Collective radiative dynamics of an ensemble of cold atoms coupled to an optical waveguide

Abstract

We experimentally and theoretically investigate collective radiative effects in an ensemble of cold atoms coupled to a single-mode optical nanofiber. Our analysis unveils the microscopic dynamics of the system, showing that collective interactions between the atoms and a single guided photon gradually build-up along the atomic array in the direction of propagation of light. These results are supported by time-resolved measurements of the light transmitted and reflected by the ensemble after excitation via nanofiber-guided laser pulses, whose rise and fall times are shorter than the atomic lifetime. Superradiant decays more than one order of magnitude faster than the single-atom free-space decay rate are observed for emission in the forward-propagating guided mode, while at the same time no speed-up of the decay rate are measured in the backward direction. In addition, position-resolved measurements of the light that is transmitted past the atoms are performed by inserting the nanofiber-coupled atomic array in a 45-m long fiber ring-resonator, which allow us to experimentally reveal the progressive growth of the collective response of the atomic ensemble. Our results highlight the unique opportunities offered by nanophotonic cold atom systems for the experimental investigation of collective light-matter interaction.

Observation of coherent coupling between super- and subradiant states of an ensemble of cold atoms collectively coupled to a single propagating optical mode

“…To theoretically describe light-matter interaction in an ensemble of waveguide-coupled atoms, we follow the formalism of Refs. [10,15,26]. In brief, we start by establishing a real-space non-Hermitian Hamiltonian for N two-level atoms coupled to a single optical mode:…”

“…An ensemble in the timed Dicke state experiences superradiant decay and collectively enhanced emission of light into the same optical mode that excited the system. Likewise, it is possible to introduce N − 1 states, that are orthogonal to the timed Dicke state and subradiant with respect to the optical mode with wavevector k. This approach is suitable for describing a considerable number of physical systems, including for instance cold atom clouds [3][4][5][6][7][8][9][10], Rydberg atoms [11,12] and emitters in solid state samples [13]. In addition, in cavity quantum electrodynamics the timed Dicke physics is at the basis of the assumptions of the Tavis-Cummings model [14,15], which describes collectively enhanced light-matter coupling between an atomic ensemble and a single mode cavity [16,17].…”

“…1(b). Throughout this Letter, we assume unidirectional propagation, an approximation which is justified by the collective enhancement of forward emission typical of the timed Dicke state [2,10] and which holds as long as the atoms are not arranged at the Bragg condition (i.e., inter-atomic distance equal to an integer multiple of λ 2 ). In addition, for simplicity we also assume that all atoms have the same coupling strength β to the waveguide, a situation which describes well, e.g., trapped atoms [7,24,25].…”

“…where χ N (t) is the complex amplitude of the light field right after the N th atom and v g is the group velocity of the guided optical mode. We note that Γ ens (t) is sometimes inferred from the decay rate of the light intensity emitted by the atoms into the considered mode, Γ light (t), [4,5,9,10,12], i.e. :…”

“…To theoretically describe the time-evolution of |ψ(t) , we follow the approach of [10,15,26], which, starting from a real-space Hamiltonian, allows us to calculate the excitation amplitudes, φ n , in the steady state by solving the time-independent Schrödinger equation. In the low excitation limit, the dynamics of the system in the timedomain can be then obtained via Fourier analysis (see Supplemental Material).…”