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Winter 2019

physics professor Tongcang Li and graduate research assistant Jonghoon Ahn in Purdue lab
Physics professor Tongcang Li and graduate research assistant Jonghoon Ahn work in Li's laboratory.

Exploring Physics with Optical Levitation

By Tongcang Li

Tongcang Li

Light exerts radiation pressure on almost everything it encounters. However, the radiation pressure is typically feeble and insensible by human beings. For example, if we reflect one watt of light from a lamp, the radiation pressure on us will be about 7 nano-Newtons (nN), which is far smaller than the gravitational force on us. On the other hand, 7 nN is about 1 million times larger than the gravitational force on an E. coli bacterial cell.

So the radiation pressure from a focused laser beam can have large effects on small particles. Optical tweezers are powerful tools that utilize the radiation pressure of tightly focused laser beams to manipulate small objects without mechanical contact [1].

Many works have used optical tweezers to control particles in liquid for biological applications. For example, optical tweezers are used to measure force spectra of single biological molecules. Optical tweezers are also essential tools in atomic, molecular and optical (AMO) physics to control ultracold atoms and molecules.

A rapidly growing interdisciplinary field is to optically levitate and control nanoparticles or microparticles in vacuum. A nanoparticle levitated in high vacuum is well isolated from the thermal noise and has an extremely high quality factor, which is excellent for precision measurements. Our group has made several pioneering contributions in optical levitation of nanoparticles for fundamental physics and applications.

Recently, we optically levitated a silica nanodumbbell in vacuum (Figure 1).

With a circularly polarized laser, we drove a nanodumbbell to rotate beyond 1 GHz [2], which is the fastest man-made rotor in the world. Our work attracted broad interest and was widely reported by Nature magazine, NBC News, Fox News and many other major media worldwide.

figure 1
Figure 1. (a) A nanodumbbell levitated by a circularly polarized laser in vacuum will rotate. (b) Measured rotation frequency of the nanodumbbell as a function of pressure. In high vacuum, it rotates beyond 1GHz. Inset: a SEM image of a silica nanodumbbell. Its diameter is about 170 nanometers (nm). (c) A nanodumbbell levitated by a linearly polarized laser. (d) Calculated torque detection sensitivity of a levitated nanodumbbell. (e) Experimental setup for optical levitation in vacuum. [2]

With a linearly polarized laser, we create a nanoscale analog of the Cavendish torsion balance for precision measurements [2, 3]. In another work, we optically levitated nanodiamonds and demonstrated electron spin control for quantum sensing and hybrid spin-optomechanics [4]. With optical levitation, we have also performed the first experimental test of the differential fluctuation theorem derived by Nobel laureate Martin Karplus and colleagues, which is an important development in non-equilibrium thermodynamics of small systems [5].

Optically Levitated Nanodumbbell Torsion Balance and GHz Nanomechanical Rotor

Torsion balances have played historic roles in the development of physics. For example, Cavendish torsion balance was used to determine the gravitational constant and the density of the Earth for the first time. Coulomb torsion balance was used in discovering the Coulomb’s law of electrostatic force.

Recently, we optically levitated silica nanodumbbells in high vacuum (Figure 1) [3].

Because of its shape, the polarizability of a nanodumbbell is anisotropic. When the trapping laser is linearly polarized, the axis of the nanodumbbell tends to align with the polarization direction of the laser beam (Figure 1c).

When an external torque changes the orientation of the nanodumbbell, the nanodumbbell will “twist” the polarization of the trapping laser, similar to the case of the lead balls twisting the wire in the original Cavendish torsion balance. In high vacuum, the levitated nanodumbbell has an exceptional torque detection sensitivity on the order of 10-28 Nm/√Hz (Figure 1d) [3]. 

The levitated nanodumbbell torsion balance can be about 20 orders more sensitive than the original Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity. When the trapping laser is circularly polarized, the nanodumbbell will rotate due to the angular momentum of photons.

The rotation speed increases when the air pressure de-creases. In high vacuum, a rotation frequency beyond 1 GHz is observed (Figure 1b), i.e., the nanodumbbell rotates more than 60 billion turns per minute. This is the fastest man-made rotor in the world. Such ultrafast rotation can be used to study the ultimate tensile strength of nanomaterials under extreme conditions and the vacuum friction due to collisions between virtual photons and the rotating nanoparticle.

