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.
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.
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.
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.
Strontium optical lattice clocks at JILA recently demonstrated record-high accuracy and stability. These advances were enabled by an ultrastable laser with fractional frequency stability of 1x10-16 at 1 second. This laser allows us to study systematic shifts of the 1S0 to 3P0 clock transition with unprecedented precision. Density-dependent frequency shifts represent an unavoidable perturbation for clocks based on many atoms. Our studies of atomic interactions in an optical lattice clock system uncover the nature of these interactions and reveal important many-body atomic correlation effects in this open quantum system. By extending our measurements to all ten nuclear-spin sublevels of the clock states, we observe the first direct evidence of SU(N) symmetric interactions in alkaline earth(-like) atoms. Using the techniques we developed in these studies, we also demonstrate a novel technique for measuring the frequency noise spectrum of an ultrastable laser. We discuss designs for the future direction of our experiment which will place 87Sr atoms within a high finesse cavity that is resonant on the 1S0 to 3P1 transition. We will use this system to study collective effects in cavity quantum electrodynamics. Most notably, strong atom-cavity coupling can enhance the spectroscopic sensitivity of our clock by creating spin-squeezed states via quantum non-demolition measurements. As a precursor to future work studying cavity-mediated collective behavior, we use the unique atomic structure of 88Sr to investigate free-space retarded dipolar coupling in an optically thick sample of atoms.
Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the level of 10(-17). This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve as the number of particles increases.
Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves, leaving room for further progress. Here we implement a "multiplexed" one-dimensional optical lattice clock, in which spatially-resolved, movable ensembles of ultra-cold strontium atoms are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser, and read-out in parallel. By performing synchronized Ramsey interrogations of ensemble pairs we observe atom-atom coherence times up to 26 seconds, a 270-fold improvement over the atom-laser coherence time, demonstrate a relative stability of 9.7(4)×10−18/τ (where τ is the averaging time in seconds), and reach a fractional uncertainty of 8.9(3)×10−20 after 3.3 hours of averaging. These results demonstrate that applications requiring ultra-high-precision comparisons between optical atomic clocks need not be limited by the stability of the local oscillator. With multiple ensemble pairs, we realize a miniaturized clock network consisting of 6 atom ensembles, resulting in 15 unique pairwise clock comparisons with relative stabilities below 3×10−17/τ. Finally, we demonstrate the capability to simultaneously load spatially-resolved, heterogeneous ensemble pairs of all four stable isotopes of strontium in a lattice. The unique capabilities offered by this platform pave the way for future studies of precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, development of clock-based gravitational wave and dark matter detectors, and novel tests of relativity including measurements of the gravitational redshift at sub-centimeter scales.