A levitated nanomechanical oscillator under ultra-high vacuum (UHV) is highly isolated from its environment. It has been predicted that this isolation leads to very low mechanical dissipation rates. However, a gap persists between predictions and experimental data. Here, we levitate a silica nanoparticle in a linear Paul trap at room temperature, at pressures as low as $7\times10^{-11}$ mbar. We measure a dissipation rate of $2π\times69(22)$ nHz, corresponding to a quality factor exceeding $10^{10}$, more than two orders of magnitude higher than previously shown. A study of the pressure dependence of the particle's damping and heating rates provides insight into the relevant dissipation mechanisms.
Levitated optomechanics has great potentials in precision measurements, thermodynamics, macroscopic quantum mechanics and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell in vacuum. The linearly-polarized optical tweezer provides a restoring torque to confine the orientation of the nanodumbbell, in analog to the torsion wire which provides restoring torque for suspended lead spheres in the Cavendish torsion balance. Our calculation shows its …
We investigate the coupled-system dynamics of two-level quantum dots placed on a vibrating nanomechanical resonator. The ensemble of quantum dots exhibits superradiance features which are transferred to the mechanical degrees of freedom representing fast quantum dynamics and enhanced phonon emission in a nanomechanical setup, resembling of the superradiance effect.
Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its line width and mechanical quality factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as high as $10^{12}$ have been predicted for levitated systems, but to date, the poor stability of these oscillators over long periods have prevented dir…
The Continuous Spontaneous Localization (CSL) model predicts a tiny break of energy conservation via a weak stochastic force acting on physical systems, which triggers the collapse of the wave function. Mechanical oscillators are a natural way to test such a force; in particular levitated micro-mechanical oscillator has been recently proposed to be an ideal system. We report a proof-of-principle experiment with a micro-oscillator generated by a micro-sphere diamagnetically levitated in a magneto-gravitational trap under high vacuum. Due to the ultra-low mechanical dissipation, the oscillator p…
A scheme is presented for entangling two separated nanomechanical oscillators by injecting broad band squeezed vacuum light and laser light into the ring cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum entanglement of the two oscillators, the squeezing parameter of the input light should be about 1. We report significant entanglement over a very wide range of power levels of the pump and temperatures of the environment.
We show how to prepare and directly measure the squeezed states of nanomechanical oscillators. An intense pulse interacts with a dielectric mirror in a cavity. The quadratic coupling between the optical pulse and the oscillator results in the reduction of a quadrature variance of the massive oscillator. Differently from others, the proposed scheme here requires neither any post-action on the optical field nor a preparation of a nonclassical optical field. Depending on the initial temperature of the system, the squeezing of the variance under the vacuum limit can be achieved only by a few repet…
We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector-atom that is simultaneously coupled to the cantilever via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the excited state is a direct measure of the Wigner characteristic function of the nanomechanical o…
We investigate nonequilibrium entanglement generation in a chain of harmonic oscillators with time-dependent linear coupling. We use optimal control theory to determine the coupling modulation that leads to maximum logarithmic negativity for a pair of opposite oscillators and show that it corresponds to a synchronization of the eigenmodes of the chain. We further analytically relate the maximum attainable entanglement to the irreversible work done to produce it, thus bridging nonequilibrium entanglement production and nonequilibrium thermodynamics.
A patterned Si nanobeam is formed which supports co-localized acoustic and optical resonances that are coupled via radiation pressure. Starting from a bath temperature of T=20K, the 3.68GHz nanomechanical mode is cooled into its quantum mechanical ground state utilizing optical radiation pressure. The mechanical mode displacement fluctuations, imprinted on the transmitted cooling laser beam, indicate that a final phonon mode occupancy of 0.85 +-0.04 is obtained.
We propose a scheme via three-level cascade atoms to entangle two optomechanical oscillators as well as two-mode fields. We show that two movable mirrors and two-mode fields can be entangled even for bad cavity limit. We also study entanglement of the output two-mode fields in frequency domain. The results show that the frequency of the mirror oscillation and the injected atomic coherence affect the output entanglement of the two-mode fields.
