Non-equilibrium diagrammatic approach to strongly interacting photons

Abstract

We develop a non-equilibrium field-theoretical approach, based on a systematic diagrammatic expansion, for strongly interacting photons in optically dense atomic media. We consider the case where the characteristic photon-propagation range $L_P$ is much larger than the interatomic spacing $a$ and where the density of atomic excitations is low enough to neglect saturation effects. In the highly polarizable medium the photons experience nonlinearities through the interactions they inherit from the atoms. If the atom-atom interaction range $L_E$ is also large compared to $a$, we show that scattering processes with momentum transfer between photons are suppressed by a factor $a/L_E$. We are then able to perform a self-consistent resummation of a specific (Hartree-like) diagram subclass and obtain quantitative results in the highly non-perturbative regime of large single-atom cooperativity. Here we find important, conceptually new collective phenomena emerging due to the dissipative nature of the interactions, which even give rise to novel phase transitions. The robustness of these is investigated by inclusion of the leading corrections in $a/L_E$. We consider specific applications to photons propagating under EIT conditions along waveguides near atomic arrays as well as within Rydberg ensembles.

arXiv commentaccepted version, 32 pages + 10 pages appendix, 32 figures

References in corpus (48)

• The Quantum Internet
• Topological Photonics
• Quantum fluids of light
• Stimulated Raman adiabatic passage in physics, chemistry and beyond
• Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber
• Quantum memory for photons: I. Dark state polaritons
• Exciton-polariton condensates
• Keldysh Field Theory for Driven Open Quantum Systems
• Quantum many-body models with cold atoms coupled to photonic crystals
• Efficient all-optical switching using slow light within a hollow fiber
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Atom-Light Interactions in Photonic Crystals
• Exponential improvement in photon storage fidelities using subradiance and "selective radiance" in atomic arrays
• Photon-Photon Interactions via Rydberg Blockade
• A Dissipatively Stabilized Mott Insulator of Photons
• Fermionized photons in an array of driven dissipative nonlinear cavities
• Cooperative non-equilibrium phase transition in a dilute Rydberg ensemble
• Nonlinear quantum optics mediated by Rydberg interactions
• Large Bragg Reflection from One-Dimensional Chains of Trapped Atoms Near a Nanoscale Waveguide
• Photon solid phases in driven arrays of nonlinearly coupled cavities
• Multi-photon Scattering Theory and Generalized Master Equations
• Universal non-equilibrium properties of dissipative Rydberg gases
• Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism
• Coherent backscattering of light off one-dimensional atomic strings
• Emergent equilibrium in many-body optical bistability
• Observation and measurement of "giant" dispersive optical non-linearities in an ensemble of cold Rydberg atoms
• Trapped Atoms in One-Dimensional Photonic Crystals
• Strongly correlated photon transport in waveguide QED with weakly coupled emitters
• Scattering resonances and bound states for strongly interacting Rydberg polaritons
• Sub-Poissonian statistics of Rydberg-interacting dark-state polaritons
• Wigner Crystallization of Single Photons in Cold Rydberg Ensemble
• Chemical potential for light by parametric coupling
• Stabilizing strongly correlated photon fluids with non-Markovian reservoirs
• Intrinsic Optical Bistability in a Strongly-Driven Rydberg Ensemble
• Dicke phase transition without total spin conservation
• Spontaneous crystallization of light and ultracold atoms
• Near-ground-state cooling of atoms optically trapped 300nm away from a hot surface
• Photon molecules in atomic gases trapped near photonic crystal waveguides
• Photon-number selective group delay in cavity induced transparency
• Many-body physics of Rydberg dark-state polaritons in the strongly interacting regime
• Correlated photon dynamics in dissipative Rydberg media
• Effective Field Theory for Rydberg Polaritons
• Photon propagation through dissipative Rydberg media at large input rates
• Fermionic formalism for driven-dissipative multi-level systems
• Classification of Dark States in Multi-level Dissipative Systems
• Critical relaxation with overdamped quasiparticles in open quantum systems
• Interaction-induced transparency for strong-coupling polaritons
• Dissipation-induced correlations in 1D bosonic systems

Cited by in corpus (9)

• Many-body localization in waveguide QED
• Experimental reconstruction of the few-photon nonlinear scattering matrix from a single quantum dot in a nanophotonic waveguide
• Long-range photon fluctuations enhance photon-mediated electron pairing and superconductivity
• Interaction-induced transparency for strong-coupling polaritons
• Multimode-polariton superradiance via Floquet engineering
• Fate of the Mollow triplet in strongly-coupled atomic arrays
• Controlling Collective Phenomena Via the Quantum State of Interaction-Mediators: Changing the Criticality of Photon-Mediated Superconductivity Via Fock States of Light
• The role of atomic interactions in cavity-induced continuous time crystals
• Routing single photons with quantum emitters coupled to nanostructures