We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows us to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.

The Heisenberg uncertainty principle sets a lower bound on the noise in a force measurement based on continuously detecting a mechanical oscillator's position. This bound, the standard quantum limit, can be reached when the oscillator subjected to the force is unperturbed by its environment and when measurement imprecision from photon shot noise is balanced against disturbance from measurement back-action. We applied an external force to the center-of-mass motion of an ultracold atom cloud in a high-finesse optical cavity and measured the resulting motion optically. When the driving force is resonant with the cloud's oscillation frequency, we achieve a sensitivity that is a factor of 4 above the standard quantum limit and consistent with theoretical predictions given the atoms' residual thermal disturbance and the photodetection quantum efficiency.

A complex quantum system can be constructed by coupling simple elements. For example, trapped-ion 1,2 or superconducting 3 quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively, quantum objects can be made to emit and exchange real photons, providing either unidirectional coupling in cascaded geometries 4-6 , or bidirectional coupling that is particularly strong when both objects are placed within a common electromagnetic resonator 7 . However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised by photon loss 8 . Here, we realize phase-coherent interactions between two addressable, spatially separated, near-groundstate mechanical oscillators within a driven optical cavity. We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics [8][9][10][11][12][13][14] .Cavity optomechanical systems comprised of a single mechanical oscillator interacting with a single electromagnetic cavity mode 15 serve useful quantum-mechanical functions, such as generating squeezed light [16][17][18] , detecting forces with quantum-limited sensitivity 19 or through back-action-evading measurement 20 , and both entangling and amplifying mechanical and optical modes 21 . Systems containing several mechanical elements offer additional capabilities. In the quantum regime, these systems may enable two-mode back-action-evading measurements 9 , creation of nonclassical states 10 , fundamental tests of quantum mechanics 8,11,12 , correlations at the quantum level with applications in highsensitivity measurements 13 , and quantum information science 14 . Realizing these proposed functions requires multiple-element cavity optomechanical systems in which quantum-mechanical optical force fluctuations dominate over thermal and technical ones.An important new feature in these multi-mechanical systems is photon-mediated forces between mechanical elements. Consider a driven cavity containing two mechanical elements with linear optomechanical coupling (Fig. 1a). Each element experiences radiation pressure proportional to the number of intracavity photons. The displacement of one element changes the cavity resonance frequency, causing a change in the intracavity photon number, and thereby modifying the force on the second element. In this manner, an effective optical spring is established between the mechanical elements (Fig. 1b). A quantized picture clarifies the role of cavity photons as the bidirectional force-mediating particle for this interaction: pump light is Stokes scattered off one element, generating a cavity photon that is absorbed through anti-Stokes scattering by the second element, and vice versa 7 (Fig. 1c). This cavity-mediated force has been shown to cause hybridization [22][23...