstract

We study the propagation of strongly interacting Rydberg polaritons through an atomic medium in a one-dimensional optical lattice. We derive an effective single-band Hubbard model to describe the dynamics of the dark-state polaritons under realistic assumptions. Within this model, we analyze the driven-dissipative transport of polaritons through the system by considering a coherent drive on one side and by including the spontaneous emission of the metastable Rydberg state. Using a variational approach to solve the many-body problem, we find strong antibunching of the outgoing photons despite the losses from the Rydberg state decay.

DOI
10.1103/physrevlett.125.263604

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We study the propagation of strongly interacting Rydberg polaritons through an atomic medium in a one-dimensional optical lattice. We derive an effective single-band Hubbard model to describe the dynamics of the dark-state polaritons under realistic assumptions. Within this model, we analyze the driven-dissipative transport of polaritons through the system by considering a coherent drive on one side and by including the spontaneous emission of the metastable Rydberg state. Using a variational approach to solve the many-body problem, we find strong antibunching of the outgoing photons despite the losses from the Rydberg state decay.
Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of a large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of nonperturbative dissipative interactions relevant to current experiments. Our model is able to capture the many-body dynamics of bright, coherent pulses through these strongly interacting media. We compare our model with available experimental data in this regime and find good agreement. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.
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.
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using 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 present a driven dissipative protocol for creating an optical analog of the Laughlin state in a system of Rydberg polaritons in a twisted optical cavity. We envision resonantly driving the system into a 4-polariton state by injecting photons in carefully selected modes. The dissipative nature of the polariton-polariton interactions leads to a decay into a two-polariton analog of the Laughlin state. Generalizations of this technique could be used to explore fractional statistics and anyon based quantum information processing. We also model recent experiments that attempt to coherently drive into this same state.
We consider a one-dimensional lattice of atoms with laser excitation to a Rydberg state and spontaneous emission. The atoms are coupled due to the dipole-dipole interaction of the Rydberg states. This driven-dissipative system has a broad range of nonequilibrium phases, such as antiferromagnetic ordering and bistability. Using the quantum trajectory method, we calculate the spatial correlation function throughout the parameter space for up to 18 lattice sites. We show that bistability significantly strengthens the spatial correlations and the entanglement.