Spin-mechanical hybrid systems have been widely used in quantum information processing. However, the spin-mechanical interaction is generally weak, making it a critical challenge to enhance the spin-mechanical interaction into the strong coupling or even ultra-strong coupling regime. Here, we propose a protocol that can significantly enhance the spin-mechanical coupling strength with a diamond spin vacancy and a levitated micromagnet. A driving electrical current is used to modulate the mechanical motion of the levitated micromagnet, which induces a two-phonon drive and can exponentially enhance the spin-phonon and phonon-medicated spin-spin coupling strengths. Furthermore, a high fidelity Schrodinger cat state and an unconventional 2-qubit geometric phase gate with high fidelity and faster gate speed can be achieved using this hybrid system. This protocol provides a promising platform for quantum information processing with NV spins coupled to levitated micromagnets.
We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micro-magnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three dimensional trapping with quality factors around one million and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degree of freedom of an individ…
We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius $R=27$ $μ$m, is levitated by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a SQUID. We perform accurate ringdown measurements on the vertical translational mode with frequency $57$ Hz, and infer the residual damping at vanishing pressure $γ/2π<9$ $μ$Hz. From this upper limit we derive improved bounds on the dissipative versions of the CSL (continuous spontaneous localizat…
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…
Quantum Metrology of Newton's Constant with Levitated Mechanical Systems
Eberhard-Karls-Universität Tübingen（蒂宾根大学）；German Aerospace Center (DLR)（德国航空航天中心）；Universita‘ degli Studi di Palermo（巴勒莫大学）；Queen’s University Belfast（贝尔法斯特女王大学）
Levitated particles are a promising platform for precision sensing of external perturbations and probing the boundary between quantum and classical worlds. A critical obstacle for these applications is the difficulty of generating nonclassical states of motion which have not been realized so far. Here, we show that strong squeezing of the motion of a levitated particle below the vacuum level is feasible with available experimental parameters. Using suitable modulation of the trapping potential (which is impossible with clamped mechanical resonators) and coherent scattering of trapping photons …
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.
Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, due to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical modes …
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$^{-…
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we …
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally assessed for the generic situation of simultaneous mechanical and thermal changes. Thermal driving is indeed generally slow and more difficult to realize than mechanical driving. Here, we use feedback cooling techniques to implement fast and controlled temperature variations of an underdamped levitated microparticle that are one order of magnitude faster than t…
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…
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…
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 theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for sub-millimeter-sized cavities the particle motion, initially thermal and well above its ground state, b…
We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite of the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping o…
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 …
Optical squeezing mediated by levitated oscillators at their quantum ground state
CNR-INO（意大利国家研究委员会红外光学研究所）；Dipartimento di Fisica e Astronomia, Univ. Di Firenze（佛罗伦萨大学物理与天文系）；INFN, Sezione di Firenze（意大利国家核物理研究院佛罗伦萨分部）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
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…
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…
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 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…
The use of levitated nanospheres represents a new paradigm for the optomechanical cooling of a small mechanical oscillator, with the prospect of realising quantum oscillators with unprecedentedly high quality factors. We investigate the dynamics of this system, especially in the so-called self-trapping regimes, where one or more optical fields simultaneously trap and cool the mechanical oscillator. The determining characteristic of this regime is that both the mechanical frequency $ω_M$ and single-photon optomechanical coupling strength parameters $g$ are a function of the optical field intens…
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）
Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence. Quantum control of mechanical motion has been achieved by engineering the radiation-pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for …
Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient is usually required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly coup…
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 …
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.
Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single NV center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive…
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite pe…
Achieving Sub-Zeptonewton Force Sensitivity and Spin-Motion Entanglement in Levitated Diamond via Pulsed Backaction Evasion
Joint Center for Quantum Information and Computer Science, University of Maryland-NIST（马里兰大学-国家标准技术研究院联合量子信息与计算机科学中心）；Department of Physics and Astronomy, University of Pittsburgh（匹兹堡大学物理与天文学系）；Pittsburgh Quantum Institute, University of Pittsburgh（匹兹堡大学匹兹堡量子研究所）；Joint Quantum Institute, University of Maryland-NIST（马里兰大学-国家标准技术研究院联合量子研究所）
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）
Measurement of a quantum system using spin-mechanical conversion
School of Physics, University of Melbourne（墨尔本大学物理学院）；Department of Physics, City College of the City University of New York（纽约市立大学城市学院物理系）；Laboratoire De Physique de l’École Normale Supérieure, École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，巴黎高等师范学院，PSL研究大学，法国国家科学研究中心，索邦大学，巴黎大学）
We explore entanglement generation between multiple optically levitated nanospheres interacting with a common optical cavity via the Coherent Scattering optomechanical interaction. We derive the many-particle Hamiltonian governing the unitary evolution of the system and show that it gives rise to quantum correlations among the various partitions of the setup, following a non-Markovian dynamics of entanglement birth, death and revivals. We also consider the effects of coupling the system to external environments and show that under reasonable experimental conditions entanglement between the mec…
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…
Macroscopic Spin GHZ States with a Levitated Ferromagnet
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；A*STAR Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（A*STAR量子创新中心（Q.InC），科学技术研究局（A*STAR））
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）
Quantum measurements of mechanical systems can produce optical squeezing via ponderomotive forces. Its observation requires high environmental isolation and efficient detection, typically achieved by using optical cavities and cryogenic cooling. Here we realize these conditions by measuring the position of an optically levitated nanoparticle at room temperature and without the overhead of an optical cavity. We use a fast heterodyne detection to reconstruct simultaneously orthogonal optical quadratures, and observe a noise reduction of $9\%\pm0.5\%$ below shot noise. Our experiment offers a nov…
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 …
Quantum Non-Gaussian State Preparation of Levitated Particles via Time-Dependent Control of Weakly Nonharmonic Hybrid Potentials
Palacký University（帕尔卡大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学与技术研究院）；ICREA - Institucio Catalana de Recerca i Estudis Avançats（ICREA-加泰罗尼亚研究高级学院）
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 …
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…
