Quantum control of a nanoparticle optically levitated in cryogenic free space

Mechanical Detection of Nuclear Decays

We report the detection of individual nuclear α decays through the mechanical recoil of the entire micron-sized particle in which the decaying nuclei are embedded. Momentum conservation ensures that such measurements are sensitive to any particles emitted in the decay, including neutral particles that may otherwise evade detection with existing techniques. Detection of the minuscule recoil of an object more than 10^{12} times more massive than the emitted particles is made possible by recently developed techniques in levitated optomechanics, which enable high-precision optical control and measurement of the mechanical motion of optically trapped particles. Observation of a change in the net charge of the particle coincident with the recoil allows decays to be identified with background levels at the micro-Becquerel level. The techniques developed here may find use in fields ranging from nuclear forensics to dark matter and neutrino physics.

Photon-efficient optical tweezers via wavefront shaping

Optical tweezers enable noncontact trapping of microscale objects using light. It is not known how tightly it is possible to three-dimensionally (3D) trap microparticles with a given photon budget. Reaching this elusive limit would enable maximally stiff particle trapping for precision measurements on the nanoscale and photon-efficient tweezing of light-sensitive objects. Here, we customize the shape of light fields to suit specific particles, with the aim of optimizing trapping stiffness in 3D. We show, theoretically, that the confinement volume of microspheres held in sculpted optical traps can be reduced by one to two orders of magnitude. Experimentally, we use a wavefront shaping-inspired strategy to passively suppress the Brownian fluctuations of microspheres in every direction concurrently, demonstrating order-of-magnitude reductions in their confinement volumes. Our work paves the way toward the fundamental limits of optical control over the mesoscopic realm.

State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential

We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.

Optically levitated micro gyroscopes with an MHz rotational vaterite rotor

The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications. The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally. In this study, we present the first rotor gyroscope based on optically levitated high-speed rotating particles. The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment. When an external angular velocity is input, the optical axis deviates from its initial position, resulting in changes in the frequency and amplitude of the rotational signal. By analyzing these changes, the angular velocity of the input can be accurately detected, making it the smallest rotor gyroscope in the world. The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10-9°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.

Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate at pressures below 10-5 Torr. We have driven a nanodiamond to rotate up to 20 MHz (1.2 × 109 rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena.

Vacuum levitation and motion control on chip

By isolating from the environment and precisely controlling mesoscopic objects, levitation in vacuum has evolved into a versatile technique that has already benefited diverse scientific directions, from force sensing and thermodynamics to materials science and chemistry. It also holds great promise for advancing the study of quantum mechanics in the unexplored macroscopic regime. However, most current levitation platforms are complex and bulky. Recent efforts in miniaturization of vacuum levitation set-ups have comprised electrostatic and optical traps, but robustness is still a concern for integration into confined settings, such as cryostats or portable devices. Here we show levitation and motion control in high vacuum of a silica nanoparticle at the surface of a hybrid optical-electrostatic chip. By combining fibre-based optical trapping and sensitive position detection with cold damping through planar electrodes, we cool the particle motion to a few hundred phonons. We envisage that our fully integrated platform is the starting point for on-chip devices combining integrated photonics and nanophotonics with precisely engineered electric potentials, enhancing control over the particle motion towards complex state preparation and read-out.

Squeezed light from an oscillator measured at the rate of oscillation

Sufficiently fast continuous measurements of the position of an oscillator approach measurements projective on position eigenstates. We evidence the transition into the projective regime for a spin oscillator within an ensemble of 2 × 1010 room-temperature atoms by observing correlations between the quadratures of the meter light field. These correlations squeeze the fluctuations of one light quadrature below the vacuum level. When the measurement is slower than the oscillation, we generate 11 . 5 - 1.5 + 2.5 dB and detect 8 . 5 - 0.1 + 0.1 dB of squeezing in a tunable band that is a fraction of the resonance frequency. When the measurement is as fast as the oscillation, we detect 4.7 dB of squeezing that spans more than one decade of frequencies below the resonance. Our results demonstrate a new regime of continuous quantum measurements on material oscillators, and set a new benchmark for the performance of a linear quantum sensor.

