No abstract

Quantum probes are atomic-sized devices mapping information of their environment to quantum mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum technologies. We realize spin-based quantum probes by immersing individual Cs atoms into an ultracold Rb bath. Controlling inelastic spin-exchange processes between probe and bath allows mapping motional and thermal information onto quantum-spin states. We show that the steady-state spin-population is well suited for absolute thermometry, reducing temperature measurements to detection of quantum spin distributions. Moreover, we find that the information gain per inelastic collision can be maximized by accessing the nonequilibrium spin dynamic. The sensitivity of nonequilibrium quantum probing effectively beats the steady-state Cramér Rao limit of quantum probing by almost an order of magnitude, while reducing the perturbation of the bath to only three quanta of angular momentum. Our work paves the way for local probing of quantum systems at the Heisenberg limit, and moreover for optimizing measurement strategies via control of nonequilibrium dynamics.

Understanding the motion of a tracer particle in a rarefied gas is of fundamental and practical importance. We report the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the nonequilibrium relaxation of the initial nonthermal state and detect the effect of single collisions which has eluded observation so far. We show that after few collisions, the measured spatial distribution of the light tracer atoms is correctly described by a generalized Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers.

Di usion can be used to infer the microscopic features of a system from the observation of its macroscopic dynamics. Brownian motion accurately describes many di usive systems, but non-Brownian and nonergodic features are often observed on short timescales. Here, we trap a single ultracold caesium atom in a periodic potential and measure its di usion [1][2][3] . We engineer the particle-environment interaction to fully control motion over a broad range of di usion constants and timescales. We use a powerful stroboscopic imaging method to detect single-particle trajectories and analyse both non-equilibrium di usion properties and the approach to ergodicity 4 . Whereas the variance and two-time correlation function exhibit apparent Brownian motion at all times, higherorder correlations reveal strong non-Brownian behaviour. We additionally observe the slow convergence of the exponential displacement distribution to a Gaussian and-unexpectedly-a much slower approach to ergodicity 5 , in perfect agreement with an analytical continuous-time random-walk model [6][7][8] . Our experimental system o ers an ideal testbed for the detailed investigation of complex di usion processes.The concept of diffusion is ubiquitous in physics 9 , chemistry 10 and biology 11 . Recent developments have lead to a better understanding of the diffusive behaviour of increasingly complex structures, from colloid particles 12 and anisotropic ellipsoids 13 to extended stiff filaments 14 and fluidized matter 15 . At the same time, the diffusion of tracer particles has become a powerful experimental tool to probe the properties of complex systems from turbulent fluids 16 to living cells 17 . In many systems, diffusion is well described by the theory of Brownian motion 1 . The hallmarks of standard Brownian diffusion are: a linear mean-square displacement (MSD), σ, where D is the diffusion coefficient and · denotes the average over many trajectories; a Gaussian displacement probability distribution, a direct consequence of the central-limit theorem; and ergodic behaviour in a potential, implying that ensemble and time averages are equal in the longtime limit. Ergodicity lies at the core of statistical mechanics and indicates that a single trajectory is representative for the ensemble 4 . However, an increasing number of systems exhibit nonergodic features owing to slow, non-exponential relaxation. Examples include blinking quantum dots 18 , the motion of lipid granules 19 , and mRNA molecules 20 and receptors in living cells 21 . These systems lie outside the range of standard statistical physics and their description is hence particularly challenging 5,22 . Of special interest is the question of the approach to ergodicity. Many relevant processes in nature indeed occur on finite timescales 19-21 during which ergodic behaviour cannot be taken for granted.We experimentally realize an ideal system consisting of a single atom moving in a periodic potential and interacting with a nearresonant light field that acts as a thermal bath. Diffusion in a per...