Laser cooling of ytterbium-erbium Co-doped nanoparticle with optical tweezers in vacuum

Abstract

A strongly focused laser beam with high power density employed in optical tweezers typically results in photothermal damage and instability to the trapped nanoparticles or bio-targets. Here, we report an effective laser cooling of trapped Yb³⁺-Er³⁺ co-doped rare-earth nanoparticle by employing a new cooling channel provided by Er³⁺ and utilizing an enhancement of the anti-Stokes emission through energy transfer between Yb³⁺ and Er³⁺. Especially in high temperature conditions, the co-doped system demonstrates a high laser cooling performance, that enable the temperature to decrease from 500 K to around room temperature. But for the initial temperature of around room temperature, the cooling temperature does not drop below freezing, which can avoid not only thermal but also cold damage to bio-targets in optical tweezers. This work provides experimental evidence of the Yb³⁺-Er³⁺ co-doping rare-earth nanoparticle for laser cooling, which can hold a potential to address the challenge of precise measurements in optical tweezers.

Introduction

Optical tweezers enable noninvasive trapping and manipulation of nanoparticles or biological cells, making them indispensable tools in quantum science¹, nanophotonics², physics^3,4, and biological science⁵. However, the focused laser beam used for trapping and manipulating in optical tweezers generates local heating, resulting in instability and photothermal damage to the trapped nanoparticles^6,7,8. In-situ effective cooling of a trapped nanoparticle reduces its center-of-mass motion and suppresses photothermal damage, thereby addressing the critical issues of thermal instability and optical damage in optical tweezer applications. Laser cooling in solid-state materials, known as anti-Stokes luminescence cooling, is a physical process that effectively lowers temperature by converting low-energy incident photons into higher-energy emitted photons, thereby extracting energy from the host lattice^9,10,11,12. Due to its non-contact, high reliability, and ability to minimize vibrations, laser cooling in solid-state materials has been widely employed to achieve low temperatures^13,14. Traditionally, single trivalent rare-earth ions, such as trivalent ytterbium^15,16,17 thulium^18,19 or erbium ions^{18,19,20,21,22,23} are doped into high-purity materials like glasses or crystals to achieve laser cooling in solid-state systems. Particularly, it has been theoretically proven that the second and higher excited states of Er³⁺ ions can be harnessed for efficient anti-Stokes emission, thereby constituting an effective cooling center²⁰. Commonly, the cooling efficiency is hindered by non-radiative transitions and background absorption^24,25,26. The theoretical study indicated that co-doped systems can enhance cooling performance through energy transfer processes between ion pairs with similar electronic energy level structures, such as holmium and thulium²⁷. The process achieves enhanced cooling performance through the introduction of multiple radiative cooling channels and the enhancement of anti-Stokes emission. While co-doping is a promising method for enhancing cooling performance, the multi-energy level structure will lead to unwanted energy transfer upconversion processes, which may negatively impact the desired cooling effect. Thus, selecting the suitable rare earth ions and their doping properties are essential to maintain a balance between the Stokes and anti-Stokes emission for cooling. Besides, while effectively cooling down, it is also necessary to prevent the temperature from dropping below freezing to avoid thermal or cold damage to optical tweezers.

In this work, we experimentally achieved laser cooling of Yb³⁺-Er³⁺ co-doped nanoparticle in optical tweezers in vacuum. Compared with singly doped nanoparticles, the Yb³⁺-Er³⁺ co-doped system facilitates efficient energy transfer from Yb³⁺ to higher energy levels of Er³⁺, which enhances anti-Stokes emission and provides multiple cooling channels, thereby significantly improving the cooling performance. Moreover, the cooling performance is strongly dependent not only on the doping concentration of Er³⁺ but also on the initial temperature of the nanoparticle. Owning to a high cooling performance obtained with a high initial temperature, the temperature of Yb³⁺-Er³⁺ co-doped nanoparticle can decrease from 500 K to around room temperature, but the cooling temperature does not drop below freezing when the initial temperature is around room temperature. Thus, the temperature of optical trapping nanoparticles can be held around room temperature, which can prevent both thermal and cold damage to bio-targets in the applications of optical tweezers.