Diamond with Sp2-Sp3 composite phase for thermometry at Millikelvin temperatures

Temperature is one of the seven fundamental physical quantities. The ability to measure temperatures approaching absolute zero has driven numerous advances in low-temperature physics and quantum physics. Currently, millikelvin temperatures and below are measured through the characterization of a certain thermal state of the system as there is no traditional thermometer capable of measuring temperatures at such low levels. In this study, we develop a kind of diamond with sp2-sp3 composite phase to tackle this problem. The synthesized composite phase diamond (CPD) exhibits a negative temperature coefficient, providing an excellent fit across a broad temperature range, and reaching a temperature measurement limit of 1 mK. Additionally, the CPD demonstrates low magnetic field sensitivity and excellent thermal stability, and can be fabricated into probes down to 1 micron in diameter, making it a promising candidate for the manufacture of next-generation cryogenic temperature sensors. This development is significant for the low-temperature physics researches, and can help facilitate the transition of quantum computing, quantum simulation, and other related technologies from research to practical applications.

Coherent control of an optical tweezer phonon laser

The creation and manipulation of coherence continues to capture the attention of scientists and engineers. The optical laser is a canonical example of a system that, in principle, exhibits complete coherence. Recent research has focused on the creation of coherent, laser-like states in other physical systems. The phonon laser is one example where it is possible to amplify self-sustained mechanical oscillations. A single mode phonon laser in a levitated optical tweezer has been demonstrated through appropriate balance of active feedback gain and damping. In this work, coherent control of the dynamics of an optical tweezer phonon laser is used to share coherence between its different modes of oscillation, creating a multimode phonon laser. The coupling of the modes is achieved by periodically rotating the asymmetric optical potential in the transverse focal plane of the trapping beam via trap laser polarization rotation. The presented theory and experiment demonstrate that coherence can be transferred across different modes of an optical tweezer phonon laser, and are a step toward using these systems for precision measurement and quantum information processing.

Ultrahigh Quality Factor of a Levitated Nanomechanical Oscillator

A levitated nanomechanical oscillator under ultrahigh vacuum 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 7×10^{-11}  mbar. We measure a dissipation rate of 2π×69(22)  nHz, corresponding to a quality factor exceeding 10^{10}, more than 2 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.

Synchronization of optically self-assembled nanorotors

Self-assembly of nanoparticles by means of interparticle optical forces provides a compelling approach toward contact-free organization and manipulation of nanoscale entities. However, exploration of the rotational degrees of freedom in this process has remained limited, primarily because of the predominant focus on spherical nanoparticles, for which individual particle orientation cannot be determined. Here, we show that gold nanorods, which self-assemble in water under the influence of circularly polarized light, exhibit synchronized rotational motion at kilohertz frequencies. The synchronization is caused by strong optical interactions and occurs despite the presence of thermal diffusion. Our findings elucidate the intricate dynamics arising from the transfer of photon spin angular momentum to optically bound matter and hold promise for advancing the emerging field of light-driven nanomachinery.

Cavity-mediated long-range interactions in levitated optomechanics

The ability to engineer cavity-mediated interactions has emerged as a powerful tool for the generation of non-local correlations and the investigation of non-equilibrium phenomena in many-body systems. Levitated optomechanical systems have recently entered the multiparticle regime, which promises the use of arrays of strongly coupled massive oscillators to explore complex interacting systems and sensing. Here we demonstrate programmable cavity-mediated interactions between nanoparticles in vacuum by combining advances in multiparticle optical levitation and cavity-based quantum control. The interaction is mediated by photons scattered by spatially separated particles in a cavity, resulting in strong coupling that is long-range in nature. We investigate the scaling of the interaction strength with cavity detuning and interparticle separation and demonstrate the tunability of interactions between different mechanical modes. Our work will enable the exploration of many-body effects in nanoparticle arrays with programmable cavity-mediated interactions, generating entanglement of motion, and the use of interacting particle arrays for optomechanical sensing.

Steady motional entanglement between two distant levitated nanoparticles

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Real-time two-axis control of a spin qubit

Optimal control of qubits requires the ability to adapt continuously to their ever-changing environment. We demonstrate a real-time control protocol for a two-electron singlet-triplet qubit with two fluctuating Hamiltonian parameters. Our approach leverages single-shot readout classification and dynamic waveform generation, allowing full Hamiltonian estimation to dynamically stabilize and optimize the qubit performance. Powered by a field-programmable gate array (FPGA), the quantum control electronics estimates the Overhauser field gradient between the two electrons in real time, enabling controlled Overhauser-driven spin rotations and thus bypassing the need for micromagnets or nuclear polarization protocols. It also estimates the exchange interaction between the two electrons and adjusts their detuning, resulting in extended coherence of Hadamard rotations when correcting for fluctuations of both qubit axes. Our study highlights the role of feedback in enhancing the performance and stability of quantum devices affected by quasistatic noise.

Fast quantum interference of a nanoparticle via optical potential control

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 108 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10-10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.

Mass-Independent Scheme to Test the Quantumness of a Massive Object

The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To this end, we incorporate crucial modifications to the standard tools for probing the quantum violation of the pivotal classical notion of macrorealism (MR): while usual tests use the same measurement arrangement at successive times, here we use two different measurement arrangements. This yields a striking result: a mass-independent violation of MR is possible for harmonic oscillator systems. In fact, our adaptation enables probing quantum violations for literally any mass, momentum, and frequency. Moreover, coarse-grained position measurements at an accuracy much worse than the standard quantum limit, as well as knowing the relevant parameters only to this precision, without requiring them to be tuned, suffice for our proposal. These should drastically simplify the experimental effort in testing the nonclassicality of massive objects ranging from atomic ions to macroscopic mirrors in LIGO.

Macroscopic Quantum Superpositions via Dynamics in a Wide Double-Well Potential

We present an experimental proposal for the rapid preparation of the center of mass of a levitated particle in a macroscopic quantum state, that is a state delocalized over a length scale much larger than its zero-point motion and that has no classical analog. This state is prepared by letting the particle evolve in a static double-well potential after a sudden switchoff of the harmonic trap, following initial center-of-mass cooling to a sufficiently pure quantum state. We provide a thorough analysis of the noise and decoherence that is relevant to current experiments with levitated nano- and microparticles. In this context, we highlight the possibility of using two particles, one evolving in each potential well, to mitigate the impact of collective sources of noise and decoherence. The generality and scalability of our proposal make it suitable for implementation with a wide range of systems, including single atoms, ions, and Bose-Einstein condensates. Our results have the potential to enable the generation of macroscopic quantum states at unprecedented scales of length and mass, thereby paving the way for experimental exploration of the gravitational field generated by a source mass in a delocalized quantum state.

Nanoscale feedback control of six degrees of freedom of a near-sphere

Manipulating the rotational as well as the translational degrees of freedom of rigid bodies has been a crucial ingredient in diverse areas, from optically controlled micro-robots, navigation, and precision measurements at macroscale to artificial and biological Brownian motors at nanoscale. Here, we demonstrate feedback cooling of all the angular motions of a near-spherical neutral nanoparticle with all the translational motions feedback-cooled to near the ground state. The occupation numbers of the three translational motions are 6 ± 1, 6 ± 1, and 0.69 ± 0.18. A tight, anisotropic optical confinement allows us to clearly observe three angular oscillations and to identify the ratio of two radii to the longest radius with a precision of 0.08 %. We develop a thermometry for three angular oscillations and realize feedback cooling of them to temperatures of lower than 0.03 K by electrically controlling the electric dipole moment of the nanoparticle.

Revealing the Velocity Uncertainties of a Levitated Particle in the Quantum Ground State

We demonstrate time-of-flight measurements for an ultracold levitated nanoparticle and reveal its velocity for the translational motion brought to the quantum ground state. We discover that the velocity distributions obtained with repeated release-and-recapture measurements are significantly broadened via librational motions of the nanoparticle. Under feedback cooling on all the librational motions, we recover the velocity distributions in reasonable agreement with an expectation from the occupation number, with approximately twice the width of the quantum limit. The strong impact of librational motions on the translational motions is understood as a result of the deviation between the libration center and the center of mass, induced by the asymmetry of the nanoparticle. Our results elucidate the importance of the control over librational motions and establish the basis for exploring quantum mechanical properties of levitated nanoparticles in terms of their velocity.

Acoustic frequency atomic spin oscillator in the quantum regime

Quantum noise reduction and entanglement-enhanced sensing in the acoustic frequency range is an outstanding challenge relevant for a number of applications including magnetometry and broadband noise reduction in gravitational wave detectors. Here we experimentally demonstrate quantum behavior of a macroscopic atomic spin oscillator in the acoustic frequency range. Quantum back-action of the spin measurement, ponderomotive squeezing of light, and virtual spring softening are observed at oscillation frequencies down to the sub-kHz range. Quantum noise sources characteristic of spin oscillators operating in the near-DC frequency range are identified and means for their mitigation are presented.

Shortcuts to Equilibrium with a Levitated Particle in the Underdamped Regime

We report on speeding-up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence toward equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nanoheat engines.

Active-feedback quantum control of an integrated low-frequency mechanical resonator

Preparing a massive mechanical resonator in a state with quantum limited motional energy provides a promising platform for studying fundamental physics with macroscopic systems and allows to realize a variety of applications, including precise sensing. While several demonstrations of such ground-state cooled systems have been achieved, in particular in sideband-resolved cavity optomechanics, for many systems overcoming the heating from the thermal bath remains a major challenge. In contrast, optomechanical systems in the sideband-unresolved limit are much easier to realize due to the relaxed requirements on their optical properties, and the possibility to use a feedback control schemes to reduce the motional energy. The achievable thermal occupation is ultimately limited by the correlation between the measurement precision and the back-action from the measurement. Here, we demonstrate measurement-based feedback cooling on a fully integrated optomechanical device fabricated using a pick-and-place method, operating in the deep sideband-unresolved limit. With the large optomechanical interaction and a low thermal decoherence rate, we achieve a minimal average phonon occupation of 0.76 when pre-cooled with liquid helium and 3.5 with liquid nitrogen. Significant sideband asymmetry for both bath temperatures verifies the quantum character of the mechanical motion. Our method and device are ideally suited for sensing applications directly operating at the quantum limit, greatly simplifying the operation of an optomechanical system in this regime.

High-Q Magnetic Levitation and Control of Superconducting Microspheres at Millikelvin Temperatures

We report the levitation of a superconducting lead-tin sphere with 100  μm diameter (corresponding to a mass of 5.6  μg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15 mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200 Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.

Levitated Optomechanics with Meta-Atoms

We propose to introduce additional control in levitated optomechanics by trapping a meta-atom, i.e., a subwavelength and high-permittivity dielectric particle supporting Mie resonances. In particular, we theoretically demonstrate that optical levitation and center-of-mass ground-state cooling of silicon nanoparticles in vacuum is not only experimentally feasible but it offers enhanced performance over widely used silica particles in terms of trap frequency, trap depth, and optomechanical coupling rates. Moreover, we show that, by adjusting the detuning of the trapping laser with respect to the particle's resonance, the sign of the polarizability becomes negative, enabling levitation in the minimum of laser intensity, e.g., at the nodes of a standing wave. The latter opens the door to trapping nanoparticles in the optical near-field combining red and blue-detuned frequencies, in analogy to two-level atoms, which is of interest for generating strong coupling to photonic nanostructures and short-distance force sensing.

Optomechanically induced optical trapping system based on photonic crystal cavities

Optical trapping has proven to be a valuable experimental technique for precisely controlling small dielectric objects. However, due to their very nature, conventional optical traps are diffraction limited and require high intensities to confine the dielectric objects. In this work, we propose a novel optical trap based on dielectric photonic crystal nanobeam cavities, which overcomes the limitations of conventional optical traps by significant factors. This is achieved by exploiting an optomechanically induced backaction mechanism between a dielectric nanoparticle and the cavities. We perform numerical simulations to show that our trap can fully levitate a submicron-scale dielectric particle with a trap width as narrow as 56 nm. It allows for achieving a high trap stiffness, therefore, a high Q-frequency product for the particle's motion while reducing the optical absorption by a factor of 43 compared to the cases for conventional optical tweezers. Moreover, we show that multiple laser tones can be used further to create a complex, dynamic potential landscape with feature sizes well below the diffraction limit. The presented optical trapping system offers new opportunities for precision sensing and fundamental quantum experiments based on levitated particles.

Gradient torque and its effect on rotational dynamics of optically trapped non-spherical particles in the elliptic Gaussian beam

Rotational motion of the optically trapped particle is a topic of enduring interest, while the changes of angular velocity in one rotation period remain largely unexplored. Here, we proposed the optical gradient torque in the elliptic Gaussian beam, and the instantaneous angular velocities of alignment and fluctuant rotation of the trapped non-spherical particles are investigated for the first time. The fluctuant rotations of optically trapped particles are observed, and the angular velocity fluctuated twice per rotation period, which can be used to determine the shape of trapped particles. Meanwhile, a compact optical wrench is invented based on the alignment, and its torque is adjustable and is larger than the torque of a linearly polarized wrench with the same power. These results provide a foundation for precisely modelling the rotational dynamics of optically trapped particles, and the presented wrench is expected to be a simple and practical micro-manipulating tool.

Collapse Models: A Theoretical, Experimental and Philosophical Review

In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question 'what are collapse models (and in general any physical theory) about?'; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role.

Locally Mediated Entanglement in Linearized Quantum Gravity

The current interest in laboratory detection of entanglement mediated by gravity was sparked by an information-theoretic argument: entanglement mediated by a local field certifies that the field is not classical. Previous derivations of the effect modeled gravity as instantaneous; here we derive it from linearized quantum general relativity while keeping Lorentz invariance explicit, using the path-integral formalism. In this framework, entanglement is clearly mediated by a quantum feature of the field. We also point out the possibility of observing "retarded" entanglement, which cannot be explained by an instantaneous interaction. This is a difficult experiment for gravity, but is plausible for the analogous electromagnetic case.

Entanglement Witness for the Weak Equivalence Principle

The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.

Interaction between an Optically Levitated Nanoparticle and Its Thermal Image: Internal Thermometry via Displacement Sensing

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 fluctuations of the dipole. The resulting force is orders of magnitude stronger than the thermal gradient force, and it strongly depends on the internal temperature of the nanoparticle for a particle-to-surface distance greater than two micrometers. We argue that it is experimentally feasible to use displacement sensing of a levitated nanoparticle in front of a surface as an internal thermometer in ultrahigh vacuum. Experimental access to the internal physics of a levitated nanoparticle in vacuum is crucial to understanding the limitations that decoherence poses to current efforts devoted to preparing a nanoparticle in a macroscopic quantum superposition state.

Optimal Cooling of Multiple Levitated Particles through Far-Field Wavefront Shaping

Light forces can be harnessed to levitate mesoscopic objects and cool them down toward their motional quantum ground state. Roadblocks on the way to scale up levitation from a single to multiple particles in close proximity are the requirements to constantly monitor the particles' positions as well as to engineer light fields that react fast and appropriately to their movements. Here, we present an approach that solves both problems at once. By exploiting the information stored in a time-dependent scattering matrix, we introduce a formalism enabling the identification of spatially modulated wavefronts, which simultaneously cool down multiple objects of arbitrary shapes. An experimental implementation is suggested based on stroboscopic scattering-matrix measurements and time-adaptive injections of modulated light fields.

