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arXiv:2412.02541 · PRX Quantum

Single-Atom Resolved Collective Spectroscopy of a One-Dimensional Atomic Array

Britton Hofer, Damien Bloch, Giulio Biagioni, Nathan Bonvalet, Antoine Browaeys, Igor Ferrier-Barbut

Published Aug 7, 2025• 7 citations
arXivHTMLPDF

Abstract

Ordered atomic arrays feature an enhanced collective optical response compared to random atomic ensembles due to constructive interference in resonant dipole-dipole interactions. One consequence of this is the existence of a large shift of the transition with respect to the bare atomic frequency. In the linear optics regime (low light intensity), one observes a spectroscopic shift of the Lorentzian atomic line often called the collective Lamb shift. For stronger driving, many excitations are present in the system rendering the calculation of this shift theoretically challenging, but its understanding is important for instance when performing Ramsey spectroscopy in optical clocks. Here we report on the study of the collective optical response of a one-dimensional array of 30 dysprosium atoms. We drive the atoms on the narrow intercombination transition isolating a two-level system, and measure the atomic state with single-shot state readout using a broad transition. In the linear optics regime, we measure the shift of the resonance in steady state due to dipole interactions, and measure how this shift depends on the interatomic distance. We further resolve at the single atom level how the excitation is distributed over the array. Then, on the same transition we perform Ramsey spectroscopy i.e., away from the linear regime. We observe a time-dependent shift, that allows us to draw the connection between the collective Lamb shift observed in the linear optics regime and in the large-excitation case.

DOI
10.1103/xf8r-ymrj

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•Jan 1, 2022•0 citations
Ordered atomic arrays feature an enhanced collective optical response compared to random atomic ensembles due to constructive interference in resonant dipole-dipole interactions. One consequence of this is the existence of a large shift of the transition with respect to the bare atomic frequency. In the linear optics regime (low light intensity), one observes a spectroscopic shift of the Lorentzian atomic line often called the collective Lamb shift. For stronger driving, many excitations are present in the system rendering the calculation of this shift theoretically challenging, but its understanding is important for instance when performing Ramsey spectroscopy in optical clocks. Here we report on the study of the collective optical response of a one-dimensional array of 30 dysprosium atoms. We drive the atoms on the narrow intercombination transition isolating a two-level system, and measure the atomic state with single-shot state readout using a broad transition. In the linear optics regime, we measure the shift of the resonance in steady state due to dipole interactions, and measure how this shift depends on the interatomic distance. We further resolve at the single atom level how the excitation is distributed over the array. Then, on the same transition we perform Ramsey spectroscopy i.e., away from the linear regime. We observe a time-dependent shift, that allows us to draw the connection between the collective Lamb shift observed in the linear optics regime and in the large-excitation case.
We experimentally study resonant light scattering by a one-dimensional randomly filled chain of cold two-level atoms. By a local measurement of the light scattered along the chain, we observe constructive interferences in light-induced dipole-dipole interactions between the atoms. They lead to a shift of the collective resonance despite the average interatomic distance being larger than the wavelength of the light. This result demonstrates that strong collective effects can be enhanced by structuring the geometrical arrangement of the ensemble. We also explore the high intensity regime where atoms cannot be described classically. We compare our measurement to a mean-field, nonlinear coupled-dipole model accounting for the saturation of the response of a single atom.
We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions, mediated by single-atom couplings to the shared electromagnetic vacuum, are shown to produce spatially-dependent cooperative Lamb shifts when spectroscopically interrogating the mHz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for state-of-the-art optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared to non-resonant geometries. Given the remarkable precision of frequency measurements and the high accuracy of the modeled response, our work demonstrates that such a clock is a novel platform for studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.
Collective couplings of atomic dipoles to a shared electromagnetic environment produce a wide range of many-body phenomena. We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions produce spatially dependent cooperative Lamb shifts when spectroscopically interrogating the millihertz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared with nonresonant geometries. Our work demonstrates a platform for precise studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.
The coherent photon scattering of atoms in an atomic array is studied. It is found that due to cooperative photon exchanges, the excitation probability of an atom in an array parallel to the direction of laser propagation ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$) will either grow or decay along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $a=j\ensuremath{\lambda}/2$ causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array, where jjj is an integer and $\ensuremath{\lambda}$ is the transition wavelength. For atomic separations of $a<\ensuremath{\lambda}/2$, a collection of nonradiating states ($\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}0$) disrupts the described trend. In order to interpret this surprising result, a band-structure calculation in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is conducted, where the decay rates and the collective Lamb shifts of the eigenmodes versus quasimomentum are obtained. This calculation shows that the collective exchange of photons in an array strongly affects its scattered radiation, allowing one to easily manipulate the collective Lamb shift and directly excite either superradiant or subradiant eigenmodes by correctly choosing the angle of the driving laser.
According to quantum electrodynamics, the exchange of virtual photons in a system of identical quantum emitters causes a shift of its energy levels. Such shifts, known as cooperative Lamb shifts, have been studied mostly in the near-field regime. However, the resonant electromagnetic interaction persists also at large distances, providing coherent coupling between distant atoms. Here, we report a direct spectroscopic observation of the cooperative Lamb shift of an optical electric-dipole transition in an array of Sr(+) ions suspended in a Paul trap at inter-ion separations much larger than the resonance wavelength. By controlling the precise positions of the ions, we studied the far-field resonant coupling in chains of up to eight ions, extending to a length of 40 μm. This method provides a novel tool for experimental exploration of cooperative emission phenomena in extended mesoscopic atomic arrays.
A principal goal of distributed quantum processing is the ability to generate, manipulate, and transfer quantum states between distant nodes of a quantum network. These protocols generally require connecting photonic and material carriers of quantum information. In this thesis, I present investigations of two experimental realizations of light-matter interfaces that allow for engineered atom-photon interactions in free-space settings. First, we utilize reconfigurable arrays of trapped single atoms to study light scattering in lowdimensional systems. We observe noncollinear phase-matching geometries that have suppressed sensitivity to particle localization. We show that the scattered radiation can be controllably enhanced or diminished as a result of Bragg interference. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays. Second, we utilize ensembles of trapped Rydberg atoms to study collective many-body phenomena that arise due to strong dipole-dipole interactions. To do so, we employ a magic-wavelength optical lattice that allows for the simultaneous trapping of both ground and Rydberg levels. Using the enhanced coherence times enabled by this trapping scheme, we measure the so-called magic lattice detunings and use them to extract the 6P3/2 − nS1/2 reduced electric dipole matrix elements. Furthermore, we perform precision measurements of differential nuclear-spin dependent light shifts in the Paschen-Back regime in order to determine the hyperfine splitting of Rydberg levels. We create a quasi-two-level system in a regime of Rydberg excitation blockade for a mesoscopic ensemble of several hundred atoms. Using this system, we study Hanbury Brown-Twiss interference between the field radiated by the atoms and an input probe field with a controllable relative phase. Finally, we demonstrate coherent driving and Ramsey interference measurements of light shifts, with timescales on the order of ≃ 10 µs. Whereas the coupling producing the Rabi oscillations is enhanced, there is no corresponding enhancement for the lightshifts. These results may prove useful in applying collective qubits with Rydberg interactions to scalable quantum networking architectures.