Understanding thermal induced escape mechanism of optical ly levitated sphere in vacuum MENGZHU HU1 NAN LI14 ZHENHAI FU 2 YIZHOU ZHANG 2 WENQIANG LI 1 HAN

2025-05-06 0 0 879.76KB 11 页 10玖币

 
Understanding thermal induced escape mechanism of 
optically levitated sphere in vacuum 
MENGZHU HU,1 NAN LI,1,4 ZHENHAI FU, 2 YIZHOU ZHANG, 2 WENQIANG LI, 1 HAN 
CAI,1 AND HUIZHU HU2,3,5 
1College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China 
2Quantum Sensing Center, Zhejiang Lab, Hangzhou 310000, China 
3State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China 
4 nanli@zju.edu.cn 
5 huhuizhu2000@zju.edu.cn 
 
Abstract: The escape phenomenon, mainly caused by thermal effects, is known as an obstacle to the 
further practical application of optical levitation system in vacuum. Irregular photophoresis induced by 
thermal effects can act as an “amplifier” of Brownian motion. Studies on this topic provide interpretation 
for particle escaping phenomenon during the pressure decreasing process, as well as valuable insights 
into the micro- and nanoscale thermal effects in optical trap in vacuum. In this paper, we derive and test 
a  dynamic  model  for  the  motion  of  an  optically  levitated  particle  in  a  non-equilibrium  state  and 
demonstrate  the  escaping  mechanism  of  heated  particles.  The  result  of  theoretical  investigations  is 
consistent with experimental escape at 0.1mbar. This work reveals and provides a theoretical basis for 
the stable operation of laser levitated oscillator in high vacuum and paves the way for the practicability 
of ultra-sensitive sensing devices.   
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 
1． Introduction 
Levitated  particles  in  vacuum  can  be  applied  in  a  wide  range  of  fields,  including  precision 
measurement of acceleration  [1,2]  and  mass [3],  ultrasensitive  force  [4,5] and torque detection [6,7], 
high-speed rotation [8,9], optical refrigeration [10], quantum ground-state cooling [11-15], and stochastic 
thermodynamics [16-18]. Unlike in liquid or air, optical tweezers operating in vacuum are well isolated 
from  the  thermal  environment,  making  them  an  excellent  candidate  for  ultrasensitive  sensing. 
Interactions with the thermal environment cause the dissipation of the center-of-mass motion and are the 
source of random forces acting on the particles.  However, the effects of laser  heating are  stronger in 
vacuum,  since  the  heat  exchange  between  particles  and  surroundings  becomes  insufficient  with 
decreased pressure.   
The thermal effects of a levitated particle have been suspected to be the cause of particle loss at 
decreased gas pressure in numerous researches [19-24]. Photophoretic force  arising  from the internal 
temperature gradient has  proved  to be the mechanism for the loss at ~30 mbar [24]. In this case, the 
particle  is  assumed  to  have  a  constant  accommodation  coefficient  α,  and  the  photophoretic  force  is 
induced by variation in the temperature Ts of the particle surface (∆Ts-force). The  ∆Ts-force  is called 
space-fixed  force  because  its  direction  is  determined  by  the  direction  of  the  radiation  and  is  almost 
independent  of  the  orientation  of  the  particle. As  a  matter  of  fact,  there  always  exists  a variation  in 
accommodation coefficient over the surface of particle due to the impurities and non-ideal particle shape. 
This results in a ∆α-force on the particle from the location of higher accommodation to the location of 
lower one. The direction of this photophoretic force is determined by the orientation of the particle and 

is independent of the direction of the illumination[25], thus ∆α-force is body-fixed. The direction of ∆α-

force varies with the orientation of the particle, which yields particle motion in any possible direction.

As a result, random walk depending on the irradiation occurs, which adds to the Brownian motion [26].

In this paper, the motion of a heated trapped sphere is investigated. First, we study the dynamics of

the sphere under both types of photophoretic forces in connection with Brownian motion. It is shown

that irregular photophoresis due to the ∆α-force enhances the stochastic process of Brownian motion.

Then, we test the model by comparing the calculated results with the experimental data and previous

work. The dynamic model allows us to assess the difference in accommodation coefficient over the

levitated sphere, implying the application of levitodynamics to material science study. Since maintaining

the trapping stability of levitated sphere is a critical task for an optically levitated system, our study paves

the way for the stable operation of optomechanical oscillator in high vacuum.

2． Principle of photophoretic force

Photophoresis is a well-known phenomenon of the light-induced motion of particles suspended in

gas [32]. There are two types of photophoretic force, namely, ∆Ts-force F∆T and ∆α-force F∆α. These are

respectively induced by variation in temperature over the surface of particles and by variation in the

thermal accommodation coefficient α. Both can cause a temperature variation in the gas surrounding the

particle. After inelastic collision, hotter gas molecules leave the particle surface faster than colder ones,

which results in a net force on the particle pointing from the hot to the cold side.

