Time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time crystal model based on a levitated charged nanoparticle in a static magnetic field without drive. Both the classical time crystal in thermal equilibrium and the quantum time crystal in the ground state can emerge in the spin rotational mode, under the strong magnetic field or the large charge-to-mass ratio limit. Besides, for the first time, the \emph{time polycrystal} is defined and naturally appears in this model. Our model paves a way for realizing time crystals in thermal equilibrium.
We show how entanglement between two optically levitated nanoparticles can be generated and detected by coherent scattering of tweezer photons into a single cavity mode. Triggered by the detection of a Stokes photon, the tweezer detuning is switched from the blue to the red; entanglement is then verified by the conditioned anti-Stokes photon flux, which oscillates with the mechanical beat frequency. The proposed setup is realizable with near-future technology and opens the door to the first experimental observation of non-classical center-of-mass correlations between two or more levitated nano…
This chapter is intended as a pedagogical introduction to the dynamics of optically levitated nanoparticles with a focus on the study of single particle thermodynamics. Much of the work studying thermodynamics with nano- and micro-particles has taken place in liquid, and this chapter will avoid reviewing this impressive body of work, focussing instead on studies of thermodynamics with nanoparticles levitated in a gas. For a recent literature review we refer the reader to Gieseler & Millen Entropy 20, 326 (2018). The authors will discuss extensions into the quantum regime where relevant through…
Nanoparticles trapped in optical tweezers emerged as an interesting platform for investigating fundamental effects in quantum physics. The ability to shape the optical trapping potential using spatial light modulation and quantum control of their motion using coherent scattering to an optical cavity mode predispose them for emulating a range of physical systems and studying quantum phenomena with massive objects. To extend these capabilities of levitated nanoparticles to quantum many-body systems, it is crucial to develop feasible strategies to couple and entangle multiple particles either dir…
Preparing and observing quantum states of nanoscale particles is a challenging task with great relevance for quantum technologies and tests of fundamental physics. In contrast to atomic systems with discrete transitions, nanoparticles exhibit a practically continuous absorption spectrum and thus their quantum dynamics cannot be easily manipulated. Here, we demonstrate that charged nanoscale dielectrics can be artificially endowed with a discrete level structure by coherently interfacing their rotational and translational motion with a superconducting qubit. We propose a pulsed scheme for the g…
We consider a nanoparticle levitated in a Paul trap in ultrahigh cryogenic vacuum, and look for the conditions which allow for a stringent noninterferometric test of spontaneous collapse models. In particular we compare different possible techniques to detect the particle motion. Key conditions which need to be achieved are extremely low residual pressure and the ability to detect the particle at ultralow power. We compare three different detection approaches based respectively on a optical cavity, optical tweezer and a electrical readout, and for each one we assess advantages, drawbacks and t…
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 …
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 …
An optically levitated nonspherical nanoparticle can exhibit both librational and translational vibrations due to orientational and translational confinements of the optical tweezer, respectively. Usually, the frequency of its librational mode in a linearly-polarized optical tweezer is much larger than the frequency of its translational mode. Because of the frequency mismatch, the intrinsic coupling between librational and translational modes is very weak in vacuum. Here we propose a scheme to couple its librational and center-of-mass modes with an optical cavity mode. By adiabatically elimina…
Imaging-based detection of the motion of the levitated nanoparticles complements a widely-used interferometric detection method, providing a precise and robust way to estimate the position of the particle. Here, we show the camera-based feedback cooling of a charged nanoparticle levitated in a linear Paul trap. A charged nanoparticle levitated in a vacuum was observed by CMOS camera systems. The nanoparticle images were processed in realtime with a microcontroller integrated with a CMOS image sensor. The phase-delayed position signal was fed-back to one of the trap electrodes resulting in the …
In this paper, results of quantum calculations are presented for feedback cooling of an optically trapped nanoparticle in the laser-shot-noise-dominant regime. We numerically investigate the system using both parametric and force feedback cooling schemes. For the same measurement efficiency, the cooling limit from the force feedback is lower than that from the parametric feedback. We also develop a set of semi-classical equations for feedback cooling that accurately match the quantum results. It is demonstrated, by rescaling the semi-classical equations, that the cooling dynamics is uniquely d…
Realizing a large-scale fully controllable quantum system is a challenging task in current physical research and has broad applications. Ultracold atom and molecule arrays in optical tweezers in vacuum have been used for quantum simulation, quantum metrology and quantum computing. Recently, quantum ground state cooling of the center-of-mass motion of a single optically levitated nanoparticle in vacuum was demonstrated, providing unprecedented opportunities for studying macroscopic quantum mechanics and precision measurements. In this work, we create a reconfigurable optically-levitated nanopar…
The superposition principle is one of the bizarre predictions of quantum mechanics. Nevertheless, it has been experimentally verified using electrons, photons, atoms, and molecules. In this article, using a $20~$nm levitated ferromagnetic FePt nanoparticle, an exotic all optical spin polarization technique and the matter-wave interferometry, we show that a mesoscopic spatial Schrodinger cat can be created. Additionally, we argue that the maximum spatial separation between the delocalized wavepackets can be $25~μm$ and is significantly larger than the object itself.
