We theoretically explore a quantum memory using a single nanoparticle levitated in an optical dipole trap and subjected to feedback cooling. This protocol is realized by storing and retrieving a single photon quantum state from a mechanical mode in levitated cavityless optomechanics. We describe the effectiveness of the photon-phonon-photon transfer in terms of the fidelity, the Wigner function, and the zero-delay second-order autocorrelation function. For experimentally accessible parameters, our numerical results indicate robust conversion of the quantum states of the input signal photon to those of the retrieved photon. We also show that high fidelity single-photon wavelength conversion is possible in the system as long as intense control pulses shorter than the mechanical damping time are used. Our work opens up the possibility of using levitated optomechanical systems for applications of quantum information processing.
We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a tracking scheme that takes into account the modulation of the laser intensity. We show that such a tracking implementation allows us to increase the feedback strength, leading…
Nonclassical optomechanical correlations enable optical control of mechanical motion beyond the limitations of classical driving. Here we investigate the feasibility of using pulsed cavity-optomechanics to create and verify nonclassical phase-sensitive correlations between light and the motion of a levitated nanoparticle in a realistic scenario. We show that optomechanical two-mode squeezing can persist even at the elevated temperatures of state-of-the-art experimental setups. We introduce a detection scheme based on optical homodyning that allows revealing nonclassical correlations without fu…
We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.
Sympathetic Cooling of Levitated Optomechanics through Nonreciprocal Coupling
Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology（北京理工大学物理学院量子技术研究中心及先进光电子量子架构与测量教育部重点实验室）
Ultra-high sensitivity detection of quantum-scale displacements in cavity optomechanics optimises the combined errors from measurement back-action and imprecisions from incoming quantum noises. This sets the well-known Standard Quantum Limit (SQL). Normal quantum cavity optomechanics allows cooling and detection of a single degree of freedom, along the cavity axis. However, a recent breakthrough that allows quantum ground-state cooling of levitated nanoparticles [Delic et al, arxiv:1911.04406], is uniquely 3D in character, with coupling along the $x$, $y$ and $z$ axes. We investigate current e…
Cavity optomechanics offers quantum cooling, quantum control and measurement of small mechanical oscillators. However the optical backactions that underpin quantum control can significantly disturb the oscillator modes: mechanical frequencies are shifted by the optical spring effect and light-matter hybridisation in strong coupling regimes; mechanical modes hybridise with each other via the cavity mode. This is even more pertinent in the field of levitated optomechanics, where optical trapping fully determines the mechanical modes and their frequencies. Here, using the coherent-scattering (CS)…
We analyze magnetometry using an optically levitated nanodiamond. We consider a configuration where a magnetic field gradient couples the mechanical oscillation of the diamond with its spin degree of freedom provided by a Nitrogen vacancy center. First, we investigate measurement of the position spectrum of the mechanical oscillator. We find that conditions of ultrahigh vacuum and feedback cooling allow a magnetic field gradient sensitivity of 1 $μ$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100 $m$Tm$^{-…
The preparation of nonclassical states of mechanical motion conclusively proves that control over such motion has reached the quantum level. We investigate ways to achieve nonclassical states of macroscopic mechanical oscillators, particularly levitated nanoparticles. We analyze the possibility of the conditional squeezing of the levitated particle induced by the homodyne detection of light in a pulsed optomechanical setup within the resolved sideband regime. We focus on the regimes that are experimentally relevant for the levitated systems where the ground-state cooling is not achievable and …
The strong light-matter optomechanical coupling offered by Coherent Scattering (CS) set-ups have allowed the experimental realisation of quantum ground state cavity cooling of the axial motion of a levitated nanoparticle [U. Delić et al., Science 367, 892 (2020)]. An appealing milestone is now quantum 2D cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarisation, one obtains two nearly equivalent modes, with similar frequencies $ω_{x}\simω_{y}$ and optomechanical couplings $g_{x}\simeq g_{y}$ -- in this experimental configurat…
Recently, remarkable advances have been made in coupling a number of high-Q modes of nano-mechanical systems to high-finesse optical cavities, with the goal of reaching regimes where quantum behavior can be observed and leveraged toward new applications. To reach this regime, the coupling between these systems and their thermal environments must be minimized. Here we propose a novel approach to this problem, in which optically levitating a nano-mechanical system can greatly reduce its thermal contact, while simultaneously eliminating dissipation arising from clamping. Through the long coherenc…
Levitated nanoparticles are being intensively investigated from two different perspectives: as a potential realisation of macroscopic quantum coherence; and as ultra-sensitive sensors of force, down to the zeptoNewton level, with a range of various applications, including the search for Dark Matter. A future aim is to merge these two strands, enabling the development of quantum-limited sensors. Here we propose that mechanical cross-correlation spectra $S_{xy}(ω)$ offer new possibilities: once detector misalignment errors are minimised, the spectral shape of $S_{xy}(ω)$ directly points out the …
We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the effect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected …
Stationary entanglement of a levitated oscillator with an optical field
Università di Firenze（佛罗伦萨大学）；INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；CNR-INO（意大利国家研究委员会光学研究所）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
We describe a proposal for a new type of optomechanical system based on a drop of liquid helium that is magnetically levitated in vacuum. In the proposed device, the drop would serve three roles: its optical whispering gallery modes would provide the optical cavity, its surface vibrations would constitute the mechanical element, and evaporation of He atoms from its surface would provide continuous refrigeration. We analyze the feasibility of such a system in light of previous experimental demonstrations of its essential components: magnetic levitation of mm-scale and cm-scale drops of liquid H…
We discuss the detection of an anisotropic particle trapped by an elliptically polarized focused Gaussian laser beam. We obtain the full rotational and translational dynamics, as well as, the measured photo-current in a general-dyne detection. As an example, we discuss a toy model of homodyne detection, which captures the main features typically found in experimental setups.