We show that squeezing of a nanomechanical mirror can be generated by injecting broad band squeezed vacuum light and laser light into the cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum momentum squeezing of the movable mirror, the squeezing parameter of the input light should be about 1. We can obtain more than 70% squeezing. Besides, for a fixed squeezing parameter, decreasing the temperature of the environment or increasing the laser power increases the momentum squeezing. We find very large squeezing with respect to thermal fluctuations, for ins…
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 show how the interference between spatially separated states of the center of mass (COM) of a mesoscopic harmonic oscillator can be evidenced by coupling it to a spin and performing solely spin manipulations and measurements (Ramsey Interferometry). We propose to use an optically levitated diamond bead containing an NV center spin. The nano-scale size of the bead makes the motional decoherence due to levitation negligible. The form of the spin-motion coupling ensures that the scheme works for thermal states so that moderate feedback cooling suffices. No separate control or observation of th…
In this comment, we agree with the formulas derived in Refs. [1,2] but show that the results are not due to "interference between spatially separated states of the center of mass of a mesoscopic harmonic oscillator".
We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.
Typical of modern quantum technologies employing nanomechanical oscillators is to demand few mechanical quantum excitations, for instance, to prolong coherence times of a particular task or, to engineer a specific non-classical state. For this reason, we devoted the present work to exhibit how to bring an initial thermalized nanomechanical oscillator near to its ground state. Particularly, we focus on extending the novel results of D. D. B. Rao \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 077203 (2016), where a mechanical object can be heated up, squeezed, or cooled down near to its ground …
The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures the mechanical energy with a precision greater than the energy of a single phonon, $\hbarω_\text{m}$. One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish differ…
In a recent letter, Gaidarzhy et al. claim to have observed evidence for quantized displacements of a nanomechanical oscillator. We contend that the evidence, analysis, claims, and conclusions presented are contrary to expectations from fundamentals of quantum mechanics and elasticity theory, and that the method used by the authors is unsuitable in principle to observe the quantized energy states of a nanomechanical structure.
Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest. One of the most fascinating features is that, chiral state conversion appears when one EP is encircled dynamically. Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the Hamiltonian along loops in the parameter plane. Utilizing the controllable rotation angle, gain …
Cavity-enhanced radiation pressure coupling between optical and mechanical degrees of freedom allows quantum-limited position measurements and gives rise to dynamical backaction enabling amplification and cooling of mechanical motion. Here we demonstrate purely dispersive coupling of high Q nanomechanical oscillators to an ultra-high finesse optical microresonator via its evanescent field, extending cavity optomechanics to nanomechanical oscillators. Dynamical backaction mediated by the optical dipole force is observed, leading to laser-like coherent nanomechanical oscillations solely due to r…
The question of how swiftly entanglement spreads over a system has attracted vital interest. In this regard, the out-of-time ordered correlator (OTOC) is a quantitative measure of the entanglement spreading process. Particular interest concerns the propagation of quantum correlations in the lattice systems, {\it e.g.}, spin chains. In a seminal paper D. A. Roberts, D. Stanford and L. Susskind, J. High Energy Phys. 03, 051, (2015) the concept of the OTOC's radius was introduced. The radius of the OTOC defines the front line reached by the spread of entanglement. Beyond this radius operators com…
We propose a scheme to prepare nanomechanical oscillators in nonclassical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonance frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be sele…
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）
Cooling the centre-of-mass motion is an important tool for levitated optomechanical systems, but it is often not clear which method can practically reach lower temperatures for a particular experiment. We directly compare the parametric and velocity feedback damping methods, which are used extensively for cooling the motion of single trapped particles in a range of traps. By performing experiments on the same particle, and with the same detection system, we demonstrate that velocity damping cools the oscillator to lower temperatures and is more resilient to imperfect experimental conditions. W…
We study the quantum properties of a nanomechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force $F_0$ close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nanomechanical oscillator are to be obtained from the Hamiltonian of the form $H= a^†a+β(a^†+a)^4/4$. This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms $a^{†2}a^2$, $(a^†a)^2$ and $a^{\dag4}+a^4-(a^{\dag2}a^2+a^2a^{\dag2})$ previously e…
The observation of quantized nanomechanical oscillations by detecting femtometer-scale displacements is a significant challenge for experimentalists. We propose that phonon blockade can serve as a signature of quantum behavior in nanomechanical resonators. In analogy to photon blockade and Coulomb blockade for electrons, the main idea for phonon blockade is that the second phonon cannot be excited when there is one phonon in the nonlinear oscillator. To realize phonon blockade, a superconducting quantum two-level system is coupled to the nanomechanical resonator and is used to induce the phono…
A one-dimensional topological superconductor features a single fermionic zero mode that is delocalized over two Majorana bound states located at the ends of the system. We study a pair of spatially separated nanomechanical oscillators tunnel-coupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electron-phonon coupling and a finite charging energy on the mesoscopic topological superconductor can lead to an effective superexchange between the oscillators via the non-local fermionic zero mode. We further show that this teleportation mechanism leads to entang…
We measure the response and thermal motion of a high-Q nanomechanical oscillator coupled to a superconducting microwave cavity in the resolved-sideband regime where the oscillator's resonance frequency exceeds the cavity's linewidth. The coupling between the microwave field and mechanical motion is strong enough for radiation pressure to overwhelm the intrinsic mechanical damping. This radiation-pressure damping cools the fundamental mechanical mode by a factor of 5 below the thermal equilibrium temperature in a dilution refrigerator to a phonon occupancy of 140 quanta.
