Cooling of Optically Levitated Particles: Principles, Implementations, and Applications

Abstract

Optically levitated particles in high vacuum offer an exceptionally isolated mechanical platform for photonic control. Effective cooling of their center-of-mass motion is essential not only for enabling ultrasensitive precision sensing but also for opening access to the quantum regime where macroscopic superposition and nonclassical states can be realized. In this review, we present a comprehensive overview of recent advances in active feedback cooling, based on real-time photonic modulation, and passive feedback cooling, driven by optomechanical interactions within optical resonators. We highlight key experimental milestones, including ground state cooling in one and two dimensions, and discuss the emerging applications of these systems in force sensing, inertial metrology, and macroscopic quantum state preparation. Particular attention is given to novel proposals for probing quantum gravity, detecting dark matter and dark energy candidates, and exploring high-frequency gravitational waves. These advancements establish levitated optomechanical systems as a powerful platform for both high-precision metrology and the investigation of fundamental quantum phenomena. Finally, we discuss the current challenges and future prospects in cooling multiple degrees of freedom, device integration, and scalability toward future quantum technologies.

1. Introduction

The concept of radiation pressure was first proposed by Johannes Kepler in the 17th century, based on his observation that comet tails always pointed away from the Sun during transit [1]. However, for centuries, there has been no practical means of effectively applying this optical radiation pressure. With the development of the world’s first sapphire laser in 1960, a directional, monochromatic, and coherent high-power light source enables unprecedented levels of optical radiation pressure. This breakthrough laid the foundation for trapping and cooling atomic ensembles, and associated techniques have advanced significantly over the last two decades [2], reducing the effective temperature of cold atoms from the Kelvin range down to the nanokelvin range [3,4,5,6,7]. Advancements in atom-cooling techniques have profoundly accelerated progress in fundamental physics, metrology, and quantum computing. In fundamental physics, the creation of the first Bose-Einstein condensate (BEC) using cold atoms marked a milestone achievement: it validated a theoretical prediction made by Einstein over 70 years ago and established a novel experimental framework for investigating quantum phenomena at macroscopic scales. In metrology, atomic cooling technology contributed to the development of highly precise atomic clocks, reducing the uncertainty of time measurement from ${10}^{-9}$ to ${10}^{-18}$ [8]. In quantum computing, a two-level atom can serve as a qubit, and many of these atoms can be assembled into a quantum computer by building atomic arrays [9,10].

The success of cooling atoms has inspired efforts to cool macroscopic objects in a similar manner. On one hand, this enables the exploration of macroscopic quantum effects, such as superposition and entanglement at a larger scale; on the other hand, in the field of precision measurement, a cooled mechanical oscillator can serve as an ultrasensitive force sensor. However, ground-state cooling of most mechanical resonators is limited by thermal contact with the environment [11,12,13,14]. To isolate the environment, a promising solution is to optically trap dielectric particles in vacuum, an approach that has been experimentally proven to produce mechanical harmonic oscillators with extremely high Q values. This technique is now commonly known as optical tweezers in vacuum. Optical tweezers originated from the research of Ashkin on optically levitated particles. In 1970, Ashkin discovered that a focused laser beam exerts optical forces on dielectric particles, typically in the form of gradient and scattering forces, which can trap small particles near the region of maximum laser intensity [15]. Using this optical force, Ashkin achieved stable optical levitation of atoms, molecules, and microparticles in air [4,16,17]. He was later awarded the Nobel Prize for his development of optical tweezers and their application in biological systems.

Li was the first to demonstrate the potential of optical tweezers in vacuum for precision measurement and fundamental physics. By accurately measuring the velocity of an optically levitated particle in a counter-propagating dual-beam trap, he confirmed the energy equipartition theorem for a Brownian particle [18]. Li also pioneered the application of active feedback cooling to optically levitated particles, aiming to cool them to their motional quantum ground state [19]. Since then, various other cooling techniques have been developed towards this goal, advancing the cooling of macroscopic objects into the quantum regime [20,21,22,23,24,25,26]. Many proposed quantum experiments are now on the verge of becoming a reality [27,28,29,30].

According to the principles of cooling, technologies for cooling optically levitated particles are primarily divided into active feedback cooling and passive feedback cooling, with the latter often referred to as cavity cooling. Figure 1 highlights the key experimental schemes that have realized ground-state cooling of levitated nanoparticles, demonstrating the highest level of cooling achieved in optical levitation to date.

The most widely used cooling technique for optical tweezers in vacuum is active feedback cooling. This method involves the precise acquisition of motion signals from optically levitated particles using photodetectors. The acquired electrical signal is then processed by a feedback circuit and converted into a negative feedback force applied to the particle, thereby reducing the motion of the particle. Through active feedback cooling, an extremely high force sensitivity on the order of ${10}^{-22}N$ has been achieved [31], making an optically levitated particle an ideal candidate for exploring new physics, such as searches for the fifth force, detection of high-frequency gravitational waves, and dark matter research [32,33,34,35]. Active feedback cooling was initially proposed to reduce thermal noise in LIGO [36], and it was experimentally validated soon after [11]. The first application in vacuum optical tweezers was demonstrated by Li [19], who reduced the temperature of the center-of-mass (COM) motion of a 3 μm microsphere to the millikelvin regime along all three axes. Following this approach, further temperature reduction of COM motion has been achieved [31,37,38,39,40,41]. Remarkably, the motional quantum ground state was recently achieved through various methods [24,25,26], demonstrating the significant potential of active feedback cooling.

Figure 1. Existing schemes for cooling to the quantum ground state: (a,e) 2D and 1D cavity cooling setups; (b) cold damping within an optical lattice; (c) electric cold damping through optimal quantum control; (d) electric cold damping in a cryogenic environment. ((a) is reprinted from [42], Copyright 2023, with permission from Springer Nature; (b) is reprinted from [26], Copyright 2022, with permission from Springer Nature; (c) is reprinted from [25], Copyright 2021, with permission from Springer Nature; (d) is reprinted from [25], Copyright 2021, with permission from Springer Nature; (e) is reprinted from [23], Copyright 2020, with permission from Springer Nature.)