Results

Principle of laser cooling co-doped nanoparticle

The laser trapping and cooling of Yb³⁺, Er³⁺ NaYF₄ co-doped nanoparticle is carried out using optical tweezers in vacuum. The β-phase NaYF₄ nanoparticles used in experiment are co-doped with 10% Yb³⁺ and X% Er³⁺ (X = 0, 0.05, 2 and 5) and have mean size of 76 nm (see Supplementary Fig. 1 in Supplementary Information). The diagram illustrates the laser trapping and cooling of a levitated Yb³⁺-Er³⁺ co-doped nanoparticle (represented by the blue sphere) within a vacuum chamber. The cooling process, mediated by anti-Stokes fluorescence, is indicated by the blue curve emanating from the nanoparticle, as shown in Fig. 1a. A laser beam at λ_t = 1030 nm (Max-Ray Photonics, 81 mW) is tightly focused through an objective with a numerical aperture of NA = 0.95 (Nikon) to form an optical dipole trap (depicted as the red optical potential in the schematic), which is used to trap a single nanoparticle. In contrast to typical cooling wavelengths around 1020 nm, we employ a 1064 nm laser (Laser Quantum, OPUS, λ_c = 1064 nm, red curve in the schematic) for nanoparticle cooling. Both theoretical models and experimental studies have proven that 1064 nm radiation can be utilized to achieve laser cooling. Furthermore, in specific systems, particularly with optimized dopant concentrations, laser cooling at 1064 nm has been demonstrated to outperform the conventional ~1020 nm approach in terms of cooling efficiency^16,25,28. A schematic of the experimental setup used for optical levitation and cooling of a nanoparticle in vacuum is shown in Supplementary Fig. 2. The anti-Stokes cooling cycle involves pump excitation (solid upward arrow in Fig. 1b), followed by thermalization (dashed upward arrow) and spontaneous decay (solid downward arrow), yielding cooling²⁴. The energy level structure of Yb³⁺ includes the ²F_7/2 ground state and the ²F_5/2 excited state, both of which are split into several sublevels whose degeneracy is broken by the crystal field within the NaYF₄ crystal. The 1064 nm laser excites the Yb³⁺ dopant ensemble from the top sublevel of the ground state to the bottom sublevel of the excited state. The excitations rapidly thermalize to higher sublevels within the excited state by absorbing energy from lattice vibrations (phonons). Consequently, the thermally populated higher sublevels relax via spontaneous emission, leading to the emission of photons at wavelengths blue-shifted relative to the 1064 nm pump laser (anti-Stokes fluorescence). In the Yb³⁺-doped system, cooling cycle typically occurs between the ²F_5/2 and ²F_7/2 levels. Due to the matched energy levels between Yb³⁺ and Er³⁺, energy undergoes efficient transfer between the two ions in a co-doped system, as indicated by the double-headed arrow in Fig. 1b. The energy absorbed by Yb³⁺ ions can transfer directly from the ²F_5/2 level to the ⁴I_9/2 level (curved arrow), or to the ⁴I_11/2 level of Er³⁺, which subsequently populates to the ⁴I_9/2 level for spontaneous emission. In any case, an additional anti-Stokes cooling cycle occurs between the ⁴I_9/2 and ⁴I_15/2 levels, resulting in enhanced cooling efficiency in the Er³⁺, Yb³⁺ co-doped system.

Fig. 1: Schematic of laser cooling co-doped nanoparticle with optical tweezers in vacuum.

a Illustration of a levitated Yb³⁺, Er³⁺ NaYF₄: nanoparticle trapped in an optical trap, emitting anti-Stokes fluorescence to achieve laser cooling. The 1030 nm laser is used for trapping, and the 1064 nm laser is used for cooling. b Energy levels of Yb³⁺-Er³⁺ co-doped system for laser cooling.