Levitated optomechanics: From single to many-body physics

The levitated optomechanics, because of its ultra-high mechanical Q > 1010, is considered to be one of the best testbeds for macroscopic quantum superpostions. In this perspective, we give a brief review on the development of the levitated optomechanics, focusing on the macroscopic quantum phenomena, and the applications in quantum precision measurement. The levitated nanodiamond with built-in nitrogen-vacancy centers is discussed as an example. Finally, we discuss the future dirctions of the levtated optomechanics, such as the space-based experiments, the arrays of levitated optomechanics and applications in quantum simulation.

Scalable all-optical cold damping of levitated nanoparticles

Motional control of levitated nanoparticles relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of the 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 an all-optical cold damping scheme based on the spatial modulation of trap position, which has the advantage of being scalable to multiple particles. The scheme relies on programmable optical tweezers to provide full independent control over the trap frequency and position of each tweezer. We show that the technique cools the centre-of-mass motion of particles along one axis down to 17 mK at a pressure of 2 × 10^-6 mbar and demonstrate its scalability by simultaneously cooling the motion of two particles. Our work paves the way towards studying quantum interactions between particles; achieving three-dimensional quantum control of particle motion without cavity-based cooling, electrodes or charged particles; and probing multipartite entanglement in levitated optomechanical systems.

Fiber-based 3D nano-printed holography with individually phase-engineered remote points

The generation of tailored light fields with spatially controlled intensity and phase distribution is essential in many areas of science and application, while creating such patterns remotely has recently defined a key challenge. Here, we present a fiber-compatible concept for the remote generation of complex multi-foci three-dimensional intensity patterns with adjusted relative phases between individual foci. By extending the well-known Huygens principle, we demonstrate, in simulations and experiments, that our interference-based approach enables controlling of both intensity and phase of individual focal points in an array of spots distributed in all three spatial directions. Holograms were implemented using 3D nano-printing on planar substrates and optical fibers, showing excellent agreement between design and implemented structures. In addition to planar substrates, holograms were also generated on modified single-mode fibers, creating intensity distributions consisting of about 200 individual foci distributed over multiple image planes. The presented scheme yields an innovative pathway for phase-controlled 3D digital holography over remote distances, yielding an enormous potential application in fields such as quantum technology, life sciences, bioanalytics and telecommunications. Overall, all fields requiring precise excitation of higher-order optical resonances, including nanophotonics, fiber optics and waveguide technology, will benefit from the concept.

Visualization of transparent particles based on optical spatial differentiation

Optical analog computing operates on the amplitude, phase, polarization, and frequency distributions of the electromagnetic field through the interaction of light and matter. The differentiation operation is widely used in all-optical image processing technology, such as edge detection. Here, we propose a concise way to observe transparent particles, incorporating the optical differential operation that occurs on a single particle. The particle's scattering and cross-polarization components combine into our differentiator. We achieve high-contrast optical images of transparent liquid crystal molecules. The visualization of aleurone grains (the structures that store protein particles in plant cells) in maize seed was experimentally demonstrated with a broadband incoherent light source. Avoiding the interference of stains, our designed method provides the possibility to observe protein particles directly in complex biological tissues.

Force-Gradient Sensing and Entanglement via Feedback Cooling of Interacting Nanoparticles

We show theoretically that feedback cooling of two levitated, interacting nanoparticles enables differential sensing of forces and the observation of stationary entanglement. The feedback drives the two particles into a stationary, nonthermal state which is susceptible to inhomogeneous force fields and which exhibits entanglement for sufficiently strong interparticle couplings. We predict that force-gradient sensing at the zepto-Newton per micron range is feasible and that entanglement due to the Coulomb interaction between charged particles can be realistically observed in state-of-the-art setups.