Figure 1. Existing schemes for cooling to the quantum ground state: (a,e) 2D and 1D cavity cooling setups; (b) cold damping within an optical lattice; (c) electric cold damping through optimal quantum control; (d) electric cold damping in a cryogenic environment. ((a) is reprinted from [42], Copyright 2023, with permission from Springer Nature; (b) is reprinted from [26], Copyright 2022, with permission from Springer Nature; (c) is reprinted from [25], Copyright 2021, with permission from Springer Nature; (d) is reprinted from [25], Copyright 2021, with permission from Springer Nature; (e) is reprinted from [23], Copyright 2020, with permission from Springer Nature.)

Cavity cooling of optically levitated particles was first explored in cold atom systems, where cavity-induced modulation of the spontaneous emission rate of two-level atoms enabled efficient cooling [43]. In the early 21st century, scientists proposed that cavity cooling could be extended to molecules, ions, and even solid particles without internal energy level structures, utilizing coherent scattering [44,45]. This laid the theoretical groundwork for cavity cooling of macroscopic levitated objects. The theory of cavity cooling for optically levitated nanoparticles was first proposed by Barker et al. [46], with the first experimental realization following three years later [47]. Since then, cavity cooling technology has led to a major breakthrough, wherein Delic et al. achieved the motional quantum ground state of an optically levitated nanoparticle [23,48,49,50], marking a significant milestone. It has been demonstrated that cavity cooling can be extended to two axes and six degrees of freedom [42,51], paving the way for multidimensional quantum control of macroscopic objects.

In recent years, several reviews have been published on the topic of cooling optically levitated particles. Optical levitation technology has been extensively reviewed [52,53], while cavity cooling has been examined within the broader context of cavity optomechanics [54,55]. Additionally, other cooling techniques have been discussed within the emerging field of levitodynamics [56,57]. This review focuses on cooling techniques for optically levitated particles and is structured as follows: We begin with a concise introduction to particle trapping and manipulation, covering the principles of optical trapping, various trapping techniques, and motion detection methods. Next, we focus on the details of active feedback cooling and passive feedback (cavity) cooling. Following this, we highlight advanced applications in precision sensing and fundamental physics. Finally, we provide an outlook on future developments in this rapidly evolving field.

2. Capture and Manipulation of Particles

This section provides a brief overview of how to stably capture and manipulate particles, as well as several displacement detection techniques, which form the foundation for cooling.

2.1. Principles of Levitation

A focused laser beam exerts two types of forces on particles: a “scattering force” in the direction of beam propagation (axial) and a “gradient force” towards the focus point (radial). The combination of these forces enables particle trapping near the region of maximum light intensity. This optical radiation force can capture particles ranging in size from tens of nanometers to tens of microns. Depending on the particle’s size, different approaches are used to compute the optical force: Rayleigh approximation $(r\le \lambda /10)$, the intermediate regime $(\lambda /10\le r\le 10\lambda )$, and geometrical optics $(r\ge 10\lambda )$.

In the Rayleigh regime, a nanoparticle in a optical trap is typically treated as a dipole, with the gradient and scattering forces expressed as follows [58]:

$$\left\{\begin{array}{c}{\mathit{F}}_{\mathrm{scat}}\left(\mathit{r}\right)=\widehat{z}{\displaystyle \frac{128{\pi }^5{R}^6}{3c{\lambda }_0^4}}{\left({\displaystyle \frac{m^2-1}{m^2+2}}\right)}^2{n}_{\mathrm{med}}^{5}I\left(r\right),\hfill \\ {\mathit{F}}_{\mathrm{grad}}\left(\mathit{r}\right)={\displaystyle \frac{2\pi n_{\mathrm{med}}{R}^3}{c}}\left({\displaystyle \frac{m^2-1}{m^2+2}}\right)\nabla I\left(r\right),\hfill \end{array}\right.$$

(1)

where $\widehat{z}$ is the unit vector on the z axis (the beam propagation direction), c is the speed of light in vacuum, ${\lambda }_0$ is the laser wavelength, R is the particle radius, m is the relative refractive index between the particle and the medium, and $n_{\mathrm{med}}$ is the refractive index of the medium and $I\left(r\right)$ is the light intensity at position r. Assuming the trapping beam is Gaussian, the light intensity can be expressed by the Gaussian function:

$$I(x,y,z)={\displaystyle \frac{I_0}{\left(\frac{z^2}{z_R^2}+1\right)}}{e}^{{\displaystyle \frac{-2x^2-2y^2}{w_0^2\left(\frac{z^2}{z_R^2}+1\right)}}},$$

(2)

Near the focal point, the gradient force simplifies to a linear restoring force in three dimensions through a first-order Taylor expansion of $I(x,y,z)$:

$$F_{\mathrm{grad},q}=-{\mathrm{k}}_{q}q,q\in \{x,y,z\},$$

(3)

where $k_q$ represents the stiffness of the harmonic potential well, and q is the position of the particle.

In the intermediate regime, more complex models are necessary, such as generalized Lorenz-Mie theory (GLMT), extended boundary condition method (EBCM), discrete dipole approximation (DDA), finite element method (FEM), and finite difference time domain (FDTD) techniques [59]. For larger particles, geometric optics provides accurate results [60].