Cooling efficiency is defined as the ratio of the cooling power to absorbed power ${\eta }_{c}=\frac{{P}_{{{\rm{cool}}}}}{{P}_{{{\rm{abs}}}}}$, and is given by

$${{{\eta }}}_{{{\rm{c}}}}={{{\eta }}}_{{{\rm{ext}}}}{{{\eta }}}_{{{\rm{abs}}}}\left(\lambda ,T\right)\frac{\lambda }{{\lambda }_{{{\rm{f}}}}}-1$$

(1)

where ${{\eta }}_{{ext}}$ represents the external quantum efficiency, ${{\eta }}_{{{\rm{abs}}}}$ is absorption efficiency, and λ and ${\lambda }_{{{\rm{f}}}}$ are the pump and mean luminescence wavelength, respectively. Since the mean luminescence wavelength of the ⁴I_9/2-⁴I_15/2 transition of Er³⁺ is shorter than that of the ²F_5/2-²F_7/2 transition of Yb³⁺, the ⁴I_9/2-⁴I_15/2 transition is more conducive to laser cooling. Moreover, according to the fundamental formula of laser cooling efficiency, the use of 1064 nm excitation offers a longer wavelength ($\lambda$). This directly translates to a higher energy difference per photon extracted during the anti-Stokes fluorescence cycle, thereby theoretically enhancing the cooling efficiency.

To identify which anti-Stokes emission of Er³⁺ contributes to laser cooling in the co-doped system, the normalized luminescence spectra of Yb³⁺-doped and Yb³⁺, Er³⁺ co-doped nanoparticles were measured, as shown in Fig. 2a. The corresponding spectral data are provided in Supplementary Data. The normalized luminescence spectrum of the Yb³⁺-Er³⁺ co-doped nanoparticle coincides with that of the Yb³⁺-doped nanoparticle in the emission range of 950–1000 nm, as shown in Fig. 2a. This observation shows that the radiative transition from the ⁴I_11/2 and ⁴I_15/2 energy levels occurs with low probability in the co-doped system. However, anti-Stokes luminescence with a shorter wavelength was observed from the transition between the ⁴I_9/2 and ⁴I_15/2 energy levels of Er³⁺, as shown in Fig. 2a. The anti-Stokes luminescence from the ⁴I_9/2 to the ⁴I_15/2 transitions provides a greater advantage in laser cooling progress in co-doped nanoparticles²⁰. Furthermore, a comparison of the normalized spectra between Yb³⁺-doped nanoparticles and Yb³⁺/Er³⁺ co-doped particles show the presence of two distinct anti-Stokes emission channels in the co-doped system. The laser cooling power ${P}_{{{\rm{cool}}}}$ is described in crystal by the equations²⁸ ${P}_{{{\rm{cool}}}}={P}_{{{\rm{pump}}}}\left[1-\exp \left(-\alpha l\right)\right]{\eta }_{{{\rm{c}}}}$, where ${P}_{{{\rm{pump}}}}$ is the laser power, $l$ the sample length and the $\alpha$ is absorption coefficient. Similarly, in co-doped nanoparticle systems, the cooling power can be enhanced by increasing the pump power employed for laser cooling. As the power of 1064 nm increases, the integrated anti-Stokes luminescence intensity of the transition between the ⁴I_9/2 and ⁴I_15/2 levels increase, as shown in Fig. 2b.

Fig. 2: Anti-Stokes luminescence of co-doped nanoparticles.

a The normalized luminescence spectra of Yb³⁺-doped (orange curve) and Yb³⁺, Er³⁺ co-doped nanoparticles (blue curve), respectively. b Dependence of the calculated integrated intensity of the ⁴I_9/2-⁴I_15/2 transition on power of 1064 nm laser.

