FIG. 1. (a) Acceleration of a particle with 12 nm radiusvs center frequency of incident laser with 1.0 meV width.� means the nonradiative damping constant of the particle.(b): Displacement of positions of nanoparticles in liquid he-lium-4 at 2 K. Vertical bars indicate the calculated diffusionlength of a particle with a classical treatment. (Realistic dif-fusion length could be much shorter than this.) For both (a) and(b), the integrated laser power is 50 �W=100 �m2.

P H Y S I C A L R E V I E W L E T T E R S week ending27 FEBRUARY 2004VOLUME 92, NUMBER 8

Iida and Ishihara Reply: The main claim in the preced-ing Comment [1] is that the numerical results in ourLetter [2] are not valid for the optical manipulation atroom temperature because the resonant enhancement ofexerted force is spoiled by various broadening effects. Inthe first place, it is not the intention of [2] to present theresults at room temperature, and hence, we do not have anobjection to this point. However, we believe that it isbeneficial for readers if we further clarify the centralaim of [2] and the reason of the choice of conditionsreplying to the criticism in [1] in order to convey thesignificance of our theoretical work.

Among the various aspects of the radiation-mattermechanical interaction, we are particularly interested inthe effects arising from the fact that the individuality ofeach nanoparticle based on the quantum-mechanical co-herence appears through the resonant optical response,which cannot be seen either for atomic systems or�m-order systems. This is why we suppose the excitonicresonance, as indicated in the title of [2], whose linewidthcan be considerably narrow in the low temperature con-ditions as well known in the field of the solid statephysics.

As for the problem of the damping constant, it must bemore fruitful to study the damping dependence of theeffects with assumed values rather than going into thedetails of the damping mechanisms because the excitoniclinewidth has various microscopic origins and much de-pends on the sample size, environment, kind of material,and so on. For this type of study, it is reasonable to use oneof observed values in the former experiments for numeri-cal demonstrations, citing the references so that one canaccess detailed information of the condition for the as-sumed value [3]. Although the cryogenic condition is notindispensable for the electronic coherence, we considerthat using the damping constant of this condition is agood choice to reveal the full potentiality of the opticalmanipulation with the resonance effect.

We believe that what is important in [2] is the resultshowing that the efficient force can be generated to real-ize the optical manipulation linked to the quantum-mechanical properties of nanoparticles if we preparethe appropriate condition. Of course, the cryogenic con-dition in the liquid helium is one of good candidates forsuch experiments. We wish to remark that the obtainedresults in [2] lead to the possibilities of favorable effectsbeyond the pessimistic perspectives in [1]. The author of[1] mentions that an enhancement factor is drasticallyreduced if the linewidth of exciton becomes wider. Thisis not necessarily true because the enhancement factoralso depends on the linewidth of the incident laser be-cause the exerted force should be evaluated based on theintegrated intensity of the peak as mentioned in [2].Figure 1(a) shows that the reduction of exerted force bythe broadening is not so serious if the incident laser hassome linewidth. The problem of the Brownian motion is

089702-1 0031-9007=04=92(8)=089702(1)$22.50

also pointed out in [1]. However, it does not necessarilyspoil the possibilities of the optical manipulation of nano-particles. For example, nanoscale size differences can berevealed as macroscale position differences much longerthan the diffusion length of particles due to the Brownianmotion as shown in Fig. 1(b). It should be noted that weassume considerably wide linewidth (2.0 meV) of theexciton in this demonstration, which shows the greatpotentiality of the optical manipulation using the reso-nance effect.

In conclusion, the Comment [1] is helpful in the respectthat it lists the various disturbing factors (especially forthe room temperature condition) that we could not dis-cuss in [2] for want of space. However, the main part of itscriticism is misdirected in consideration of the centralaim of the Letter [2].

Takuya Iida and Hajime IshiharaDepartment of Materials Engineering ScienceOsaka UniversityToyonaka, Osaka 560-8531, Japan

Received 5 November 2003; published 26 February 2004DOI: 10.1103/PhysRevLett.92.089702PACS numbers: 78.67.Bf, 71.35.–y, 78.90.+t

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*Electronic address: ishi@mp.es.osaka-u.ac.jp[1] M. Pelton, preceding Comment, Phys. Rev. Lett. 92,

089701 (2004).[2] T. Iida and H. Ishihara, Phys. Rev. Lett. 90, 057403

(2003).[3] Although the author of [1] criticizes our choice of damp-

ing referring to the confinement induced broadening, itshould be noted, on the other hand, that the confinementinduced sharpening due to the reduction of the density ofstates of phonons has also been reported in, for example,M. Ikezawa and Y. Masumoto, Phys. Rev. B 61, 12 662(2000); P. Borri, W. Langbein, S. Schneider, U. Woggon,R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett.87, 157401 (2001).

4 The American Physical Society 089702-1