No Arabic abstract
We report quantum ground state cooling of a levitated nanoparticle in a room temperature environment. Using coherent scattering into an optical cavity we cool the center of mass motion of a $143$ nm diameter silica particle by more than $7$ orders of magnitude to $n_x=0.43pm0.03$ phonons along the cavity axis, corresponding to a temperature of $12~mu$K. We infer a heating rate of $Gamma_x/2pi = 21pm 3$ kHz, which results in a coherence time of $7.6~mu$s -- or $15$ coherent oscillations -- while the particle is optically trapped at a pressure of $10^{-6}$ mbar. The inferred optomechanical coupling rate of $g_x/2pi = 71$ kHz places the system well into the regime of strong cooperativity ($C approx 5$). We expect that a combination of ultra-high vacuum with free-fall dynamics will allow to further expand the spatio-temporal coherence of such nanoparticles by several orders of magnitude, thereby opening up new opportunities for macrosopic quantum experiments.
The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering. Today, the increasing demand for applied quantum technologies requires to adapt this level of control to individual quantum systems. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback. Successful implementations thus far include experiments on the level of optical and atomic systems. Here we demonstrate real-time optimal control of the quantum trajectory of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of $n=0.56pm0.02$ quanta, realizing quantum ground state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.
Near-field, radially symmetric optical potentials centred around a levitated nanosphere can be used for sympathetic cooling and for creating a bound nanosphere-atom system analogous to a large molecule. We demonstrate that the long range, Coulomb-like potential produced by a single blue detuned field increases the collisional cross-section by eight orders of magnitude, allowing fast sympathetic cooling of a trapped nanosphere to microKelvin temperatures using cold atoms. By using two optical fields to create a combination of repulsive and attractive potentials, we demonstrate that a cold atom can be bound to a nanosphere creating a new levitated hybrid quantum system suitable for exploring quantum mechanics with massive particles.
Quantum control of a system requires the manipulation of quantum states faster than any decoherence rate. For mesoscopic systems, this has so far only been reached by few cryogenic systems. An important milestone towards quantum control is the so-called strong coupling regime, which in cavity optomechanics corresponds to an optomechanical coupling strength larger than cavity decay rate and mechanical damping. Here, we demonstrate the strong coupling regime at room temperature between a levitated silica particle and a high finesse optical cavity. Normal mode splitting is achieved by employing coherent scattering, instead of directly driving the cavity. The coupling strength achieved here approaches three times the cavity linewidth, crossing deep into the strong coupling regime. Entering the strong coupling regime is an essential step towards quantum control with mesoscopic objects at room temperature.
We employ spin-dependent optical dipole forces to characterize the transverse center-of-mass (COM) motional mode of a two-dimensional Wigner crystal of hundreds of $^9$Be$^+$. By comparing the measured spin dephasing produced by the spin-dependent force with the predictions of a semiclassical dephasing model, we obtain absolute mode temperatures in excellent agreement with both the Doppler laser cooling limit and measurements obtained from a previously published technique (B. C. Sawyer et al. Phys. Rev. Lett. textbf{108}, 213003 (2012)). Furthermore, the structure of the dephasing histograms allows for discrimination between initial thermal and coherent states of motion. We also apply the techniques discussed here to measure, for the first time, the ambient heating rate of the COM mode of a 2D Coulomb crystal in a Penning trap. This measurement places an upper limit on the anomalous single-ion heating rate due to electric field noise from the trap electrode surfaces of $frac{dbar{n}}{dt}sim 5$ s$^{-1}$ for our trap at a frequency of 795 kHz, where $bar{n}$ is the mean occupation of quantized COM motion in the axial harmonic well.
We report three-dimensional cooling of a levitated nanoparticle inside an optical cavity. The cooling mechanism is provided by cavity-enhanced coherent scattering off an optical tweezer. The observed 3D dynamics and cooling rates are as theoretically expected from the presence of both linear and quadratic terms in the interaction between the particle motion and the cavity field. By achieving nanometer-level control over the particle location we optimize the position-dependent coupling and demonstrate axial cooling by two orders of magnitude at background pressures as high as $6times10^{-2}$ mbar. We also estimate a significant ($> 40$ dB) suppression of laser phase noise, and hence of residual heating, which is a specific feature of the coherent scattering scheme. The observed performance implies that quantum ground state cavity cooling of levitated nanoparticles can be achieved for background pressures below $10^{-7}$ mbar.