Cooling performance of co-doped nanoparticles

Temperature acquisition via spectral analysis, as a non-invasive thermometry technique, has been widely adopted in laser cooling experiments^16,17. The temperature of the levitated nanoparticle is obtained from the luminescence spectra by using the luminescence intensity ratio (LIR) method. The populations of the thermally coupled ²H_11/2 and ⁴S_3/2 energy levels of Er³⁺ rapidly reach a Boltzmann distribution due to efficient thermalization between the levels. This equilibrium is illustrated in Supplementary Fig. 3 and detailed in the Methods section. The emission regions of 515–535 nm and 535–545 nm correspond to the transitions from ²H_11/2 and ⁴S_3/2 to the ground state ⁴I_15/2, respectively. Area 1 (515–535 nm) and area 2 (535–545 nm) are the bands of intensity integration used for the temperature calculation. To ensure accurate temperature calculations, the emission peak at 557 nm was excluded, as it originates from the ²H_2/9 level to ⁴I_13/2 transition. Furthermore, this transition constitutes a three-photon process, which means that its nonlinear dependence on excitation power would introduce significant complexity and potential error into the temperature calculations²⁹. It is observed that the integrated intensity of area 1 is significantly weaker after the introduction of the 1064 nm cooling laser, indicating fewer populations in the higher energy (²H_11/2) due to the decrease in temperature of the nanoparticle, as shown in Fig. 3a. The temperature of the nanoparticle is 393.4 K with the trapping laser and decreases to 348.1 K after the introduction of 1064 nm. In addition, the luminescence spectrum of Yb³⁺ can also be used to calculate the temperature¹⁷, as shown in the inset in Fig. 3a. By normalizing the 970 nm emission, it is observed that there is less luminescence intensity from the higher energy levels (green region) and more luminescence intensity from lower energy levels (purple region) when the 1064 nm laser is introduced, which also indicates the cooling effects induced by the 1064 nm laser. Furthermore, a cross-verification was carried out by employing Yb³⁺ ions as a thermometric probe to validate the measurements based on Er³⁺. The results demonstrate excellent agreement between the temperatures determined by the two ions, as shown in Supplementary Fig. 4.

Fig. 3: Laser cooling of Yb³⁺/Er³⁺co-doped nanoparticles.

a The normalized luminescence spectra of Er³⁺ with the inset showing the normalized spectra of Yb³⁺, measured with (blue curves) and without (orange curves) the 1064 nm cooling laser. b Temperatures of the levitated nanoparticle under different pressures, measured without (orange dots) and with (blue dots) 1064 nm laser excitation. c Power-dependent laser cooling at different initial temperatures of 298 K (orange data), 334 K (purple data), and 502 K (blue data), respectively. The error bars in the figures represent the standard deviation of repeated spectral measurements.

The temperature (T_in) of levitated nanoparticle depends on thermalization with surrounding gas (${\dot{q}}_{{{\rm{h}}}/{{\rm{c}}}}^{{{\rm{gas}}}}$), laser heating $({\dot{q}}_{h}^{{{\rm{laser}}}}=(\alpha (T)+{\alpha }_{{{\rm{b}}}})I)$ and cooling through anti-Stokes emission (${\dot{q}}_{{{\rm{cool}}}}^{{{\rm{lum}}}}=-{\eta }_{{{\rm{e}}}}\frac{{\omega }_{{{\rm{f}}}}}{{\omega }_{{{\rm{p}}}}}\alpha (T)I$). The ${\alpha }_{{{\rm{b}}}}$ is background absorption coefficient, and $\alpha (T)$ is the temperature-dependent absorption coefficient of the rare-earth ion, which can be given by $\alpha (T)=\frac{{\sigma }_{12}{N}_{t}}{1+\exp \left[{{\hslash }}\Delta /{k}_{B}T\right]}\frac{1}{1+I/{I}_{s}}$, where ${\sigma }_{12}$ is the atomic absorption cross section, ${N}_{t}$ is the doping concentration, and ${I}_{s}$ is the saturation intensity³⁰. The heat equation of the system is simply given by the following equation³¹

$$m{c}_{{{\rm{v}}}}\frac{d{T}_{{\mathrm{int}}}}{{dt}}={\dot{q}}_{{{\rm{h}}}/{{\rm{c}}}}^{{{\rm{gas}}}}+{\dot{q}}_{{{\rm{h}}}}^{{{\rm{laser}}}}+{\dot{q}}_{{{\rm{c}}}}^{{{\rm{lum}}}}$$

(2)

At ambient pressure, the mean free path (${\lambda }_{{{\rm{MFP}}}}$) of gas molecules is about 68 nm, and the thermalization rate with the surrounding gas in this regime (${Kn}\le 10{{\rm{with}}}{Kn}\approx 1$) can be described by the following equation³²

$${\dot{q}}_{{{\rm{heat}}}/{{\rm{cool}}}}^{{{\rm{gas}}}}=\frac{8\pi {r}^{2}{k}_{g}({T}_{{{\rm{gas}}}})}{2r+{\lambda }_{{{\rm{MFP}}}}G}({T}_{{\mathrm{int}}}-{T}_{{{\rm{gas}}}})$$

(3)

The factor G = $(18{\gamma }_{{{\rm{sh}}}}-10)/{\alpha }_{{{\rm{g}}}}({\gamma }_{{{\rm{sh}}}}+1),$ where ${\alpha }_{{{\rm{g}}}}$ is the thermal accommodation coefficient, ${k}_{{{\rm{g}}}}$ is thermal conductivity (heat conduction coefficient) of gas and $r$ is the radius of the nanoparticle, and ${\gamma }_{{sh}}$ = 7/5 is the specific heat ratio of gas.

When the pressures below 100 mbar (${Kn}\ge 10$), the model is expressed by

$${\dot{q}}_{{{\rm{heat}}}/{{\rm{cool}}}}^{{{\rm{gas}}}}=\frac{{\alpha }_{{{\rm{g}}}}}{2}\pi {r}^{2}\bar{v}\frac{{\gamma }_{{sh}}+1}{{\gamma }_{{sh}}-1}\left(\frac{{T}_{i{{\rm{nt}}}}}{{T}_{{{\rm{gas}}}}}-1\right){P}_{{{\rm{gas}}}}$$

(4)

$\bar{v}$ is the mean thermal speed of air molecules.

Given that thermal conduction to the surrounding gas is one key factor determining the temperature of a levitated nanoparticle, we explore the cooling performance at different gas pressures, as shown in Fig. 3b. The power of the 1064 nm laser is 40 mW. The results show a steady decrease in nanoparticle temperature when the 1064 nm cooling laser was introduced, and a higher cooling effect can be achieved at lower pressures (higher temperatures). Although the temperature of the nanoparticle rises with decreasing gas pressure due to the lack of thermal conduction between the nanoparticle and the gas molecules, as well as continuous heating by the trapping laser, the 1064 nm cooling laser significantly reduces the rate at which the temperature rises between 100 mbar and 7 mbar. At ambient pressure (1000 mbar), no cooling effect is observed because the internal temperature of the levitated nanoparticle is primarily determined by laser absorption energy and thermalization through gas collisions. Under the condition, the presence of gas molecules prevents cooling below ambient temperature. As the pressure decreases, convective effects become less significant, making the cooling process mainly governed by the competition between laser absorption and anti-Stokes emissions.

To investigate the power dependence of the cooling performance, we measured its variation with 1064 nm laser power across initial temperatures of 298 K, 334 K, and 502 K, as shown in Fig. 3c. At an initial temperature of 298 K, no cooling effect is observed at any 1064 nm power. A significant cooling effect can be seen when the temperature is higher than the room temperature. The temperature drops by about 10 K at the initial temperature of 334 K and by up to 120 K at the initial temperature of 502 K, reaching approximately room temperature. The cooling performance increases and then decreases as the power rises, reaching its optimum value at 40 mW. Cooling performance is initially improved due to the increased population in the ⁴I_9/2 energy level, resulting in increased anti-Stokes luminescence intensity as power increases. However, two primary factors limit the cooling efficiency, on the one hand, the presence of non-radiative transitions in the rare earth ion, and on the other hand, the presence of impurities in the host matrix that induce parasitic absorption and heat generation²⁰. The absorption efficiency related to background absorption can be expressed as ${\eta }_{{{\rm{abs}}}}=\frac{{{\rm{\alpha }}}({{\rm{I}}})}{{{\rm{\alpha }}}({{\rm{I}}})+{\alpha }_{{{\rm{b}}}}}={\left[1+\frac{{\alpha }_{{{\rm{b}}}}(1+I/{I}_{{{\rm{s}}}})}{{\alpha }_{0}}\right]}^{-1}$¹³. The background absorption coefficient can be ignored if the I«I_s, because the absorption cross section of the background absorption is smaller compared to that of Yb³⁺. The increase in I enhances the factor related to ${\alpha }_{{{\rm{b}}}}$, which has a negative effect on the cooling performance. As multiphoton processes are more sensitive to power increases, higher power induces additional energy level transitions which have a negative impact on cooling performance^29,33. The cooling performance is hampered when the heating rate exceeds the cooling rate, primarily due to high pump powers inducing additional energy level transitions and enhancing background absorption.

The dependence of cooling performance on Er³⁺ concentration

Due to the competition between Stokes and anti-Stokes emission of Er³⁺, the cooling performance should be closely related to the doping concentration. As shown in Fig. 4, nanoparticles doped with 10% Yb³⁺ and X% Er³⁺ (X = 0, 0.05, 2 and 5) demonstrate distinct laser cooling performances. All nanoparticles co-doped with Yb³⁺ and Er³⁺ exhibit cooling capabilities, even at an Er³⁺ concentration of 0.05%, as indicated by the purple data. The 2% Er³⁺ doping level shows the optimal cooling performance, as depicted by the blue data. Higher dopant concentration shows the lower cooling performance, due to the increased probability of cross-relaxation processes, where a part of energy is dissipated as heat rather than emitted as photons^27,34,35. This leads to reduced cooling performance for nanoparticles doped with 5% Er³⁺, as shown by green data. To further investigate the doping dependence, Supplementary Fig. 5 provides cooling data covering an extended series of Er³⁺ concentrations. Furthermore, we measured the time-resolved spectra of 10% Yb³⁺ and X% Er³⁺ (X = 1, 2, 5) co-doped nanoparticles, as shown in Supplementary Fig. 6. The results indicate that the sample with 2% Er³⁺ exhibits a shorter lifetime, suggesting the highest radiative rate at this concentration, which is consistent with the optimal cooling performance observed experimentally. The 1% Er³⁺ sample exhibits the longest lifetime, indicating inefficient energy transfer due to an insufficient number of acceptors, which limits the cooling power. The 5% Er³⁺ sample also exhibits a long lifetime but the minimal cooling efficiency, as a result of concentration quenching. In this process, excessive Er³⁺ ions promote cross-relaxation, converting excitation energy into heat. Notably, nanoparticles single doping (without Er³⁺ doping) did not exhibit cooling performance under any initial temperature or power conditions, as demonstrated by the orange data and the inset. Compared to Yb³⁺-Er³⁺ co-doped nanoparticles, those doped solely with Yb³⁺ possess a single cooling cycle and reduced anti-Stokes luminescence, resulting in an efficiency of heating from non-radiative processes that exceeds the cooling efficiency. The differences in cooling performance between co-doped and single-doped nanoparticles further demonstrate the high cooling performance of co-doped nanoparticles.

Fig. 4: Different cooling effect between Yb³⁺-Er³⁺ co-doped and Yb³⁺ doped nanoparticles.

Initial temperature-dependent evolution of laser cooling performances in nanoparticles doped with 10% Yb³⁺ and X% Er³⁺ (X = 0, 0.05, 2 and 5). The inset shows the power-dependent laser cooling performance of nanoparticles without Er³⁺ doping at initial temperature of 359 K. The error bars in the inset represent the standard deviation of repeated spectral measurements.