Despite these varied approaches, in most cases, an optically levitated particle can be treated as a three-dimensional harmonic oscillator, regardless of its size. For example, the dynamics of the particle along the x-axis are described by the Langevin equation [61]:

$$\ddot{x}\left(t\right)+{\gamma }_0\dot{x}\left(t\right)+{\mathrm{\Omega }}_x^{2}x\left(t\right)={\displaystyle \frac{\sqrt{2k_B{T}_{env}{\gamma }_0}}{m}}\xi \left(t\right),$$

(4)

where ${\gamma }_0$ is the damping coefficient, ${\mathrm{\Omega }}_x$ is the x-axis oscillation frequency, $k_B$ is the Boltzmann constant, $T_{env}$ is the environmental temperature, m is the mass of the particle, and $\xi \left(t\right)$ represents a white noise process with the correlation function $〈\xi \left(t\right)\xi \left(t^{\prime }\right)〉=\delta (t-t^{\prime })$. The right-hand side captures only thermal noise due to gas molecule collisions; other noise sources are addressed in Section 3. Apart from optical levitation, other levitation mechanisms, such as electric and magnetic levitation, exist, but they are beyond the scope of this review.

2.2. Loading Technique

To capture a particle, it must first be moved to the effective trapping region at a sufficiently low speed, a process known as loading. Two common techniques for loading are piezoelectric transducer (PZT) loading [40] and ultrasonic atomizer loading [23]. The PZT method utilizes high-frequency oscillations of a glass slide to propel particles attached to the target position, typically used for microspheres. In contrast, the ultrasonic atomizer sprays a particle-laden solution into the chamber, allowing particles to diffuse into the trapping region, which is often applied to nanospheres. However, neither technique is suitable for high vacuum environments. Typically, the loading process occurs at atmospheric pressure or low vacuum, followed by pumping to high vacuum post-trapping, which leads to inefficiencies and high particle loss. To enable direct loading in high vacuum, various methods have been proposed, including electrospray [62], laser-induced acoustic desorption [63], load lock [64], and loading via hollow-core fibers [65].

2.3. Motion Detection Technique

The motional information of an optically levitated particle, such as displacement, resonance frequency, and other indirectly inferred parameters, is essential for system characterization and control. This information is typically extracted from the analysis of light scattered by the particle. In most setups, the scattered light is collected either in the forward or backward direction using a lens. Variations in the spatial intensity distribution induced by particle motion are detected using a camera, a quadrant photodetector (QPD), or a balanced photodetector in conjunction with a D-shaped mirror. The acquired signals are then processed by a spectrum analyzer to retrieve motion information along various degrees of freedom, often represented in the frequency domain:

$$S_{xx}^{\mathrm{th}}\left(\omega \right)={\displaystyle \frac{k_B{T}_{com}}{m{\mathrm{\Omega }}_x^2}}{\displaystyle \frac{2{\gamma }_0{\mathrm{\Omega }}_x^2}{{({\mathrm{\Omega }}_x^2-{\omega }^2)}^2+{\omega }^2{\gamma }_0^2}},$$

(5)

where $S_{xx}^{\mathrm{th}}\left(\omega \right)$ is referred as the power spectral density (PSD) function, characterized by a Lorentzian profile. By fitting the PSD, essential parameters can be determined, such as the resonance frequency ${\mathrm{\Omega }}_x$, the damping rate ${\gamma }_0$, and the COM temperature $T_{com}$. The signal-to-noise ratio (SNR) and the sensitivity of motion detection are essential parameters that define the effectiveness of active feedback cooling. To improve motion detection capabilities, the optimal detection angle has been investigated for various axes of motion [66], and a photodetector with a threshold power of up to 70 mW has been developed [67]. However, the ultimate limit of detection accuracy is governed by the Heisenberg limit, as high-precision measurements can exert backaction on the particle’s motion. Currently, the detection precision is nearing this fundamental limit [24,25].

2.4. Noise Analysis

An ideal optically levitated particle behaves as a three-dimensional harmonic oscillator. In reality, however, it is unavoidably subject to various noise sources, including thermal noise, recoil heating, measurement impression noise, and other perturbations like laser intensity and phase noise (as illustrated in Figure 2). These noise sources can cause particle loss under high vacuum conditions and lead to quantum decoherence. Considering these effects, the Langevin equation of the particle can be expressed as follows:

$$\ddot{x}\left(t\right)+{\gamma }_0\dot{x}\left(t\right)+{\mathrm{\Omega }}_x^{2}x\left(t\right)={\displaystyle \frac{F_{th}+F_{recoil}+F_{other}}{m}},$$

(6)

where $F_{th}$ is the stochastic thermal force, $F_{recoil}$ is the recoil heating force, and $F_{other}$ contains other minor noise sources. This section provides an overview of the dominant noise sources encountered in levitated optomechanical systems.

2.4.1. Thermal Noise

Thermal noise, also referred as gas collision noise, arises from the random collisions between residual gas molecules and the levitated particle, resulting in Brownian motion. This phenomenon was experimentally verified by Li using a balanced detection scheme [18]. The stochastic thermal force can be expressed as follows:

$$F_{th}=\sqrt{2{\gamma }_{0}m{k}_B{T}_{env}}\xi \left(t\right),$$

(7)

Reducing the background pressure or implementing cryogenic techniques effectively suppresses this noise. The PSD spectrum resulting from thermal noise, as described in Equation (5), constitutes the dominant noise contribution in typical optically levitated systems.

2.4.2. Quantum Noise

Quantum noise in continuous position measurement has two fundamental components: (i) measurement imprecision noise, arising from the quantum nature of the probe (for example, photon shot noise), and (ii) quantum backaction noise, which in optical levitation appears as photon recoil heating from random momentum exchange with scattered photons. These two contributions are related by the Heisenberg uncertainty principle:

$$\sqrt{S_{xx}^{\mathrm{imp}}{S}_{FF}^{\mathrm{qba}}}={\displaystyle \frac{\hslash }{2\sqrt{\eta }}}\ge {\displaystyle \frac{\hslash }{2}},$$

(8)

where ℏ is the reduced Planck constant, $S_{xx}^{\mathrm{imp}}$ denotes the measurement imprecision noise, $S_{FF}^{\mathrm{qba}}$ represents the quantum backaction force noise, and $\eta ={\eta }_d{\eta }_e$ quantifies the total measurement efficiency, incorporating both detection efficiency ${\eta }_d$ and environmental coupling losses ${\eta }_e$.

