Many-body physics of Rydberg dark-state polaritons in the strongly interacting regime

Abstract

Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of strongly interacting quasi-particles, termed Rydberg polaritons. We derive a onedimensional model describing the time evolution of these polaritons under paraxial propagation conditions, which we verify by numerical two-excitation simulations. We determine conditions allowing for a description by an effective Hamiltonian of a single-species polariton, and calculate ground-state correlations by use of the density matrix renormalization group (DMRG). Under typical stationary slow-light EIT conditions it is difficult to reach the strongly interacting regime where the interaction energy dominates the kinetic energy. We show that by employing time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasi crystalline order. We analyze the dynamics and resulting correlations for a translational invariant system in terms of a time-dependent Luttinger liquid theory and exact few-particle simulations and address the effects of nonadiabatic corrections and initial excitations.

Quantum and Nonlinear Optics in Strongly Interacting Atomic Ensembles

“…The average time delay between transmitted photons, R −1 o , however, was substantially larger than the correlation time of the observed g (2) (τ ) ( see FIG.13), which, consequently does not exhibit any features beyond short-ranged "nearest-neighbour" correlations. While long-range ordered photon states still await experimental verification, theoretical work has made intriguing predictions about the formation of regular photon crystals by dispersive nonlinearities based on a perturbative treatment of Rydberg-Rydberg atom interactions (Moos et al, 2015;Otterbach et al, 2013).…”

Contactless nonlinear optics mediated by long-range Rydberg interactions

“…We measure these correlations as a function of interaction strength, distance and storage time, demonstrating an e ective interaction between photons separated by 15 times their wavelength. Contactless e ective photon-photon interactions 16 are relevant for scalable multichannel photonic devices 15,17 and the study of strongly correlated many-body dynamics using light 18 . In vacuum, photon-photon interactions are so weak that they are discernible only at cosmological scales 19 .…”

“…4) indicates that interaction-induced phase shifts make an important contribution to the overall interaction. Although the channels are separated by more than the radius, r b (80S 1/2 ) ≈ 9 µm < d, for inter-channel dipole blockade between collective excitations 11,27 , blockade effects beyond d associated with the storage protocol 18 may also contribute to the interaction.…”

Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons

“…In turn, it has recently been proposed to use Rydberg slow light polaritons for the generation of a quantum two qubit gate [18,19], which seem to be in contradiction to the above no-go theorem. In the present manuscript, we resolve this puzzle by demonstrating that the microscopic description of Rydberg polaritons also provides a consistent quantum theory of a Kerr nonlinearity without the necessity to introduce a strong noise term.Rydberg slow light polaritons have emerged as a highly promising candidate to engineer strong interactions between optical photons with a tremendous recent experimental [16,[20][21][22][23][24][25][26][27][28][29][30] and theoretical [19,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] progress. A variety of applications were shown such as a deterministic single photon source [50], an atomphoton entanglement generation [51], as well as a single photon switch [27] and transistors [26,28,29].…”

“…Moreover, the regime of strong interaction between photons has been experimentally demonstrated leading to a medium transparent only to single photons [22], as well as the appearance of bound states for photons [25]. From theoretical point of view, the effective low energy theory is well understood from a microscopic approach [32,52], but a full description of the propagation of photons through the medium is limited to extensive numerical simulations and low photon number [19,22,25,34,[41][42][43][44][45].In this manuscript, we provide the full input-output formalism of Rydberg polaritons for weak and intermediate interaction strengths, where the dispersion relation for the polaritons is well described by the slow light velocity alone, but arbitrary incoming photon number and shape of the atomic medium. The analysis is OPEN ACCESS RECEIVED…”