A single Nitrogen Vacancy (NV) center hosted in a diamond nanocrystal is positioned at the extremity of a SiC nanowire. This novel hybrid system couples the degrees of freedom of two radically different systems, i.e. a nanomechanical oscillator and a single quantum object. The dynamics of the nano-resonator is probed through time resolved nanocrystal fluorescence and photon correlation measurements, conveying the influence of a mechanical degree of freedom given to a non-classical photon emitter. Moreover, by immersing the system in a strong magnetic field gradient, we induce a magnetic coupli…
Ultralow dissipation plays an important role in sensing applications and exploring macroscopic quantum phenomena using micro-and nano-mechanical systems. We report a diamagnetic-levitated micro-mechanical oscillator operating at a low temperature of 3K with measured dissipation as low as 0.59 $μ$Hz and a quality factor as high as $2 \times 10^7$. To the best of our knowledge the achieved dissipation is the lowest in micro- and nano-mechanical systems to date, orders of magnitude improvement over the reported state-of-the-art systems based on different principles. The cryogenic diamagnetic-levi…
We study the consequence of the frequency errors of individual oscillators on the scalability of quantum computing based on nanomechanical resonators. We show the fidelity change of the quantum operation due to the frequency shifts numerically. We present a method to perfectly compensate for these negative effects. Our method is robust to whatever large frequency errors.
We describe the construction and characterisation of a nano-oscillator formed by a Paul trap. The frequency and temperature stability of the nano-oscillator was measured over several days allowing us to identify the major sources of trap and environmental fluctuations. We measure an overall frequency stability of 2 ppm/hr and a temperature stability of more than 5 hours via the Allan deviation. Importantly, we find that the charge on the nanoscillator is stable over a timescale of at least two weeks and that the mass of the oscillator, can be measured with a 3 % uncertainty. This allows us to …
We report the observation of discrete displacement of nanomechanical oscillators with gigahertz-range resonance frequencies at millikelvin temperatures. The oscillators are nanomachined single-crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. With this novel design, femtometer-level displacement of the frequency-determining element is amplified into collective motion of the entire micron-sized structure. The observed discrete response possibly results from energy quantization at the onset of the quantum regime in t…
Optomechanical cavities in the well-resolved-sideband regime are ideally suited for the study of a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and generation of non-classical states. For these experiments, the mechanical oscillator should be prepared in its ground state; residual motion beyond the zero-point motion must be negligible. The requisite cooling of the mechanical motion can be achieved using the radiation pressure of light in the cavity by selectively driving the anti-Stokes optomechanical transition. To date,…
We describe the measurement of the secular motion of a levitated nanoparticle in a Paul trap with a CMOS camera. This simple method enables us to reach signal-to-noise ratios as good as 10$^{6}$ with a displacement sensitivity better than 10$^{-16}\,m^{2}$/Hz. This method can be used to extract trap parameters as well as the properties of the levitated particles. We demonstrate continuous monitoring of the particle dynamics on timescales of the order of weeks. We show that by using the improvement given by super-resolution imaging, a significant reduction in the noise floor can be attained, wi…
We demonstrate robust and reliable signatures for the transition from quantum to classical behavior in the position probability distribution of a damped double-well system using the Qunatum State Diffusion approach to open quantum systems. We argue that these signatures are within experimental reach, for example in a doubly-clamped nanomechanical beam.