In optical levitation systems, photon recoil constitutes the form of quantum backaction (for this reason, $S_{FF}^{\mathrm{qba}}$ will be replaced by $S_{FF}^{\mathrm{rec}}$ in the following discussions). While negligible for macroscopic objects, photon recoil becomes a dominant heating mechanism when its rate exceeds the thermal decoherence rate, typically under ultra-high vacuum (${10}^{-8}$ mbar). Assuming the polarization direction of the optical tweezer aligns with the x-axis, the recoil force in the dipole scattering regime is as follows [68]:

$${\overrightarrow{F}}_{rec}(\theta ,\varphi ,t)=\sqrt{s\left(\theta \right)}{\displaystyle \frac{P_{scatt}\left(t\right)}{c}}(cos\theta ,sin\theta cos\varphi ,sin\theta sin\varphi ),$$

(9)

where $s\left(\theta \right)={\displaystyle \frac{3}{8\pi }}sin\theta$ denotes the dipole scattering pattern, $P_{scatt}\left(t\right)$ is the instantaneous scattered power, and $(\theta$, $\varphi )$ are the polar and azimuthal angle, respectively. The contribution of recoil heating to the x-axis force power spectral density is given by the following:

$$S_{FF}^{\mathrm{rec}}\left(\omega \right)={\displaystyle \frac{P_{scatt}\hslash {\omega }_l}{5\pi c^2}},$$

(10)

where ${\omega }_l$ is the frequency of the trapping laser.

Consequently, the total measured displacement noise $S_{xx}\left(\omega \right)$ is given by the following [25]:

$$S_{xx}\left(\omega \right)=S_{xx}^{\mathrm{th}}+S_{xx}^{\mathrm{imp}}+S_{FF}^{\mathrm{rec}}{\left|{\chi }_{\mathrm{m}}\left(\omega \right)\right|}^2,$$

(11)

where ${\chi }_{\mathrm{m}}\left(\mathrm{\Omega }\right)={\left[m({\mathrm{\Omega }}^2-{\omega }^2-\mathrm{i}\gamma \omega )\right]}^{-1}$ is the mechanical susceptibility of the levitated particle.

3. Methods of Cooling

Due to the heating effects of different noise sources, cooling remains a central challenge in levitated optomechanics. Achieving a lower COM temperature can enhance the sensing accuracy of physical quantities such as force and acceleration in precision measurements. In quantum physics, cooling macroscopic particles to their motional quantum ground state is a crucial milestone for exploring macroscopic quantum mechanics. Currently, several research groups have successfully achieved the single-axis [23,24,25,26] and dual-axis [42] ground-state cooling of nanoparticles and are now progressing toward the simultaneous ground-state cooling of multiple degrees of freedom [51,69].

Two parameters can be used to describe the cooling effectiveness of particles: the COM temperature, which is calculated by fitting the PSD of the particle, and the phonon number, which can be obtained through sideband thermometry. This section will provide a detailed overview of various cooling techniques in optical trapping and levitation systems, along with an evaluation of the cooling performance of different approaches.

3.1. Active Feedback Cooling

The principle of active feedback cooling relies on converting the electrical signals obtained from particle motion detection into a negative feedback force applied to the particle, utilizing modulators such as acousto-optic modulators (AOMs) under the control of a feedback circuit. The efficiency of active feedback cooling depends critically on three factors: quantum-limited measurement precision, optimal control algorithms, and high detection efficiency [56]. Based on the type of feedback signal, active feedback cooling methods can be categorized into velocity feedback cooling and parametric feedback cooling.

3.1.1. Velocity Feedback Cooling

Velocity feedback cooling was first proposed by Ashkin in the 1970s [16,70]. However, it was not realized at the time due to limitations in displacement measurement precision. The first successful demonstration was achieved by Li [19], who used three orthogonal 532 nm laser beams to perform feedback cooling on a nanoparticle confined in a dual-beam optical trap. As illustrated in Figure 3a, the working principle is straightforward: the velocity of the particle is derived from its position signal via numerical differentiation, and a feedback force is applied in the opposite direction of its velocity using an AOM. This method effectively introduces a damping term ${\gamma }_{tot}={\gamma }_0+{\gamma }_{fb}$ into the equation of motion, a technique commonly referred as cold damping. Accordingly, Equation (6) can be modified as follows:

$$\ddot{x}\left(t\right)+({\gamma }_0+{\gamma }_{fb})\dot{x}\left(t\right)+{\mathrm{\Omega }}_x^{2}x\left(t\right)={\displaystyle \frac{F_{tot}}{m}},$$

(12)

where $F_{tot}$ is the total force acting on the particle.

In addition to optical forces, other types of feedback forces have also been explored. To address the limitations of optical cooling due to photon recoil heating, Millen et al. proposed using electrostatic forces to cool charged levitated particles by modulating the electric field around the particle via electrode plates or within a Paul trap. They theoretically demonstrated the feasibility of achieving ground-state cooling through purely electrical feedback [71]. This approach soon led to rapid experimental progress [21,72,73], culminating in the successful realization of ground-state cooling [25]. As shown in Figure 3c, a nanoparticle is optically levitated in cryogenic free space, with motion signals obtained through heterodyne and homodyne detection. The feedback signal is processed through a filter and transmitted directly to the electrode plates, generating Coulomb forces that damp the motion of the charged particle.

Additionally, velocity feedback through optical lattice modulation has also been experimentally demonstrated [26]. As shown in Figure 3b, a nanoparticle is trapped in an optical lattice with carrier frequency ${\omega }_0$, with sidebands at ${\omega }_0\pm {\omega }_a$. These sidebands create opposing optical gradient forces at the position of the particle. By dynamically modulating the relative amplitudes of the sidebands, an oscillating force can be applied to the neutral nanoparticle. This method was further extended to achieve simultaneous feedback cooling of all six degrees of freedom for near-spherical particles [69].