Electron Spin Control of Optically Levitated Nanodiamonds

Diamond nitrogen-vacancy (NV) centers have broad applications in quantum information and nanoscale sensing. An NV center is formed by a substitution nitrogen atom and a nearby vacancy in the diamond lattice. The electronic ground state of a negatively charged NV center has spin 1. The NV electron spin can be initialized by a green laser and controlled by microwave radiation.

They can have long coherence times even at room temperature. Combining such NV spin systems with mechanical resonators will provide a hybrid quantum system for many applications. Recently, we optically levitated a nanodiamond and performed electron spin control of its built-in NV centers in low vacuum (Figure 2) [4].

figure 2
Figure 2. (a) Schematic of the experiment on electron spin control of a levitated nanodiamond. (b) Electron spin resonance spectra of a nanodiamond at different pressure. (c) Molecular structure of a NV center in nanodiamond. [4]

We also investigated the effects of trap power and measured the absolute internal temperature of levitated nanodiamonds with electron spin resonance (ESR). We observed that the strength of ESR is enhanced when the air pressure is reduced.

Our results show that optical levitation of nanodiamonds in vacuum not only can improve the mechanical quality of its oscillation but also enhance the ESR contrast, which paves the way toward a novel levitated spin-optomechanical system for quantum sensing and studying macroscopic quantum mechanics. We also observed different effects of oxygen gas and helium gas on NV centers, indicating potential applications of NV centers in gas sensing [4].

Experimental Test of the Differential Fluctuation Theorem with Optical Levitation

Nonequilibrium processes of small systems are ubiquitous but are often challenging to comprehend. In the past two decades, several thermodynamic relations of non-equilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights.

A famous example is the Jarzynski equality. However, the Jarzynski equality requires the initial state to be in thermal equilibrium, although the process can be out of equilibrium.

In 2008, Nobel laureate Martin Karplus and co-workers derived a differential fluctuation theorem (DFT) for work production during non-equilibrium processes with arbitrary initial conditions. It is remarkable that the DFT unifies various fluctuation theorems. Recently, we performed the first experimental test of the DFT (Fig. 3) [5].

figure 3
Figure 3. (a) Experimental scheme for testing the differential fluctuation theorem with a levitated nano¬sphere in air. (b) Black curves represent examples of experimental phase-space trajectories. (c) Test of the differential fluctuation theorem in the underdamped regime. [5]

We used an optically levitated nanosphere in air at different pressures to test the DFT in both underdamped and overdamped regimes. Because our ultrasensitive optical tweezer can measure the instantaneous velocity of a levitated nanoparticle, we tested the theorem in both spatial and velocity spaces. We also tested several theorems that can be derived from DFT directly.

Our study experimentally verified these fundamental theorems and deepened our understanding of the second law of thermodynamics. 

Acknowledgements: Researchers are sup-ported by the National Science Foundation, the Office of Naval Research, the Defense Advanced Research Projects Agency (DARPA), the Tellabs Foundation and the Rolf Scharenberg Graduate Research Fellowship.

References

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288 (1986).
  2. J. Ahn, Z. Xu, J. Bang, Y.H. Deng, T. M. Hoang, Q. Han, R.M. Ma, Tongcang Li. “Optically levitated nanodumbbell torsion balance and GHz nanomechanical rotor,” Phys. Rev. Lett., 121, 033603 (2018).
  3. T. M. Hoang, Y. Ma, J. Ahn, J. Bang, F. Robicheaux, Z.-Q. Yin, Tongcang Li. “Torsional optomechanics of a levitated nonspherical nanoparticle,” Phys. Rev. Lett. 117, 123604 (2016).
  4. T. M. Hoang, J. Ahn, J. Bang, Tongcang Li. “Electron spin control of optically levitated nanodiamonds in vacuum,” Nature Communications 7, 12550 (2016).
  5. T. M. Hoang, R. Pan, J. Ahn, J. Bang, H. T. Quan, Tongcang Li. “Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states,” Phys. Rev. Lett., 120, 080602 (2018).