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympatheticall…
Following the first demonstration of a levitated nanosphere cooled to the quantum ground state in 2020 [1], macroscopic quantum sensors are seemingly on the horizon. The nanosphere's large mass as compared to other quantum systems enhances the susceptibility of the nanoparticle to gravitational and inertial forces. In this viewpoint we describe the features of experiments with optically levitated nanoparticles [2] and their proposed utility for acceleration sensing. Unique to the levitated nanoparticle platform is the ability to implement not only quantum noise limited transduction, predicted …
We experimentally study the interference of dipole scattered light from two optically levitated nanoparticles in vacuum, which present an environment free of particle-substrate interactions. We illuminate the two trapped nanoparticles with a linearly polarized probe beam orthogonal to the propagation of the trapping laser beams. The scattered light from the nanoparticles are collected by a high numerical aperture (NA) objective lens and imaged. The interference fringes from the scattered vector light for the different dipole orientations in image and Fourier space are observed. Especially, the…
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…
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…
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 …
We develop a theory for cavity cooling of the center-of-mass motion of a levitated nanoparticle through coherent scattering into an optical cavity. We analytically determine the full coupled Hamiltonian for the nanoparticle, cavity, and free electromagnetic field. By tracing out the latter, we obtain a Master Equation for the cavity and the center of mass motion, where the decoherence rates ascribed to recoil heating, gas pressure, and trap displacement noise are calculated explicitly. Then, we benchmark our model by reproducing published experimental results for three-dimensional cooling. Fin…
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 optomechanics is showing potential for precise force measurements. Here, we report a case study, to show experimentally the capacity of such a force sensor. Using an electric field as a tool to detect a Coulomb force applied onto a levitated nanosphere. We experimentally observe the spatial displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC field. We further apply an AC field and demonstrate resonant enhancement of force sensing when a driving frequency, $ω_{AC}$, and the frequency of the levitated mechanical oscillator, $ω_0$, converge. We directly measure a f…
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…
We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to $T_{min}=10$mK at a p…
We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal f…
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 that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The translational centre of mass motion along the optical axis of the trapped nanoparticle has been cooled by three orders of magnitude, from a temperature of 300K to a temperature of 162 +/- 15mK.
We report on measurements of photon induced heating of silica nanospheres levitated in vacuum by a thermal light source formed by a superluminescent diode. Heating of the nanospheres motion along the three trap axes was measured as a function of gas pressure and for two particle sizes. Heating rates were also compared with the much lower reheating of the same sphere when levitated by a laser. We find the measured trap heating rates are dominated by the much larger heating rates expected from the recoil of thermal photons.
All three motional modes of a charged dielectric nanoparticle in a Paul trap are cooled by direct feedback to temperatures of a few mK. We test two methods, one based on electrical forces and the other on optical forces; for both methods, we find similar cooling efficiencies. Cooling is characterized for both feedback forces as a function of feedback parameters, background pressure, and the particle's position.
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…
The field of levitodynamics has made significant progress towards controlling and studying the motion of a levitated nanoparticle. Motional control relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce a novel all-optical cold damping scheme based on spatial modulation of the trap position that i…
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…
We experimentally observe the dipole scattering of a nanoparticle using a high numerical aperture (NA) imaging system. The optically levitated nanoparticle provides an environment free of particle-substrate interaction. We illuminate the silica nanoparticle in vacuum with a 532 nm laser beam orthogonally to the propagation direction of the 1064 nm trapping laser beam strongly focused by the same high NA objective used to collect the scattering, which results in a dark background and high signal-noise ratio. The dipole orientations of the nanoparticle induced by the linear polarization of the i…
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 varie…
We report an experimental observation of a record-breaking ultra-high rotation frequency about 6 GHz in an optically levitated nanoparticle system. We optically trap a nanoparticle in the gravity direction with a high numerical aperture (NA) objective lens, which shows significant advantages in compensating the influences of the scattering force and the photophoretic force on the trap, especially at intermediate pressure (about 100 Pa). This allows us to trap a nanoparticle from atmospheric to low pressure ($10^{-3}$ Pa) without using feedback cooling. We measure a highest rotation frequency a…
Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of $1.7\times 10^{-12} \text{m}/\sqrt{\text{Hz}}$, corresponding to a…
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) n…
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）
Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report the first 5D cooling of a levitated nanoparticle. We cool the 3 center-of-mass motion modes and 2 torsional vibration modes of a levitated nanodumb…