Conclusion

High effective cooling performance can be achieved in Yb³⁺-Er³⁺ co-doped nanoparticle through the additional cooling channel and enhanced anti-Stokes fluorescence by introduced Er³⁺. The cooling performance is found to be strongly dependent on the initial temperature of the nanoparticle and the doping concentration of Er³⁺. The best cooling effect can be obtained by using a doping concentration of 2% of Er³⁺, which results in a cooling of more than 120 K. The cooling performance is more significant at high initial temperature, which enables the temperature to decrease from 500 K to around room temperature, but the cooling temperature does not drop below freezing when the initial temperature is around room temperature. In other words, this cooling design allows nanoparticles, especially biological targets, to remain around room temperature in optical tweezers, which can avoid both thermal and cold damage to bio-targets in optical trapping applications. This approach aims to enable the trapped nanomaterials and biomolecules to remain at room temperature to improve the accuracy of precise measurements, which can bring new possibilities in the laser trapping for essential applications in nanotechnology and life science.

Methods

Synthesis of Yb³⁺-Er³⁺ co-doped nanoparticles

Ytterbium (III) chloride hexahydrate (YbCl₃·6H₂O), Yttrium chloride hexahydrate (YCl₃·6H₂O, Aladdin), Erbium chloride hexahydrate (ErCl₃·6H₂O), Gadolinium chloride hexahydrate (GdCl₃·6H₂O) and Oleic acid (CH₃(CH₂)₇CH = CH(CH₂)₇COOH) were purchased from Sigma-Aldrich. Sodium hydroxide (NaOH) and Ammonium fluoride (NH₄F) were purchased from Sinopharm Chemical Reagent Co., Ltd. All chemicals were used without further purification.

For 2% Er³⁺ sample, a total of 0.3 g NaOH dissolved in 1.5 mL of DI water. The solution was then stirred with a mixture of 5 mL ethanol and 5 mL oleic acid. Then 2 ml of RECl₃ (0.2 M, RE = Y, Yb, Er, Gd) and 1 ml of NH₄F (2 M) were added to the mixture. The solution was then transferred into a 20 mL Teflon-lined autoclave and heated at 200 °C for 2 h. After cooling to room temperature, the precipitates were collected by centrifugation at 8000 rpm for 15 minutes and washed three times with ethanol and deionized water. The collected powders were dispersed in ethanol for subsequent nanoparticle trapping.

Sample trapped

The sample was diluted. The nanoparticles were introduced into the vacuum chamber via atomization and subsequently trapped by the laser.

Method of temperature measurement

The thermally coupled ²H_11/2 and ⁴S_3/2 energy levels of Er³⁺ is most widely employed in luminescence intensity ratio (LIR) thermometry. The LIR follows a Boltzmann distribution, as described by the equation^36,37. This equilibrium is established via ultrafast thermalization (fs–ps), a process orders of magnitude faster than spontaneous emission^38,39.

$${LIR}=\frac{{I}_{520}}{{I}_{540}}=\frac{{g}_{2}{A}_{2}{h\upsilon }_{2}}{{g}_{1}{A}_{1}{h\upsilon }_{1}}* \exp \left(-\frac{\Delta E}{{k}_{b}T}\right)=B* \exp \left(-\frac{\Delta E}{{{{\rm{k}}}}_{{{\rm{b}}}}T}\right)$$

(5)

g, A, $\upsilon$ denote the degeneracy, the spontaneous emission rate, and the frequency of the respective energy levels, and $h$ and k_b denote Planck’s constant and Boltzmann’s constant, respectively. ΔE is the energy difference between the ²H_11/2 and ⁴S_3/2 energy levels.

The constants $B$ and $\Delta E$ are calibrated using heating platforms before experiment. The LIR of the ²H_11/2 and ⁴S_3/2 energy levels correlates strongly with temperature. The results of the fitting show that the $\Delta E$ is 747 cm^-1 and the fitting parameter $B$ is 19, respectively (Supplementary Fig. 3 in Supplementary Information).