3.1.2. Parametric Feedback Cooling

Parametric feedback cooling was first applied to cool optically levitated particles in a single-beam trap [20]. Unlike velocity feedback cooling, this method achieves cooling by dynamically modulating the stiffness of the optical trap. A typical setup for parametric feedback cooling is illustrated in Figure 4. The displacement of the particle along three orthogonal axes is detected using a balanced photodetector and converted into electrical signals. These signals are then frequency-doubled, phase-shifted, and combined to form a feedback signal, which is fed into an electro-optic modulator (EOM). The EOM modulates the trapping laser intensity, effectively altering the trap stiffness and thereby cooling the particle. In this scheme, the particle experiences an optical force of the form: $F_{\mathrm{opt}}\left(t\right)=\Delta k_{\mathrm{trap}}\left(t\right)x\left(t\right)$. As a result, the Langevin equation can be rewritten as follows:

$$\ddot{x}\left(t\right)+{\gamma }_0\dot{x}\left(t\right)+\{1-Gsin\left[2({\mathrm{\Omega }}_{x}t+{\theta }_o)\right]\}{\mathrm{\Omega }}_x^{2}x\left(t\right)={\displaystyle \frac{F_{tot}}{m}},$$

(13)

where G is the modulation depth of the trap stiffness and ${\theta }_0$ is the phase offset, both of which define a time-varying potential well experienced by the particle.

To enhance cooling performance, researchers have explored two main approaches: improving detection efficiency [67,74] and optimizing control strategies [40,75]. Recent theoretical works have also proposed optimal quantum control schemes based on numerical simulations and analytical modeling, which aim to bring parametric feedback cooling closer to the ground-state regime [76,77].

Although parametric feedback cooling is widely employed in optical tweezer systems due to its simplicity and practical effectiveness, it is generally less efficient and more sensitive to experimental noise compared to velocity feedback cooling [78]. To date, ground-state cooling of levitated particles has not been achieved using parametric feedback alone. As such, it is often used as an initial stage before more advanced cooling methods are applied.

3.2. Passive Feedback Cooling

Passive feedback cooling, commonly referred as cavity cooling in levitated optomechanics, involves a configuration in which particles are cooled through an intrinsic optical feedback mechanism mediated by an optical cavity. In this process, no external control loop is required: cooling arises naturally from the interaction between the particle and the cavity field. The concept of cavity cooling was initially developed for atomic systems [44,45,79]. Traditional Doppler cooling requires atoms to have a two-level structure, which limits its applicability to atoms and molecules with more complex energy level configurations. In contrast, cavity cooling circumvents this limitation by utilizing photon–cavity interactions, enabling cooling for a broader range of systems, including complex molecules and mesoscopic particles.

Cavity cooling schemes are generally categorized into dispersive coupling and coherent scattering mechanisms. Among these, the coherent scattering approach has proven particularly effective at suppressing technical noise, such as laser intensity fluctuations. Recent experimental advancements employing this method have demonstrated ground-state cooling of an optically levitated nanoparticle in both single-axis and dual-axis configurations [23,42].

3.2.1. Dispersive Coupling Scheme

Based on the cavity cooling theories developed for atoms and solid-state mechanical oscillators [80,81,82,83,84,85], a dispersive coupling scheme for a single dielectric nanoparticle has been proposed [46,47,48,49].

As illustrated in Figure 5a, in this configuration, the drive mode $\omega$ is red-detuned from the cavity mode ${\omega }_{cav}$. The presence of the particle alters the length of the intra-cavity optical path, thereby shifting the resonance frequency ${\omega }_{cav}$ of the cavity and inducing dispersive optomechanical coupling.

From a dynamical perspective, cooling occurs in the resolved sideband regime ($\kappa <\mathrm{\Omega }$), due to the finite response time of the cavity field, particle motion induces a delayed change in intra-cavity power. This delay generates a velocity-dependent optical force that effectively acts as additional damping, known as optical damping. The efficiency of this cavity-induced cooling can be quantified by an effective damping rate:

$$\begin{array}{ccc}\hfill {\gamma }_0^{\mathrm{eff}}\left(\omega \right)& =& {\gamma }_0+{\displaystyle \frac{4G^2{\mathrm{\Omega }}_x\Delta \kappa }{\left({\left(\frac{\kappa }{2}\right)}^2+{(\omega +\Delta )}^2\right)\left({\left(\frac{\kappa }{2}\right)}^2+{(\omega -\Delta )}^2\right)}},\hfill \end{array}$$

(14)

where G is the dispersive coupling rate defined as $G=-{\displaystyle \frac{\partial {\omega }_c}{\partial x}}$ (with ${\omega }_c$ as the cavity resonance frequency and x as the position of the particle), $\Delta$ refers to the frequency detuning between the cavity mode ${\omega }_{cav}$ and the drive mode $\omega$, and $\kappa$ denotes the cavity decay rate.

The cooling effect is maximized when the detuning $\Delta$ is close to the mechanical frequency ${\mathrm{\Omega }}_x$, and the particle is positioned halfway between the node and the antinode of the cavity field, where the linear optomechanical coupling is strongest. At this location, the optical intensity gradient is largest, so small particle displacements most effectively modulate the intracavity field, enabling the most efficient energy exchange between mechanical motion and the optical field. As illustrated in Figure 5, to position the particle in this optimal location within the cavity mode, an additional external field is required to provide the necessary trapping potential, such as an optical tweezer [22], different cavity mode [47], or an electric field [48].

However, despite addressing the issue of particle escape during passive cooling [48], the cooling performance of the dispersive coupling scheme remains influenced by the co-trapping effect of the cavity drive field [23]. To achieve ground-state cooling, it is necessary to use more photons for cooling; however, the introduced larger phase noise can reversely limit the efficiency of the cooling process [86,87] as there is an inherent trade-off between high cooling efficiency and low phase noise in dispersive coupling systems.

3.2.2. Coherent Scattering Scheme

To overcome the limitations of the dispersive cavity cooling scheme, Delic et al. proposed the coherent scattering scheme [50]. As illustrated in Figure 6a, photons scattered by the nanoparticle into the cavity are coherent with the trapping light. These coherently scattered photons, which occupy the cavity, are red-detuned relative to the cavity resonance and can thus be used to cool the particle. In contrast, in the dispersive coupling scheme, the photons involved in cooling originate from a drive field incident along the cavity axis. To provide a physically intuitive picture, the cavity enhances the anti-Stokes scattering process, in which the scattered photons have higher energy than the incident photons. Due to energy conservation, this leads to a reduction in the kinetic energy of the particle, which is why efficient cooling requires $\kappa <\mathrm{\Omega }$: in this regime, anti-Stokes scattering is preferentially enhanced while Stokes scattering is suppressed. The dispersive coupling scheme can also be viewed through the lens of coherent scattering, where the interaction between the particle and the cavity mode is influenced by the scattering cross-section at the location of the particle. However, the cooling effciency is limited by the small scattering cross section due to the large beam waist of the cavity mode. In contrast, this limitation can be overcomed by the focused trapping light in the coherent scattering scheme.

Figure 6. Advances in cavity cooling of a levitated nanoparticle. (a) Coherent scattering-based cavity cooling configuration. (b) In a coherent scattering cavity cooling experiment, the phonon occupation number of the particle as a function of detuning. When the pressure is below ${10}^{-6}$ mbar and the red detuning is comparable to the mechanical frequency, motional ground state cooling of the particle can be achieved. (c) Schematic of a setup for ground state cooling along two axes. (d) Illustration of cavity cooling for all six degrees of freedom of an ellipsoidal particle. ((a,b) are reprinted from [23], Copyright 2020; (c) is reprinted from [42], Copyright 2023; (d) is reprinted from [51], Copyright 2023, with permission from Springer Nature.)

Figure 6. Advances in cavity cooling of a levitated nanoparticle. (a) Coherent scattering-based cavity cooling configuration. (b) In a coherent scattering cavity cooling experiment, the phonon occupation number of the particle as a function of detuning. When the pressure is below ${10}^{-6}$ mbar and the red detuning is comparable to the mechanical frequency, motional ground state cooling of the particle can be achieved. (c) Schematic of a setup for ground state cooling along two axes. (d) Illustration of cavity cooling for all six degrees of freedom of an ellipsoidal particle. ((a,b) are reprinted from [23], Copyright 2020; (c) is reprinted from [42], Copyright 2023; (d) is reprinted from [51], Copyright 2023, with permission from Springer Nature.)

As illustrated in Figure 6, cavity cooling through coherent scattering has recently seen rapid experimental progress. This technique facilitated the first realization of single-axis motional ground-state cooling of a nanoparticle (Figure 6a,b) [23]. Building on this, dual-axis ground-state cooling was achieved through polarization control of the trapping light (Figure 6c) [42]. Furthermore, it has been demonstrated that simultaneous cavity cooling of both translational and vibrational modes is feasible (Figure 6d) [51,69]. More recently, high-purity ground-state cooling of a vibrational mode of an anisotropic nanoparticle has also been realized [88]. Building on existing experimental advances, some theoretical studies have proposed that coherent scattering can also enable ground-state cooling of multiple particles [89].

While significant progress has been made with the cooling techniques discussed above, each method still faces fundamental limitations. For instance, parametric feedback cooling is hindered by enhanced backaction noise and frequency drifts of the trapped particle arising from trap potential instabilities, which, to date, have prevented the achievement of ground-state cooling [78]. Velocity feedback cooling has enabled ground-state cooling, but further reduction of the phonon occupations is constrained by measurement efficiency and quantum backaction noise [24,25]. In contrast, cavity cooling can, in principle, achieve even lower phonon occupations—as small as 0.04 with reduced laser phase noise [88]—although the required experimental setup is typically more complex.

4. Applications

A nanoparticle optically levitated in high vacuum exhibits a strong decoupling from the environment, offering a significant advantage compared to traditional mechanical resonators such as membranes and suspended mirrors. This isolation eliminates mechanical clamping noise, and when cooling is applied, the levitated particle demonstrate exceptionally high mechanical quality factors and force sensing capabilities at the zeptonewton (zN) level [20,90]. Remarkably, motional ground-state cooling can even be achieved at room temperature [23,42], marking a major milestone towards accessing the macroscopic quantum regime. Consequently, the cooled optically levitated particle holds immense potential for both precision sensing and fundamental physics research.

4.1. Precision Sensing

An optically levitated particle possesses translational and rotational degrees of freedom along all three spatial axes, making it an ideal candidate for sensing both force and torque. Experimental platforms based on cooled optically levitated particles have been developed to measure extremely weak forces [31], acceleration [40], and rotation or torque [91,92,93]. Owing to their ultra-high sensitivity and broad dynamic range, these systems hold the potential to surpass conventional commercial sensors in various precision measurement applications.

4.1.1. Force

From nanoscale atomic force microscopy to gravitational wave detection, ultrasensitive force sensing finds a wide range of applications. Force sensing with levitated nanoparticles exploits their exceptional mechanical isolation and tunability. Compared to conventional micro- and nano-mechanical resonators, cooled levitated particles offer ultra-low thermal noise and three-dimensional control, making them particularly well-suited for precision measurements. As a result, force sensing with optically levitated particle has currently achieved sensitivities at the attonewton(aN) level, and through averaging over extended measurement durations, a force response down to the zN regime can be attained [90]. Moreover, by employing ultraviolet (UV) discharge or electrode plate discharge, the charges carried by the particle can be controlled, enabling electric field force sensing [34,40,41]. Typically, forces are inferred by measuring the displacement of the trapped particle, which can be extracted from the PSD spectrum. In addition to dynamic force detection, high-precision static force measurements can be realized via free-fall experiments [39].

