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Register a new userLarge Quantum Delocalization of a Levitated Nanoparticle using Optimal Control: Applications for Force Sensing and Entangling via Weak Forces
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We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility to invert it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticles center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.
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The superposition principle is one of the main tenets of quantum mechanics. Despite its counter-intuitiveness, it has been experimentally verified using electrons, photons, atoms, and molecules. However, a similar experimental demonstration using a nano or a micro particle is non-existent. Here in this Letter, exploiting macroscopic quantum coherence and quantum tunneling, we propose an experiment using levitated magnetic nanoparticle to demonstrate such an effect. It is shown that the spatial separation between the delocalized wavepackets of a $20~$nm ferrimagnetic yttrium iron garnet (YIG) nanoparticle can be as large as $5~$$mu$m. We argue that this large spatial separation can be used to test different modifications such as collapse models to the standard quantum mechanics. Furthermore, we show that the spatial superposition of a core-shell structure, a YIG core and a non-magnetic silica shell, can be used to probe quantum gravity.
Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting quantum sensors from environmental noise, while leaving their strong coupling to the target field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on numerical search could prove very effective. Here we adapt optimal control theory to the quantum sensing scenario, by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the unknown field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a Nitrogen Vacancy center in diamond, finding improved sensitivity to a broad set of time varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantaged it bestows, will prove beneficial to many quantum sensing applications.
We use an optimal control protocol to cool one mode of the center of mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center of mass temperature of 5 mK at $3times 10^{-7}$ mbar and transients 10 to 600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.
We experimentally realize cavity cooling of all three translational degrees of motion of a levitated nanoparticle in vacuum. The particle is trapped by a cavity-independent optical tweezer and coherently scatters tweezer light into the blue detuned cavity mode. For vacuum pressures around $10^{-5},{rm mbar}$, minimal temperatures along the cavity axis in the mK regime are observed. Simultaneously, the center-of-mass (COM) motion along the other two spatial directions is cooled to minimal temperatures of a few hundred $rm mK$. Measuring temperatures and damping rates as the pressure is varied, we find that the cooling efficiencies depend on the particle position within the intracavity standing wave. This data and the behaviour of the COM temperatures as functions of cavity detuning and tweezer power are consistent with a theoretical analysis of the experiment. Experimental limits and opportunities of our approach are outlined.
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.
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