We consider an array of optically levitated nanospheres in vacuum and investigate nontrivial phonon transports in this system. The levitated nanospheres are coupled by optical binding. Key parameters of this system, such as the interaction range, trapping frequencies and mechanical dissipation, are all highly tunable. By tuning the spacing between neighboring spheres, the mechanical dissipation and the trapping frequency of each sphere, counter-intuitive phenomena such as prethermalization and nonreciprocal phonon transport can be achieved. Our system provides a great platform to investigate n…
We theoretically show that the dipole force of an ensemble of quantum emitters embedded in a dielectric nanosphere can be exploited to achieve near-field optical levitation. The key ingredient is that the polarizability from the ensemble of embedded quantum emitters can be larger than the bulk polarizability of the sphere, thereby enabling the use of repulsive optical potentials and consequently the levitation using optical near-fields. In levitated cavity quantum optomechanics, this could be used to boost the single-photon coupling by combining larger polarizability to mass ratio, larger fiel…
Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution …
Levitated nanospheres in optical cavities open a novel route to study many-body systems out of solution and highly isolated from the environment. We show that properly tuned optical parameters allow for the study of the non-equilibrium dynamics of composite nano-particles with non-isotropic optical friction. We find friction induced ordering and nematic transitions with non-equilibrium analogs to liquid crystal phases for ensembles of dimers.
Counterintuitively, experiments show that an electromagnetically levitated particle escapes from its trap when the ambient pressure is reduced below a certain level even if the particle's motion is cooled by a resonator-based or feedback-based mechanism. Here, we theoretically show that the ambient pressure must be kept well above a critical value arising from gradient force fluctuations (viz., fluctuations in part of the EM force whose Hamiltonian is quadratic in the position of the particle). Also, we consider other force fluctuations, and determine whether different realizations of feedback…
In recent years quantum phenomena have been experimentally demonstrated on variety of optomechanical systems ranging from micro-oscillators to photonic crystals. Since single photon couplings are quite small, most experimental approaches rely on the realization of high finesse Fabry-Perot cavities in order to enhance the effective coupling. Here we show that by exploiting a, long path, low finesse fiber Fabry-Perot interferometer ground state cooling can be achieved. We model a 100 m long cavity with a finesse of 10 and analyze the impact of additional noise sources arising from the fiber. As …
Levitated optomechanical systems are rapidly becoming leading tools for precision sensing, enabling a high level of control over the sensor's center of mass motion, rotation and electric charge state. Higher-order multipole moments in the charge distribution, however, remain a major source of backgrounds. By applying controlled precessive torques to the dipole moment of a levitated microsphere in vacuum, we demonstrate cancellation of dipole-induced backgrounds by 2 orders of magnitude. We measure the dipole moments of ng-mass spheres and determine their scaling with sphere size, finding that …
Quantum control of levitated dielectric particles is an emerging subject in quantum optomechanics. A major challenge is to efficiently measure and manipulate the particle's motion at the Heisenberg uncertainty limit. Here we present a nanophotonic interface suited to address this problem. By optically trapping a 150 nm silica particle and placing it in the near field of a photonic crystal cavity, we achieve tunable single-photon optomechanical coupling of up to $g_0/2π=9$ kHz, three orders of magnitude larger than previously reported for levitated cavity optomechanical systems. Efficient colle…
Optically trapped dielectric objects are well suited for reaching the quantum regime of their center of mass motion in an ultra-high vacuum environment. We show that ground state cooling of an optically trapped nanosphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle. Unlike cavity cooling in the resolved sideband limit, this system requires only a modest cavity finesse and it allows the cooling to be turned off, permitting subsequent observation of strongly-coupled dynamics between the atoms and sphere. Nanos…
We report on the two-dimensional (2D) dynamics of a levitated nanoparticle in an optical cavity. The motion of the nanosphere is strongly coupled to the cavity field by coherent scattering and heavily cooled in the plane orthogonal to the tweezer axis. Due to the characteristics of the 2D motion and the strong optomechanical coupling, the motional sideband asymmetry that reveals the quantum nature of the dynamics is not limited to mere scale factors between Stokes and anti-Stokes peaks, as customary in quantum optomechanics, but assumes a peculiar spectral dependence. We introduce and discuss …
Optical levitation of nanoscale particles has emerged as a platform for precision measurement. Extremely low damping, together with optical interferometric position detection, makes possible exquisite force measurement and promises low-energy tests of fundamental physics. Essential to such measurement is an understanding of the confidence with which parameters can be inferred from spectra estimated from the indirect measurement provided by interferometry. We present an apparatus optimized for sensitivity along one motional degree of freedom, a theoretical model of the spectrum, and maximum lik…
We demonstrate a technique to estimate the strength of non-linearities present in the trapping potential of an optically levitated nanoparticle. By applying a brief pulsed reduction in trapping laser power of the system such as to squeeze the phase space distribution and then matching the time evolution of the shape of the phase space distribution to that of numerical simulations, one can estimate the strength of the non-linearity present in the system. We apply this technique to estimate the strength of the Duffing non-linearity present in the optical trapping potential.
