Ultrathin Tunable Optomechanical Metalens.

Reconfigurable metasurfaces offer great promises to enhance photonics technology by combining integration with improved functionalities. Recently, reconfigurability in otherwise static metasurfaces has been achieved by modifying the electric permittivity of the meta-atoms themselves or their immediate surrounding. Yet, it remains challenging to achieve significant and fast tunability without increasing bulkiness. Here, we demonstrate an ultrathin tunable metalens whose focal distance can be changed through optomechanical control with moderate continuous wave intensities. We achieve fast focal length changes of more than 5% with response time of the order of 10 µs.

Precision Calibration of the Duffing Oscillator with Phase Control.

The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to an external excitation. When changing the amplitude or frequency of the external excitation, a sudden jump in the response function reveals the nonlinear dynamics prominently. However, this bistability leaves part of the full response function unobserved, which limits the precise measurement of the system parameters. Here, we exploit the often unknown fact that the response of a Duffing oscillator with nonlinear damping is a unique function of its phase. By actively stabilizing the oscillator's phase we map out the full response function. This phase control allows us to precisely determine the system parameters. Our results are particularly important for characterizing nanoscale resonators, where nonlinear effects are observed readily and which hold great promise for next generation of ultrasensitive force and mass measurements. We demonstrate our approach experimentally with an optically levitated particle in high vacuum.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator.

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Quantum Acoustomechanics with a Micromagnet.

We show theoretically how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state or to enter into the strong quantum coupling regime. The center of mass can thus be used to probe and manipulate an acoustic mode, thereby opening new possibilities for out-of-equilibrium quantum mesoscopic physics. Our results hold for experimentally feasible parameters and apply to levitated micromagnets as well as micromagnets deposited on a clamped nanomechanical oscillator.

Resolved-Sideband Cooling of a Levitated Nanoparticle in the Presence of Laser Phase Noise.

We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to T_{min}=10 mK at a pressure of p=3×10^{-7} mbar, solely limited by phase noise. Finally we present possible strategies towards motional ground state cooling in the presence of phase noise.

Levitated Nanoparticles for Microscopic Thermodynamics-A Review.

Levitated Nanoparticles have received much attention for their potential to perform quantum mechanical experiments even at room temperature. However, even in the regime where the particle dynamics are purely classical, there is a lot of interesting physics that can be explored. Here we review the application of levitated nanoparticles as a new experimental platform to explore stochastic thermodynamics in small systems.

Direct measurement of Kramers turnover with a levitated nanoparticle.

Understanding the thermally activated escape from a metastable state is at the heart of important phenomena such as the folding dynamics of proteins, the kinetics of chemical reactions or the stability of mechanical systems. In 1940, Kramers calculated escape rates both in the high damping and low damping regimes, and suggested that the rate must have a maximum for intermediate damping. This phenomenon, today known as the Kramers turnover, has triggered important theoretical and numerical studies. However, as yet, there is no direct and quantitative experimental verification of this turnover. Using a nanoparticle trapped in a bistable optical potential, we experimentally measure the nanoparticle's transition rates for variable damping and directly resolve the Kramers turnover. Our measurements are in agreement with an analytical model that is free of adjustable parameters. The levitated nanoparticle presented here is a versatile experimental platform for studying and simulating a wide range of stochastic processes and testing theoretical models and predictions.

Cooling Mechanical Oscillators by Coherent Control.

In optomechanics, electromagnetic fields are harnessed to control a single mode of a mechanically compliant system, while other mechanical degrees of freedom remain unaffected due to the modes' mutual orthogonality and high quality factor. Extension of the optical control beyond the directly addressed mode would require a controlled coupling between mechanical modes. Here, we introduce an optically controlled coupling between two oscillation modes of an optically levitated nanoparticle. We sympathetically cool one oscillation mode by coupling it coherently to the second mode, which is feedback cooled. Furthermore, we demonstrate coherent energy transfer between mechanical modes and discuss its application for ground-state cooling.

Direct Measurement of Photon Recoil from a Levitated Nanoparticle.

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 Ω_{0}, this measurement backaction adds quanta ℏΩ_{0} 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 microkelvin 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.

Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state.

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize 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.

Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle.

We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source can be used to controllably drive the nanoparticle into the nonlinear regime, thereby generating strong coupling between the different translational modes of the nanoparticle. Our work contributes to the understanding of the nonlinear dynamics of levitated nanoparticles in high vacuum and paves the way for studies of pattern formation, chaos, and stochastic resonance.

Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond.

We present what we believe to be the first evidence of nitrogen vacancy (NV) photoluminescence (PL) from a nanodiamond suspended in a free-space optical dipole trap at atmospheric pressure. The PL rates are shown to decrease with increasing trap laser power, but are inconsistent with a thermal quenching process. For a continuous-wave trap, the neutral charge state (NV(0)) appears to be suppressed. Chopping the trap laser yields higher total count rates and results in a mixture of both NV(0) and the negative charge state (NV(-).

Subkelvin parametric feedback cooling of a laser-trapped nanoparticle.

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.