Collective effects in the photon statistics of thermal atomic ensembles

Abstract

We investigate the collective scattering of coherent light from a thermal alkali-metal vapor with temperatures ranging from 350 to 450 K, corresponding to average atomic spacings between 0.7λ and 0.1λ. We develop a theoretical model treating the atomic ensemble as coherent, interacting, radiating dipoles. We show that the two-time second-order correlation function of a thermal ensemble can be described by an average of randomly positioned atomic pairs. Our model illustrates good qualitative agreement with the experimental results. Furthermore, we show how fine-tuning of the experimental parameters may make it possible to explore several photon statistics regimes.

Weak localization of light in hot atomic vapors

“…A central motivation for studying light scattering in clouds of moving atoms is to clarify how decoherence emerges when turning from a cold gas to a hot, "classical" one. Recently, this problem has triggered much interest in the context of collective scattering [17,18], metrology [19], and quantum information [20]. A typical illustration of the role of decoherence is provided by the weak localization * cherroret@lkb.upmc.fr effect, which corresponds to the interference between two optical paths involving the same sequence of atomic scattering events but traveled in opposite directions.…”

Quantum emission of light with densely packed driven dipoles

“…This ongoing interest has led to the development of a variety of cell designs, and it is possible to create etched two-dimensional and onedimensional nanochannels [58], where thermal vapor placed in such etched arrays will typically have more than one atom per site (N 1). We use a model developed to treat the collective scattering of coherent light from a thermal vapor [59] to theoretically study the photon statistics of the emitted light for ensembles of dipoles in different spatial configurations, including regular or random two-dimensional arrangements (see Fig. 1).…”

“…where σ + j = |e j j g| and σ − j = |g j j e| are the usual raising and lowering operators for the jth emitter, and 2γ j j = 2 is the Einstein A coefficient for spontaneous emission from a single dipole. The collective parameters γ jl ( j = l ) and g jl describe the damping rate and the dipole-dipole coupling arising from the mutual influence of the emitters via the electromagnetic field [59]. In a running-wave laser field we write j = R exp(−i k L • r j ), where R is the maximum Rabi frequency.…”

“…( 1) to study the system dynamics of the system by determining correlation functions for the operators σ ± j ( j = 1, 2), via the identity Q = Tr S {ρ Q} for any operator Q. For the two-dipole configuration, we obtain a closed system of 15 first-order differential equations of motion for the expectation values of the operators and correlations [59,60], and solve these for the steady state by assuming ( σ ± j ) 2 = 0 and noting that operators for different emitters commute at the same time. In general we wish to study the second-order correlation function of fluorescence photons emitted by an ensemble of N 2 dipoles and detected by a single photodetector at a point R in the far-field zone of the radiation emitted by the emitter system [61],…”

“…Following the procedure in Ref. [59], we use Eq. ( 1) to solve the dynamics for random pairs of emitters and average the photon statistics of multiple different random pairs.…”