We present a theory describing the semiclassical dynamics of a superconducting flux qubit inductively coupled to a nanomechanical oscillator. Focusing on the influence of the qubit on the mechanical element, and on the nonlinear phenomena displayed by this device, we show that it exhibits retardation effects and self-excited oscillations. These can be harnessed for the generation of non-classical states of the mechanical oscillator. In addition, we find that this system shares several fundamental properties with cavity optomechanical systems, and elucidate the analogy between these two classes…
Engineering nano-mechanical quantum systems possessing ultra-long motional coherence times allow for applications in ultra-sensitive quantum sensing, motional quantum memories and motional interfaces between other carriers of quantum information such as photons, quantum dots and superconducting systems. To achieve ultra-high motional Q one must work hard to remove all forms of motional noise and heating. We examine a magneto-nanomechanical quantum system that consists of a 3D arrangement of miniature superconducting loops which is stably levitated in a static inhomogenous magnetic field. The r…
Levitated Milligram-scale Ferromagnetic Magnetometer at Room Temperature
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家级重点实验室和物理系）；Institute of Chemical Materials, China Academy of Engineering Physics（中国工程物理研究院化工材料研究所）
The center-of-mass motion of a single optically levitated nanoparticle resembles three uncoupled harmonic oscillators. We show how a suitable modulation of the optical trapping potential can give rise to a coupling between two of these oscillators, such that their dynamics are governed by a classical equation of motion that resembles the Schrödinger equation for a two-level system. Based on experimental data, we illustrate the dynamics of this parametrically coupled system both in the frequency and in the time domain. We discuss the limitations and differences of the mechanical analogue in com…
We present a ground state cooling scheme for a nanomechanical resonator linearly coupled with a LC oscillator. The linear coupling, when periodically modulated at red detuning, up-converts the low-frequency nanomechanical mode to the high-frequency LC oscillator mode and generates backaction force that can cool the resonator to its ground state in the resolved-sideband regime. We also study the effect of the quantum backaction noise on the cooling due to the counter rotating term in the linear coupling. The scheme can be compared with laser cooling for the atomic systems and can be realized in…
Levitated oscillators with millimeter or sub-millimeter size are particularly attractive due to their potential role in studying various fundamental problems and practical applications. One of the crucial issues towards these goals is to achieve efficient measurements of oscillator motion, while this remains a challenge. Here we theoretically propose a lens-free optical detection scheme, which can be used to detect the motion of a millimeter or sub-millimeter levitated oscillator with a measurement efficiency close to the standard quantum limit with a modest optical power. We demonstrate exper…
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 de…
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 …
An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $\approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed st…
We use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase (η= -π/2) where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a …
Elastic strain engineering utilizes stress to realize unusual material properties. For instance, strain can be used to enhance the electron mobility of a semiconductor, enabling more efficient solar cells and smaller, faster transistors. In the context of nanomechanics, the pursuit of resonators with ultra-high coherence has led to intense study of a complementary strain engineering technique, "dissipation dilution", whereby the stiffness of a material is effectively increased without added loss. Dissipation dilution is known to underlie the anomalously high Q factor of Si$_3$N$_4$ nanomechani…
We experimentally demonstrate stable trapping of a permanent magnet sphere above a lead superconductor, in vacuum pressures of $4 \times 10^{-8}$~mbar. The levitating magnet behaves as a harmonic oscillator, with frequencies in the 4-31~Hz range detected, and shows promise to be an ultrasensitive acceleration sensor. We directly apply an acceleration to the magnet with a current carrying wire, which we use to measure a background noise of $\sim 10^{-10} \ \text{m}/\sqrt{\text{Hz}}$ at 30.75~Hz frequency. With current experimental parameters, we find an acceleration sensitivity of $S_a^{1/2} = …
We present optical sideband spectroscopy measurements of a mesoscopic mechanical oscillator cooled near its quantum ground state. The mechanical oscillator, corresponding to a 3.99GHz acoustic mode of a patterned silicon nanobeam, is coupled via radiation pressure to a pair of co-localized 200THz optical modes. The mechanical mode is cooled close to its quantum ground state from a bath temperature of 18K using radiation pressure back-action stemming from the optical pumping of one of the optical cavity resonances. An optical probe beam, resonant with the second optical cavity resonance, is use…
Single-atom detection with a quantum-controlled mechanical oscillator
ETH Zürich（苏黎世联邦理工学院）；Photonics Laboratory, ETH Zürich（苏黎世联邦理工学院光子学实验室）；Quantum Center, ETH Zürich（苏黎世联邦理工学院量子中心）；Laboratory of Physical Chemistry, ETH Zürich（苏黎世联邦理工学院物理化学实验室）；Kavli Institute of Nanoscience, Department of Quantum Nanoscience, TU Delft（代尔夫特理工大学量子纳米科学系卡弗里纳米科学研究所）
