Cooperative Lamb Shift in a Mesoscopic Atomic Array

Abstract

Whenever several quantum light emitters are brought in proximity with one another, their interaction with common electromagnetic fields couples them, giving rise to cooperative shifts in their resonance frequency. Such collective line shifts are central to modern atomic physics, being closely related to superradiance[1] on one hand and the Lamb shift[2] on the other. Although collective shifts have been theoretically predicted more than fifty years ago [3], the effect has not been observed yet in a controllable system of a few isolated emitters. Here, we report a direct spectroscopic observation of the cooperative shift of an optical electric dipole transition in a system of up to eight Sr + ions suspended in a Paul trap. We study collective resonance shift in the previously unexplored regime of far-field coupling, and provide the first observation of cooperative effects in an array of quantum emitters. These results pave the way towards experimental exploration of cooperative emission phenomena in mesoscopic systems.Soon after the discovery of superradiance by Dicke[1], it was realized [3][4][5] that superradiance phenomena are accompanied by a dispersive counterpart that shifts the resonance energies of the collective excitations relative to those of isolated emitters. The superradiance effects and the resonance shift originate, respectively, from the real and imaginary parts of resonant dipole-dipole interaction between emitters. The collective shifts arise via emission and reabsorption of virtual photons, and are therefore referred to as cooperative Lamb shift [6][7][8][9][10].Although cooperative phenomena have received a great deal of scientific attention, the experimental observations of collective Lamb shift have been relatively few. Cooperative shifts have been detected in a three-photon excitation resonance in Xenon [11] and, recently, in the absorption line of Rubidium vapor confined to an ultrathin cell [7]. In both cases, the cooperative shifts, arising from statistically averaged interaction of a large ensemble of atoms, were proportional to the atomic density.In a different approach, the energy level shifts due to resonant dipole-dipole interaction in the near field were studied in a system of two fluorescent molecules embedded in a dielectric film [12]. Such near-field interactions * These authors contributed equally to this work have also played an essential role in a number of experiments with Rydberg atoms [13][14][15]. In particular, the near-field cooperative shift in a system of two atoms has been utilized to prevent the transition of more than one atom to the Rydberg state, bringing about a phenomenon known as Rydberg blockade [16][17][18].Cooperative phenomena can be amplified by placing the emitters inside a resonator. Cavity-enhanced cooperative frequency shift in a nuclear excitation has been observed in a layer of Fe atoms embedded in a planar waveguide [8]. The coupling between emitters can also be enhanced by interaction with a single mirror. Such arrangement enabled the observation...

Exact electrodynamics versus standard optics for a slab of cold dense gas

“…This subject is obviously very old, but cold atomic samples afford an opportunity for experiments in unprecedented regimes and in unprecedented detail. Correspondingly, new experiments are emerging rapidly [1][2][3][4][5][6][7][8][9][10]. The measurements of the optical response have been dominated by trapped inhomogeneous atomic ensembles, but also those with atoms confined in a slab geometry are emerging in increasing numbers in both thermal vapor cells using a hot gas [11] and in the ultracold regime [12].…”

Cooperative Interactions in Lattices of Atomic Dipoles

“…For example, the first experimental demonstration of superradiance and subradiance for an ensemble of microscopically resolvable particles was for a pair of ions separated with varying separation [4]. Similar recent studies have measured cooperative shifts in ion chains up to N = 8 [5], superradiance for 0.19 〈N 〉 2.6 atoms coupled along a 1D waveguide [10], and excitation hopping along 1D atoms chains (N = 3 [50]) which may also exhibit subradiance (N = 20 [40]). …”

“…1.3). These have been realised experimentally in a number of different systems, including quantum dots [2], nuclei [3], ions [4,5,6], Bose-Einstein condensates [7], cold atoms [8,9,10,11] and atoms at room-temperature [12]. Additional cooperative phenomena can include highly directional scattering [13], excitation localization [14,15,16], and modified optical transmission and scattering [17,18,19].…”

“…4.2) also means that the interaction across the lattice has a strongly resonant behaviour. These two factors combined mean that periodically structured lattices of atoms can result in striking cooperative behaviour [5,14,40,64,65]. Reducing the dimensionality of the system also allows us to tailor the anisotropic dipole-dipole interaction, and the eigenmodes in lattices are typically much cleaner and more distinct than in random ensembles, exhibiting well defined patterns and structures.…”

“…7,8) or two (Chaps. 5,6) or the three possible dipole polarisations, reducing the effective atomic Hamiltonians to 3-level or 2-level systems respectively.…”