As shown in Figure 7, a 58 nm silica nanoparticle is levitated in an optical trap using a high-numerical-aperture (NA = 0.85) objective. The particle has a mass of approximately 2 femtogram (fg), corresponding to a gravitational force of about 20 aN. The COM motion of the particle is initially cooled via parametric feedback. After confinement, the optical trap is briefly turned off, allowing the particle to undergo free fall under gravity. After a delay of 100 μs, the trap is reactivated, and the particle re-enters the potential well with a significantly larger amplitude of motion. In this underdamped state, high-precision measurement of the particle displacement is possible, from which the gravitational force can be obtained. Using this method, a static force sensitivity of 10 aN was achieved.

The ultimate precision of force sensing is primarily limited by thermal noise, described by the following [37]:

$$F_{\min }=\sqrt{{\displaystyle \frac{4k_B{T}_{com}{\omega }_{0}mb}{Q}}},$$

(15)

where b is the measurement bandwidth, and Q is the mechanical quality factor. This relation shows that low-mass levitated particles offer a clear advantage in force sensitivity. Although levitated systems cannot match the ultimate sensitivity limits of atomic sensors, their larger mass makes them particularly suitable for probing poorly understood short-range interactions, such as Casimir and van der Waals forces [94], and for testing deviations from Newtonian gravity [95].

4.1.2. Acceleration

Acceleration sensing plays a vital role in inertial navigation. In acceleration sensing, the large mass and high mechanical quality factor of a cooled, levitated oscillator provide unique advantages. They enable measurements of weak accelerations at frequencies inaccessible to atomic interferometers or bulk mechanical sensors, offering a complementary platform for precision inertial sensing. Currently, such systems have achieved acceleration sensitivity at the ng level [40], comparable to that of atomic interferometers [96,97]. The thermal-noise-limited acceleration sensitivity can be derived by dividing the thermal force sensitivity by the particle mass m:

$$a_{\min }=\sqrt{{\displaystyle \frac{4k_B{T}_{com}{\omega }_{0}b}{Qm}}}$$

(16)

This relationship indicates that larger particle mass is advantageous for improving acceleration sensitivity. In recent years, significant progress has been made in enhancing the acceleration sensitivity of optical levitation systems [40,98]. For example, a system developed at Yale University demonstrated a record acceleration sensitivity of 0.4 μg$/\sqrt{\mathrm{Hz}}$ [99], reaching the ${10}^{-9}\mathrm{g}$ level after an integration time of $1.4\times {10}^4\mathrm{s}$.

A schematic of the experimental setup is shown in Figure 8. In this configuration, a low numerical aperture (NA = 0.03) lens is used to trap the microsphere vertically, thereby reducing the stiffness of the three-dimensional optical potential. Parametric feedback cooling is implemented using an AOM and a piezoelectric deflection mirror. Additionally, two green laser beams are employed to detect the motion of the particle along three orthogonal axes. Electrodes on either side of the particle generate alternating electric fields. As previously mentioned, techniques such as high-voltage discharge and ultraviolet photoemission enable precise control of net charge of the particle. This charge control, in conjunction with the application of a calibrated AC electric field, allows the measurement performance of the system to be characterized through the PSD spectrum of a single-charge microsphere.

4.1.3. Rotation and Torque

High-precision gyroscopes are essential for applications in aerospace and inertial navigation, and high-speed mechanical rotors provide an effective mean of measuring angular velocity. Levitated nanoparticles offer exceptional sensitivity to rotation and torque due to their small moment of inertia and isolation from environmental noise. These features enable the detection of extremely weak torques, beyond the reach of conventional torsional resonators. In optical levitation systems, circularly polarized trapping light can transfer angular momentum from photons to the particle, inducing rotation. Under high vacuum conditions, where damping is minimal, microspheres have been demonstrated to reach rotational frequencies in the GHz range [92,93,100]. Furthermore, researchers have observed active cooling effects arising from the coupling between translational and rotational motions, enabling cooling of the COM translational temperature to as low as 40 K [101].

Levitated nanodumbbells provide additional degrees of freedom, allowing for the simultaneous control of both rotational and torsional motion [100]. As shown in Figure 9, when trapped by linearly polarized light, the nanodumbbell experiences a restoring optical torque, which restricts its free rotation. Conversely, circularly polarized light induces stable, high-speed rotation about the optical axis. Using this configuration, a maximum rotation frequency of 1 GHz was achieved, and the corresponding theoretical torque detection limit was analyzed. The minimum detectable torque limited by thermal noise is given by the following:

$$M_{\min }=\sqrt{4k_B{T}_{com}{I}_z{\gamma }_{\theta }/\Delta t}$$

(17)

where $I_z$ is the moment of inertia about the z-axis, ${\gamma }_{\theta }$ is the rotational damping rate, and $\Delta t$ is the measurement time. Under ultra-high vacuum (${10}^{-8}$ torr), the predicted torque sensitivities for 170 nm and 50 nm nanodumbbells are ${10}^{-27}$$\mathrm{N}·\mathrm{m}/\sqrt{\mathrm{Hz}}$ and ${10}^{-29}$$\mathrm{N}·\mathrm{m}/\sqrt{\mathrm{Hz}}$, respectively, surpassing those of state-of-the-art nanoscale torque sensors [102]. This theoretical prediction has been validated experimentally [93]. By employing a 1550 nm circularly polarized laser, the researchers achieved a rotational speed of 5.2 $\mathrm{GHz}$, and applied an additional torque using a 1020 nm circularly polarized beam. A torque sensitivity of $(4.2\pm 1.2)\times {10}^{-27}$$\mathrm{N}·\mathrm{m}/\sqrt{\mathrm{Hz}}$ was experimentally measured. This exceptional sensitivity opens new avenues for investigating phenomena such as vacuum friction and nanoscale magnetism.

Recently, cavity cooling technology has enabled cooling of all three translational and three rotational degrees of freedom, with rotational degrees cooled to the millikelvin range. The orientation of ellipsoidal nanoparticles can be nearly fixed, facilitating characterization through diffraction methods [51,69].