Dipole moment background measurement and suppression for levitated charge sensors

Optically levitated macroscopic objects are a powerful tool in the field of force sensing, owing to high sensitivity, absolute force calibration, environmental isolation, and the advanced degree of control over their dynamics that have been achieved. However, limitations arise from the spurious forces caused by electrical polarization effects that, even for nominally neutral objects, affect the force sensing because of the interaction of dipole moments with gradients of external electric fields. Here, we introduce a technique to measure, model, and eliminate dipole moment interactions, limiting the performance of sensors using levitated objects. This process leads to a noise-limited measurement with a sensitivity of 3.3 × 10^-5 e. As a demonstration, this is applied to the search for unknown charges of a magnitude much below that of an electron or for exceedingly small unbalances between electron and proton charges.

Extractable work in quantum electromechanics

Recent experiments have demonstrated the generation of coherent mechanical oscillations in a suspended carbon nanotube, which are driven by an electric current through the device above a certain voltage threshold, in close analogy with a lasing transition. We investigate this phenomenon from the perspective of work extraction, by modeling a nanoelectromechanical device as a quantum flywheel or battery that converts electrical power into stored mechanical energy. We introduce a microscopic model that qualitatively matches the experimental finding, and we compute the Wigner function of the quantum vibrational mode in its nonequilibrium steady state. We characterize the threshold for self-sustained oscillations using two approaches to quantifying work deposition in nonequilibrium quantum thermodynamics: the ergotropy and the nonequilibrium free energy. We find that ergotropy serves as an order parameter for the phonon lasing transition. The framework we employ to describe work extraction is general and widely transferable to other mesoscopic quantum devices.

Spin-Controlled Quantum Interference of Levitated Nanorotors

We describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particle's three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology.

Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles

Arrays of optically trapped nanoparticles have emerged as a platform for the study of complex nonequilibrium phenomena. Analogous to atomic many-body systems, one of the crucial ingredients is the ability to precisely control the interactions between particles. However, the optical interactions studied thus far only provide conservative optical binding forces of limited tunability. In this work, we exploit the phase coherence between the optical fields that drive the light-induced dipole-dipole interaction to couple two nanoparticles. In addition, we effectively switch off the optical interaction and observe electrostatic coupling between charged particles. Our results provide a route to developing fully programmable many-body systems of interacting nanoparticles with tunable nonreciprocal interactions, which are instrumental for exploring entanglement and topological phases in arrays of levitated nanoparticles.

Optical Trapping of High-Aspect-Ratio NaYF Hexagonal Prisms for kHz-MHz Gravitational Wave Detectors

We present experimental results on optical trapping of Yb-doped β-NaYF subwavelength-thickness high-aspect-ratio hexagonal prisms with a micron-scale radius. The prisms are trapped in vacuum using an optical standing wave, with the normal vector to their face oriented along the beam propagation direction, yielding much higher trapping frequencies than those typically achieved with microspheres of similar mass. This platelike geometry simultaneously enables trapping with low photon-recoil-heating, high mass, and high trap frequency, potentially leading to advances in high frequency gravitational wave searches in the Levitated Sensor Detector, currently under construction. The material used here has previously been shown to exhibit internal cooling via laser refrigeration when optically trapped and illuminated with light of suitable wavelength. Employing such laser refrigeration methods in the context of our work may enable higher trapping intensity and thus higher trap frequencies for gravitational wave searches approaching the several hundred kilohertz range.

Ponderomotive Squeezing of Light by a Levitated Nanoparticle in Free Space

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 a nanoparticle levitated in a free-space optical tweezer. We observe a reduction of the optical fluctuations by up to 25% below the vacuum level, in a bandwidth of about 15 kHz. Our results are explained well by a linearized dipole interaction between the nanoparticle and the electromagnetic continuum. These ponderomotive correlations open the door to quantum-enhanced sensing and metrology with levitated systems, such as force measurements below the standard quantum limit.