An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tenso…
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10$^{-5}$mbar and with feedback engaged the pressure is reduced to 10$^{-6}$mbar. Modifications to the …
High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise …
We experimentally squeeze the thermal motional state of an optically levitated nanosphere, by fast switching between two trapping frequencies. The measured phase space distribution of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7dB of squeezing along one motional direction. The experiment features a large number of thermal excitations, therefore remaining in the classical regime. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing below the zero-point level, if preceded by ground state cooling o…
We investigate experimentally the dynamics of a non-spherical levitated nanoparticle in vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both, the simulation and approximate expressions, we find in good agreement with experiments. We measure a torque of $1.9 \pm 0.5 \times 10^{-23}$ Nm at $1 \times 10^{-1}$ mbar, with an estimated torque sensitivity of $3.6 \pm 1.1…
We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this re…
We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0~kV to 10~kV on a nearby charged needle tip. We find consistent results across negative and positive needle voltages, with the Fano line-shape feature able to exist at both higher and lower frequencies than the fundamental oscillator frequency. We can use the Fano parameter to characterize our system to be sensitive to static interactions which are ever-present. Currently, we can distingu…
The strong coupling between elementary excitations of the electromagnetic field (photons) and quantized mechanical vibrations (phonons) produces hybrid quasi-particle states, known as phonon-polaritons. Their typical signature is the avoided crossing between the eigenfrequencies of the coupled system, as paradigmatically illustrated by the Jaynes-Cummings Hamiltonian, and observed in quantum electrodynamics experiments where cavity photons are coupled to atoms, ions, excitons, spin ensambles and superconducting qubits. In this work, we demonstrate the generation of phonon-polaritons in the qua…
Particles with electric charge 10^(-12)e in bulk mass are not excluded by present experiments. In the present letter we provide a feasible scheme to measure the millicharged particles via the optical cavity coupled to a levitated microsphere. The results show that the optical probe spectrum of the micro-oscillator presents a distinct shift due to the existence of millicharged particles. Owing to the very narrow linewidth(10^(-7) Hz) of the optical Kerr effect, this shift will be more obvious, which makes the millicharges more easy to be detectable. We propose a method to eliminate the polariza…
Coherent scattering of photons is a novel mechanism of optomechanical coupling for optically levitated nanoparticles promising strong, versatile interactions with light and between nanoparticles. We show that it allows efficient deterministic generation of Gaussian entanglement between two particles in separate tweezers. A combination of red- and blue-detuned tweezers brings a mechanical Bogoliubov mode to its ground state. An additional, dispersively coupled cavity mode can reduce noise in the orthogonal mode, resulting in strong entanglement as quantified by the logarithmic negativity and ve…
High purity two-dimensional levitated mechanical oscillator
Dipartimento di Fisica e Astronomia, Università di Firenze（佛罗伦萨大学物理与天文学系）；INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；CNR-INO（意大利国家研究委员会光电子学与光学研究所）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered non-negligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession ab…
A mechanically compliant element can be set into motion by the interaction with light. In turn, this light-driven motion can give rise to ponderomotive correlations in the electromagnetic field. In optomechanical systems, cavities are often employed to enhance these correlations up to the point where they generate quantum squeezing of light. In free-space scenarios, where no cavity is used, observation of squeezing remains possible but challenging due to the weakness of the interaction, and has not been reported so far. Here, we measure the ponderomotively squeezed state of light scattered by …
Electron spins of diamond nitrogen-vacancy (NV) centers are important quantum resources for nanoscale sensing and quantum information. Combining NV spins with levitated optomechanical resonators will provide a hybrid quantum system for novel applications. Here we optically levitate a nanodiamond and demonstrate electron spin control of its built-in NV centers in low vacuum. We observe that the strength of electron spin resonance (ESR) is enhanced when the air pressure is reduced. To better understand this system, we investigate the effects of trap power and measure the absolute internal temper…
