We optically trap a single nanoparticle in high vacuum and cool its three spatial degrees of freedom by means of active parametric feedback. Using a single laser beam for both trapping and cooling we demonstrate a temperature compression ratio of four orders of magnitude. The absence of a clamping mechanism provides robust decoupling from the heat bath and eliminates the requirement of cryogenic precooling. The small size and mass of the nanoparticle yield high resonance frequencies and high quality factors along with low recoil heating, which are essential conditions for ground state cooling and for low decoherence. The trapping and cooling scheme presented here opens new routes for testing quantum mechanics with mesoscopic objects and for ultrasensitive metrology and sensing.

The momentum transfer between a photon and an object defines a fundamental limit for the precision with which the object can be measured. If the object oscillates at a frequency Ω0, this measurement back-action adds quantahΩ0 to the oscillator's energy at a rate Γ recoil , a process called photon recoil heating, and sets bounds to coherence times in cavity optomechanical systems. Here, we use an optically levitated nanoparticle in ultrahigh vacuum to directly measure Γ recoil . By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to micro-Kelvin temperatures and measure its reheating rate under the influence of the radiation field. The recoil heating rate is measured for different particle sizes and for different excitation powers, without the need for cavity optics or cryogenic environments. The measurements are in quantitative agreement with theoretical predictions and provide valuable guidance for the realization of quantum ground-state cooling protocols and the measurement of ultrasmall forces.

Nano- and micromechanical oscillators with high quality (Q) factors have gained much attention for their potential application as ultrasensitive detectors. In contrast to micro-fabricated devices, optically trapped nanoparticles in vacuum do not suffer from clamping losses, hence leading to much larger Q-factors. We find that for a levitated nanoparticle the thermal energy suffices to drive the motion of the nanoparticle into the nonlinear regime. First, we experimentally measure and fully characterize the frequency fluctuations originating from thermal motion and nonlinearities. Second, we demonstrate that feedback cooling can be used to mitigate these fluctuations. The high level of control allows us to fully exploit the force sensing capabilities of the nanoresonator. Our approach offers a force sensitivity of 20 zN $Hz^{-1/2}$, which is the highest value reported to date at room temperature, sufficient to sense ultra-weak interactions, such as non-Newtonian gravity-like forces.Comment: 12 pages, 5 figure

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterise the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance. PACS numbers:One of the tenets of statistical physics is the central limit theorem. It allows systems with many microscopic degrees of freedom to be reduced to only a few macroscopic thermodynamic variables. The central limit theorem states that, independently of the distribution of the microscopic variables, a macroscopic extensive quantity U , such as the total energy of a system with N degrees of freedom, follows a Gaussian distribution with mean U ∝ N and variance σ The statistical properties of the fluctuations of thermodynamic quantities like heat, work and entropy production are described by exact relations known as fluctuation theorems [2][3][4][5], which permit to express the inequalities familiar from macroscopic thermodynamics as equalities [6,7]. Fluctuation relations are particularly important for understanding fundamental chemical and biological processes, which occur on the mesoscale where the dynamics are dominated by thermal fluctuations [8]. They allow us, for instance, to relate the work along non-equilibrium trajectories to thermodynamic free-energy differences [9,10] [16,17]. Most of these experiments are described by an overdamped Langevin equation. However, systems in the underdamped regime [18], or in quantum systems [19] where the concept of a classical trajectory looses its meaning, are less explored.Here, we study the thermal relaxation of a highly underdamped nanomechanical oscillator from a non-equilibrium steady state towards equilibrium. Because of the low damping of our system, the dynamics can be precisely controlled even at the quantum level [20][21][22]. This high level of control allows us to produce non-thermal steady states and makes nanomechanical oscillators ideal candidates for investigating non-equilibrium fluctuations for transitions between arbitrary steady states. While for the initial steady state detailed balance is violated, the relaxation dynamics are described by a microscopically reversible Langevin equation that satisfies detailed balance [23]. Under these conditions, a...

run), and the combination of low pressure ( < ∼ 10 −13 Pa) and low temperature ( < ∼ 20 K) while having full optical access. These conditions cannot be fulfilled with ground-based experiments. E. Technological heritage for MAQROMAQRO benefits from recent developments in space technology. In particular, MAQRO relies on technological heritage from LISA Pathfinder (LPF) [18], the LISA technology package (LTP) [19], GAIA[20], GOCE[21,22], Microscope [23,24] and the James Webb Space Telescope (JWST) [25]. The spacecraft, launcher, ground segment and orbit (L1/L2) are identical to LPF.The most apparent modifications to the LPF design are an external, passively cooled optical instrument thermally shielded from the spacecraft, and the use of two capacitive inertial sensors from ONERA technology. In addition, the propulsion system will be mounted differently to achieve the required low vacuum level at the external subsystem, and to achieve low thruster noise in one spatial direction. The additional optical instruments and the external platform will reach TRL 5 at the start of the BCD phases. For all other elements, the TRL is 6-9 because of the technological heritage from LPF and other missions.