Squeezed Light from a Levitated Nanoparticle at Room Temperature

Quantum measurements of mechanical systems can generate optical squeezing via ponderomotive forces. Its observation requires high environmental isolation and efficient detection, typically achieved by using cryogenic cooling and optical cavities. 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%±0.5% below shot noise. Our experiment offers a novel, cavityless platform for squeezed-light enhanced sensing. At the same time it delineates a clear and simple strategy toward observation of stationary optomechanical entanglement.

Optical cold damping of neutral nanoparticles near the ground state in an optical lattice

We propose and demonstrate purely optical feedback cooling of neutral nanoparticles in an optical lattice to an occupation number of 0.85 ± 0.20. The cooling force is derived from the optical gradients of displaced optical lattices produced with two sidebands on the trapping laser. To achieve highly accurate position observations required for cooling near the ground state, we reduce the laser intensity noise to a relative power noise of 6×10^-8/Hz in a frequency band of 30 kHz to 600 kHz. We establish a reproducible method for neutralizing nanoparticles at high vacuum via a combination of discharging and irradiating an ultraviolet light. Our results form an important basis for the investigation of quantum mechanical properties of ultracold nanoparticles and are also useful for precision measurements with neutral nanoparticles.

Giant Diffusion of Nanomechanical Rotors in a Tilted Washboard Potential

We present an experimental realization of a biased optical periodic potential in the low friction limit. The noise-induced bistability between locked (torsional) and running (spinning) states in the rotational motion of a nanodumbbell is driven by an elliptically polarized light beam tilting the angular potential. By varying the gas pressure around the point of maximum intermittency, the rotational effective diffusion coefficient increases by more than 3 orders of magnitude over free-space diffusion. These experimental results are in agreement with a simple two-state model that is derived from the Langevin equation through using timescale separation. Our work provides a new experimental platform to study the weak thermal noise limit for diffusion in this system.

Position Measurement of a Levitated Nanoparticle via Interference with Its Mirror Image

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 1.7×10^{-12}  m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.

Measurement-based preparation of multimode mechanical states

Nanomechanical resonators are a key tool for future quantum technologies, such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature nonclassical states is a major outstanding challenge. It has been suggested that this could be achieved using a fast continuous measurement to break the usual symmetry between position and momentum. Here, we demonstrate this symmetry breaking and use it to prepare a thermally squeezed mechanical state. Our experiments take advantage of collective measurements on multiple mechanical modes, which we show can increase the measurement speed and improve state preparation. Theoretically, we show that this result extends to the quantum regime, relaxing the requirements to generate nonclassical states. We predict that multimode conditioning can enable room temperature quantum squeezing with existing technology. Our work paves the way toward room temperature quantum nanomechanical devices and toward their application in quantum technology and fundamental science.

Precision Calibration of the Duffing Oscillator with Phase Control

The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to an external excitation. When changing the amplitude or frequency of the external excitation, a sudden jump in the response function reveals the nonlinear dynamics prominently. However, this bistability leaves part of the full response function unobserved, which limits the precise measurement of the system parameters. Here, we exploit the often unknown fact that the response of a Duffing oscillator with nonlinear damping is a unique function of its phase. By actively stabilizing the oscillator's phase we map out the full response function. This phase control allows us to precisely determine the system parameters. Our results are particularly important for characterizing nanoscale resonators, where nonlinear effects are observed readily and which hold great promise for next generation of ultrasensitive force and mass measurements. We demonstrate our approach experimentally with an optically levitated particle in high vacuum.

Interference of the scattered vector light fields from two optically levitated nanoparticles

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 interference fringes of two scattered light fields with polarization vortex show the π shift of the interference fringes between inside and outside the center region of the two nanoparticles in the image space. As far as we know, this is the first experimental observation of the interference of scattered vector light fields from two dipoles in free space. This work also provides a simple and direct method to determine the spatial scales between optically levitated nanoparticles by the interference fringes.