4.2. Fundamental Physics

With the aid of advanced cooling techniques, levitated optomechanical systems have entered the quantum regime, offering a promising platform for fundamental physics research. Specifically, on this platform, it is anticipated that macro-scale quantum superposition and entanglement states can be realized [27,103] and near-field matter wave interference can be observed [95], and we explore whether gravity can be quantized [104]. Moreover, the ultra-high sensing capabilities enable the exploration of new physics, such as the search for dark matter [34,105] and the detection of high-frequency gravitational waves [33,106].

4.2.1. New Physics

Dark matter (DM) is a hypothetical form of matter invoked to explain various astrophysical and cosmological observations, including the anomalous rotation curves of galaxies, gravitational lensing effects, and imprints on the cosmic microwave background (CMB). Despite overwhelming indirect evidence, the extremely weak interaction of dark matter with ordinary matter has thus far precluded direct detection, rendering its identification one of the most profound challenges in contemporary physics [35]. Among the proposed candidates are millicharged and low-mass particles, which may impart tiny momentum kicks to matter. Levitated nanoparticles are particularly promising for dark matter searches due to their relatively high mass, combined with extreme force sensitivity, which allows them to probe parameter regimes inaccessible to atomic or solid-state detectors. Building on this advantage, their extreme mechanical sensitivity enables the detection of ultraweak collisions through minute displacement measurements, providing a viable platform for direct dark matter detection (Figure 10a).

In addition to dark matter searches, optically levitated systems are well suited for probing dark energy. Several theoretical models posit that new scalar fields responsible for dark energy may mediate short-range forces stronger than Newtonian gravity, particularly below characteristic length scales of approximately 80 μm [105]. As shown in Figure 10c, the zN-level force sensitivity attainable with optical levitation enables precise measurements that can test such screened interactions [32,107,108].

The landmark detection of gravitational waves by LIGO has generated broad interest in extending the observable frequency range of gravitational wave detectors [109]. Levitated optomechanical systems offer a promising alternative for probing gravitational waves in the kHz to MHz regime, where traditional interferometers face sensitivity limitations. As shown in Figure 10b, one proposed approach involves levitating a multi-layer dielectric disk within a cavity-enhanced two-arm interferometric configuration [33,106]. Numerical simulations indicate that such systems could detect high-frequency gravitational waves originating from exotic astrophysical events, including axion-induced emissions around rotating black holes and mergers of sub-solar-mass primordial black holes within our galaxy.

4.2.2. Macroscopic Quantum Physics

Testing the validity of quantum mechanics at macroscopic scales remains a central question in modern physics, with quantum superposition and entanglement being among its most counterintuitive and foundational concepts. Realizing matter-wave interference with macroscopic particles represents a natural and promising approach for probing the limits of the quantum superposition principle. Such interference has been demonstrated for a range of systems, including electrons, neutrons, atoms, and even complex molecules [110]. However, extending these results to more massive objects is technically challenging due to rapid decoherence induced by environmental interactions. Optically levitated micro- and nanoparticles offer a compelling platform for advancing such investigations. Numerous proposals have been put forward to realize matter-wave interference with levitated optomechanical systems [95], and a critical technology—ground-state cooling of COM motion—has now been demonstrated in multiple experimental setups, which will accelerate the progress of macroscopic quantum state preparation. As shown in Figure 11a, a recent study employed an electro-optical hybrid trap to expand the standard deviation of the thermal motion of a nanoparticle by a factor of 24. The authors suggest that under ultra-high vacuum and ground-state cooling conditions, a wavefunction expansion on the order of 250 pm could be achieved [29].

Furthermore, levitated optomechanical systems also offer a unique testbed for investigating the quantum nature of gravity. Unlike the other fundamental forces, which have well-established quantum descriptions, gravity remains classically described within the framework of general relativity, hindering unification with quantum mechanics. Feynman proposed that placing a massive particle in a spatial superposition could reveal the quantum character of gravity through its gravitational interaction with a second mass, yielding predictions that differ depending on whether gravity is classical or quantum. Building upon this idea, several theoretical proposals have emerged to test gravity-induced entanglement using levitated particles [27,28,111]. In one such scheme, depicted in Figure 11b, a test particle in a macroscopic quantum superposition state in a double potential well is connected to a two-level auxiliary qubit through a massive resonator. By measuring the auxiliary qubit, one could determine whether gravity possesses quantum characteristics [27]. Alternative proposals have explored the use of spin systems subjected to magnetic field gradients to map spin states into spatial quantum superpositions, thus offering new avenues for generating macroscopic spatially separated quantum states [28].

Figure 11c shows the conceptual design of the European MAQRO mission, which aims to test quantum superposition at macroscopic scales by preparing and observing levitated dielectric particles in space. Leveraging the unique conditions of microgravity, ultra-high vacuum, and cryogenic temperatures, MAQRO is designed to suppress environmental decoherence beyond terrestrial limits, enabling long-duration free-fall and high-fidelity matter-wave interference of massive objects. The mission combines advanced techniques in quantum optomechanics, optical trapping, and matter-wave interferometry to explore the foundations of quantum mechanics in a previously inaccessible regime.

5. Outlook

Cooling technology lies at the heart of levitated optomechanical systems in vacuum, which unlocks a broad spectrum of applications, ranging from ultrasensitive force and torque sensing to the preparation of macroscopic quantum states. These capabilities position optical tweezers as a powerful platform for both precision metrology and fundamental physics investigations. Despite recent advances, several key challenges remain. These include achieving ground-state cooling of multiple degrees of freedom and multiple particles simultaneously, scaling down and integrating the sensing systems for practical deployment, and pushing the boundaries of macroscopic quantum experiments. Furthermore, realizing the full potential of levitated systems in probing dark matter, dark energy, and high-frequency gravitational waves will require further technical innovation and theoretical development. Continued progress in these areas will not only enhance the versatility of levitated optomechanical platforms but also open new frontiers in quantum science and fundamental physics.