The ∆Ts-force is directed along or against the direction of incident light (Fig.1(a)). A semi-

empirical expression for F∆T has been given by Rohatschek [27] on spherical particles for the entire range

of pressure p, such as:

max max

max

FF p

=

, (1)

max 23T

pD a



max 2p

F D I



  



8RT



where

denotes the average thermal velocity of gas molecules at temperature T, M denotes the molar

mass of the gas,



represents the dynamic viscosity of gas, and R=8.31J/(molK) is the gas constant.

The thermal creep coefficient



is related to the thermal accommodation coefficient α; therefore, D is a

factor determined entirely by the gas properties, independent of the pressure p and particle‘s radius a. J1

represents the asymmetry parameter that involves an integration of normalized absorbed light intensity

over the particle volume [28]. For a weakly absorbing sphere with a complex refractive index of

m n ik=+

illuminated by a homogeneous plane wave at the light wavelength λ, J1 can be obtained by

the formula [29,30]:

3( 1) 2

285

J nkx nkx

−



=−





(2)

where

2/xa



and

1kx

. It is also applicable to our studied configuration with the particle

illuminated by focused laser beams with non-uniform intensity profiles, the intensity of the light field

near the equilibrium position can be considered to be uniform. We assume that the light is +z-propagating,

J1 < 0 leads to positive photophoresis in the +𝑧-direction, namely, the particle moves in the direction

away from the radiation source . I represents the flux density of illumination at the particle position, and

kp is the thermal conductivity of the particle. The expression of F∆T can achieve a maximum force Fmax

at a pressure pmax, where the particle size is comparable to the mean free path of gas molecules.

The particle can experience pure ∆Ts-force only if the accommodation coefficient α is uniform.

However, the accommodation coefficient α shall have variation over the particle surface, e.g., that arising

from the difference in surface shape and roughness or different material composition of the particle.

Therefore, even if the particle is heated evenly, there is still ∆α-force acting on the particle (Fig.1(a)).

For a simple model in which the surface of spherical particle is divided into two hemi-spheres with two

different accommodation coefficients α1 and α2, the expression for instantaneous ∆α-force is given by

the following equation [28]:

( )

1 1 1

cpp







−

=   

(3)

where γ = cp/cv represents the ratio of the specific heats of the gas, and H denotes the net energy flux

transferred by gas molecules. For a sphere in air, γ =1.4 [31,32]:

( )

12 1

cpp







=  

(4)

Here,

  

 = −

( )

  

, and

max

23p p DT a



is a characteristic pressure

inversely proportional to the radius. The energy flux absorbed by the sphere is H=Qaπa2I, and Qa is the

absorption efficiency of the sphere [32]. The direction of ∆α-force (F∆α) points from the side of the higher

accommodation coefficient to the lower one. This force is independent of the direction of incident light

and is determined by the particle orientation, which is also called body-fixed force here. Since the effect

of collisions between a particle and surrounding gas molecules can result in random force and torque, all

particles perform Brownian displacement and Brownian rotation. As a result, the direction of ∆α-force is

randomly distributed, which will make Brownian motion more vigorous. Illuminated particles may

perform irregular photophoresis and exhibit an irregular motion shown in the insert of Fig.1(b), which is

similar to Brownian motion but stronger. It is also obvious fom the formula (1) and (4) that photophoretic

forces strongly depend on the pressure. The ∆Ts-force reach its maximum at a pressure which enables

the particle size comparable to the mean free path of gas molecules. The ∆α-force increases with

decreasing pressure as well as increasing mean free path of gas molecules. For a pressure of mbar or

below, the mean free path is approximately at the scale of tens of microns. This means that the

photophoretic force is an important force for μm-sized particles at pressures of a few mbar or below.

Thus, for a levitated microsphere in an optical trap in low-pressure environments, the motion of sphere

can be highly influenced by photophoresis.

3． Motion of heated particle

Typically, due to impurities, the particle in the optical trap will absorb part of the trapping light and

convert it into heat. If the gas pressure is low, the interaction between the gas molecules and the particle

is insufficient. Then, the energy absorbed by the particle cannot be dissipated and the particle will be in

a state of thermal non-equilibrium. In addition, differences in surface roughness and composition will

result in variations in the accommodation coefficient over the particle surface. Thus, particle motion is

also affected by the randomly oriented photophoretic force F∆α. In our experiment, we observed a

phenomenon that the microspheres can easily escape from the optical trap with no feedback when the

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

UnderstandingthermalinducedescapemechanismofopticallylevitatedsphereinvacuumMENGZHUHU,1NANLI,1,4ZHENHAIFU,2YIZHOUZHANG,2WENQIANGLI,1HANCAI,1ANDHUIZHUHU2,3,51CollegeofOpticalScienceandEngineering,ZhejiangUniversity,Hangzhou310027,China2QuantumSensingCenter,ZhejiangLab,Hangzhou310000,China3StateKeyLab...

展开>> 收起<<

Understanding thermal induced escape mechanism of optical ly levitated sphere in vacuum MENGZHU HU1 NAN LI14 ZHENHAI FU 2 YIZHOU ZHANG 2 WENQIANG LI 1 HAN.pdf

共11页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Understanding thermal induced escape mechanism of optical ly levitated sphere in vacuum MENGZHU HU1 NAN LI14 ZHENHAI FU 2 YIZHOU ZHANG 2 WENQIANG LI 1 HAN

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: