Coherent mixing of mechanical excitations in nano … · Qiang Lin, Jessie Rosenberg, Darrick Chang, Ryan Camacho, Matt Eichenﬁeld, Kerry J. Vahala and Oskar Painter* The combination

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Coherent mixing of mechanical excitations innano-optomechanical structuresQiang Lin, Jessie Rosenberg, Darrick Chang, Ryan Camacho, Matt Eichenfield, Kerry J. Vahala

and Oskar Painter*

The combination of the large per-photon optical force and small motional mass achievable in nanocavity optomechanicalsystems results in strong dynamical back-action between mechanical motion and the cavity light field. In this Article, westudy the optical control of mechanical motion within two different nanocavity structures, a zipper nanobeam photoniccrystal cavity and a double-microdisk whispering-gallery resonator. The strong optical gradient force within these cavitiesis shown to introduce significant optical rigidity into the structure, with the dressed mechanical states renormalized intooptically bright and optically dark modes of motion. With the addition of internal mechanical coupling between mechanicalmodes, a form of optically controlled mechanical transparency is demonstrated in analogy to electromagnetically inducedtransparency of three-level atomic media. Based upon these measurements, a proposal for coherently transferring radio-frequency/microwave signals between the optical field and a long-lived dark mechanical state is described.

The coherent mixing of multiple excitation pathways provides theunderlying mechanism for many physical phenomena. Well-known examples include the Fano resonance1 and electromag-

netically induced transparency (EIT)2, arising from the interferencebetween excitations of discrete states and/or a continuum background.In the past few decades, Fano-like or EIT-like resonances have beendiscovered in a variety of physical systems, such as electron transportin quantum wells/dots3,4, phonon interactions in solids5,6, inversion-free lasers7,8, coupled photonic microcavities9–12, and plasmonicmetamaterials13. Here we report a new class of coherent excitationmixing that appears in the mechanical degree of freedom ofnano-optomechanical systems (NOMS). We use two canonicalsystems, coupled microdisks and coupled photonic-crystal nano-beams, to show that the large optical stiffening introduced by theoptical gradient force actuates significant coherent mixing of mech-anical excitations, not only leading to renormalization of themechanical modes, but also producing Fano-like and EIT-like opto-mechanical interference, both of which are fully tunable by opticalmeans. The demonstrated phenomena introduce the possibilityfor classical/quantum information processing via optomechanicalsystems, providing an on-chip platform for tunable optical buffer-ing, storage and photonic–phononic quantum state transfer.

Light forces within micromechanical systems have attractedconsiderable interest of late due to the demonstration of all-optical amplification and self-cooling of mesoscopic mechanicalresonators14–18. This technique for sensing and control of mechan-ical motion relies on the radiation pressure forces that build up in amechanically compliant, high-finesse optical cavity, resulting instrong dynamical back-action between the cavity field and mechan-ical motion. More recently19–24, it has been realized that guided wavenanostructures can also be used to generate extremely large per-photon optical forces via the gradient optical force25. The combi-nation of tailorable mechanical geometry, small motional massand large per-photon force in such nano-structures results in aregime of operation in which the dynamic response of thecoupled optomechanical system can significantly differ from thatof the bare mechanical structure. In particular, the mechanicalmotion can be renormalized by the optical spring effect22,24,26–30,

creating a highly anistropic, intensity-dependent effective elasticmodulus of the optomechanical structure.

In this work, we focus on two specific implementations of nano-scale cavity optomechanical systems (Fig. 1), in which dynamicalback-action effects are particularly strong. The first system consistsof two patterned nanobeams in the near-field of each other,forming what has been termed a zipper cavity22,31. In this cavity struc-ture, the patterning of the nanobeams localizes light through Braggscattering, resulting in a series of high-finesse (F � 3� 104),near-infrared (l� 1,550 nm) optical supermodes of the beam pair.Clamping to the substrate at either end of the suspended beamsresults in a fundamental in-plane mechanical beam resonance of fre-quency �8 MHz. The second cavity optomechanical system is basedupon a whispering-gallery microdisk optical cavity structure. By creat-ing a pair of microdisks, one on top of the other, with a nanoscale gapin between, strong optical gradient forces may be generated betweenthe microdisks while maintaining the benefits of the low-loss, high-Q(Q� 1� 106) character of the whispering-gallery cavity. As shownschematically in Fig. 1a, the double-disk structure23 is supportedand pinned at its centre, allowing the perimeter of the disks tovibrate in myriad different ways. Of particular interest in both thezipper and double-disk systems is the differential motion of the nano-beams or disks, in which the modulation of the gap between theelements creates a large dispersive shift in the internally propagatingcavity light field. It is this type of motion that is strongly coupled tothe light field, and for which the dynamical back-action is strongest.

We begin with an analysis of the zipper cavity, in which the strongoptically induced rigidity associated with differential in-plane motion ofthe nanobeams results in a dressing of the mechanical motion by thelight field. As described in the Methods and in ref. 22, an optical-fibre nanoprobe couples light into and out of the zipper cavity.Optical excitation provides both a means to transduce mechanicalmotion (which is imparted on the transmitted light field throughphase and intensity modulation) and to apply an optical-intensity-dependent mechanical rigidity via the strong optical gradient force.By fitting a Lorentzian to the two lowest-order in-plane mechanicalresonances in the radio-frequency (RF) optical transmission spectrum,we display in Fig. 2a and b the resonance frequency and resonance

Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA. *e-mail: [email protected]

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linewidth, respectively, of the two coupled mechanical modes of thenanobeam pair as a function of laser-cavity detuning. At large detuning(low intracavity photon number) the nanobeams’ motion is transducedwithout inducing significant optical rigidity, and the measured mechan-ical resonances are split by�200 kHz, with similar linewidths (damping)and transduced amplitudes (Fig. 2c). As the laser is tuned into resonancefrom the blue side of the cavity, and the intracavity photon numberincreases (to�7,000), the higher-frequency resonance is seen to signifi-cantly increase in frequency, while the lower frequency mode tunes to theaverage of the independent beam frequencies with its transduced ampli-tude significantly weaker. The linewidth of the high-frequency resonancealso tends to increase, while that of the lower frequency mode drops.Tuning from the red side of the cavity resonance reverses the sign ofthe frequency shifts and the roles of the high- and low-frequency modes.

A qualitative understanding of the light-induced tuning anddamping of the zipper cavity nanobeam motion emerges if one con-siders the effects of squeeze-film damping32. Squeeze-film effects, aresult of trapped gas between the beams (measurements were per-formed in 1 atm of nitrogen), tend to strongly dampen differentialmotion of the beams and should be negligible for common motionof the beams. Similarly, the optical gradient force acts most stronglyon the differential beam motion and negligibly on the common-mode motion. The sign of the resulting optical spring is positive forblue detuning and negative for red detuning from the cavity resonance.

Putting all of this together, a consistent picture emerges from the datain Fig. 2, in which the nanobeams begin with large detuning, movingindependently, with similar damping (the frequency splitting of�200 kHz is attributable to fabrication assymmetries in the beams).As the detuning is reduced and approaches the cavity half-linewidth,the motion of the nanobeams is dressed by the internal cavity fieldinto differential motion with a large additional optical spring constant(either positive or negative) and large squeeze-film damping com-ponent, and common motion with reduced squeeze-film dampingand minimal coupling to the light field. Owing to the strong light-field coupling of the differential mode and the correspondingly weakcoupling of the common mode, we term these dressed motionalstates ‘optically bright’ and ‘optically dark’, respectively.

A quantitative model of the dressed system can be obtained byconsidering the following set of coupled equations for the mechan-ical motion of the nanobeams:

d2x1dt2þ Gm

dx1dtþV2m1x1 ¼

F1 þ Fo þ Fqm

ð1Þ

d2x2dt2þ Gm

dx2dtþV2m2x2 ¼

F2 � Fo � Fqm

ð2Þ

Here, Fo is the optical gradient force, Fq is the viscous force from thesqueeze-film effect, and Fj ( j¼ 1, 2) is the Langevin force due to

c

a

d

f

1 μm

W

s

a

e

b

1 μm

Figure 1 | Illustration of the double-disk and zipper nano-optomechanical structures. a,b, Schematic (a) and enlarged scanning electron microscopic (SEM)

image (b) of the double-disk NOMS. c, FEM-simulated electric field intensity of a transverse electric (TE) polarized, bonded (even parity) whispering-gallery

supermode between the two microdisks (shown in cross-section and for resonance wavelength lc� 1,550 nm). The double-disk bonded supermode has anoptomechanical coupling coefficient of gOM/2p� 33 GHz nm21. The device studied here has a measured resonance wavelength of lc¼ 1,538 nm and anintrinsic and loaded quality (Q) factor of 1.07� 106 and 0.7� 106, respectively. d–f, Schematic (d), SEM image (e) and FEM-simulated bonded (even parity)optical supermode (f) of the zipper cavity. The zipper cavity bonded supermode has an optomechanical coupling coefficient of gOM/2p� 68 GHz nm21, ameasured resonance wavelength of lc¼ 1,545 nm, and an intrinsic and loaded Q-factor of 3.0� 104 and 2.8� 104, respectively. For additional details for bothdevices see the Methods, the Supplementary Information and refs 22,23.

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coupling of the beams to a thermal bath (further details of the prop-erties of these three forces are described in the SupplementaryInformation). The parameters xj andVmj ( j¼ 1, 2) are the mechanicaldisplacement and the resonance frequency of the uncoupled, individ-ual beams. We have assumed, for simplicity, that the bare mass (m)and the intrinsic mechanical damping (Gm) are the same for each ofthe nanobeams (a more complete treatment is given in theSupplementary Information). The resulting spectral intensity of thethermally excited optically bright (xb ; x1 2 x2) differential beammotion can be shown to be (see Supplementary Information)

SxbðVÞ ¼kBTGm

mb

� jL1ðVÞj2þ jL2ðVÞj

2

jL1ðVÞL2ðVÞ �12½ foðVÞ=mb þ iGqV�½L1ðVÞ þ L2ðVÞ�j

2

ð3Þ

where Lj(V)¼Vmj2 2V2 2 iGmV ( j¼ 1, 2), mb¼m/2 (�10.75 pg)is the effective mass of the differential mode, T is the bath temp-erature, and Gq represents the damping rate introduced by thesqueezed gas film between the beams. fo(V) represents the modifi-cation to the mechanical susceptibility of the differential beammotion by the optical gradient force, and is approximately givenin the bad-cavity limit (Gt� Vm) by

foðVÞ � �2g2OMja0j

2D0vc

D20þ ðGt=2Þ2 þ iGtV

½D20þ ðGt=2Þ2�2

ð4Þ

where gOM [;dvc/dxb� 2p(68 GHz nm21)] is the optomechanicalcoupling coefficient, ja0j2 is the time-averaged optical cavity

energy, and Gt [�2p(6.9 GHz)] is the energy decay rate of theloaded optical cavity resonance. Lorentzian fits to the double reson-ances of Sxb(V) yield the frequency and damping curves shown assolid lines in Fig. 2a,b, displaying excellent agreement with theexperimental measurements.

A similar optically induced renormalization mechanism appliesto the double-disk cavity structure shown in Fig. 1a–c. In thiscase, the large optical spring effect for the differential motion ofthe two microdisks excites another, more intriguing form of coher-ent optomechanical mixing with the optically dark common modeof the disks. Unlike in the zipper cavity, finite-element-method(FEM) modelling of the mechanics of the double-disk structureindicates a significant frequency splitting between the differentialand common modes of motion of the double disk (shown inFig. 3a,b), primarily due to the difference in the extent of the under-cut between the disk layers and the extent of the central pedestal thatpins the two disk layers. The result is that the differential, or ‘flap-ping’ motion, of the undercut disk region has a lower frequencyof 7.95 MHz, and the common motion of the disks results in ahigher-frequency (14.2 MHz) ‘breathing’ motion of the entiredouble-disk structure.

The RF spectrum of the transmitted optical intensity through adouble-disk cavity, measured using the same fibre probing tech-nique as for the zipper cavity (see Methods), is shown in Fig. 3cversus laser-cavity detuning. For the largest detuning (in whichthe optical spring is negligible) the spectrum shows a broad(2.1 MHz) resonance at 8.3 MHz and a much narrower(0.11 MHz) resonance at 13.6 MHz, in good correspondence withthe expected frequencies of the flapping and breathing modes,respectively. The difference in damping between the two resonancescan be attributed to the strong squeeze-film damping of the differ-ential flapping motion of the disks. As shown in Fig. 3c, the flapping

0 0.5 1 1.5 20

0.2

0.25

0.05

0.1

0.15

Normalized detuning (Δ0/Γt)

−2 −1.5 −1 −0.5

−2 −1.5 −1 −0.5

0 0.5 1 1.5 2Normalized detuning (Δ0/Γt)

Mec

hani

cal l

inew

idth

(MH

z)

b

7.4

7.6

7.8

8.0

8.2

8.4M

echa

nica

l fre

quen

cy (M

Hz)

ae

f

7.2 7.6 8.0 8.4 8.8

−70

−80

−60

Pow

er s

pect

ral d

ensi

ty (d

Bm H

z−1 )

Frequency (MHz)

7.2 7.6 8.0 8.4 8.8Frequency (MHz)

−100

−110

−90

Pow

er s

pect

ral d

ensi

ty (d

Bm H

z−1 )

c

d

Nphoton

Nphoton

Figure 2 | Optical renormalization of mechanical vibrations in the zipper cavity. a,b, Mechanical frequency (a) and linewidth (b) of the fundamental in-plane

mechanical resonances of the zipper cavity’s coupled nanobeams as a function of laser frequency detuning. The input power for these measurements is 127mW,corresponding to a maximum cavity photon number of �7,000 on resonance. The circles show the experimental data and the solid lines correspond to a fit tothe data using equation (3). c,d, Optically transduced RF spectrum at a laser-cavity detuning of D0/Gt¼ 2.1 (c) and D0/Gt¼0.32 (d). e,f, The two nanobeamsvibrate independently when the laser-cavity detuning is large, but are renormalized to the cooperative differential (e) and common (f) motions near resonance.

ARTICLES NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.5




mode can be tuned in frequency by means of the optical springeffect from its bare value of 8.3 MHz all the way to 15.7 MHz(optical input power of Pi¼ 315 mW). In the process, the flappingmode is tuned across the breathing mode at 13.6 MHz. Althoughthe optically dark breathing mode is barely visible in the transducedspectrum at large laser-cavity detunings, its spectral amplitude isconsiderably enhanced as the optically bright flapping mode istuned into resonance. In addition, a strong Fano-like lineshape,with �13 dB anti-resonance, appears in the power spectrum nearresonance of the two modes (Fig. 3f,g,h).

As shown schematically in Fig. 4a, the Fano-like interference in theoptically bright power spectral density can be attributed to an internalmechanical coupling between the flapping and breathing mechanicalmodes. This is quite similar to the phonon–phonon interactionduring the structural phase transition in solids5,33–37, in which theinternal coupling between phonon modes produces Fano-like reson-ances in the Raman-scattering spectra. A Hamiltonian for thecoupled optomechanical system can be written as

Hm ¼p2b

2mbþ 1

2mbV

2mbx

2b þ

p2d2mdþ 1

2mdV

2mdx

2d þ kxbxd ð5Þ

where xj , pj , Vj and mj ( j¼ b,d) are the mechanical displacement,kinetic momentum, intrinsic mechanical frequency andeffective motional mass, respectively, for the optically bright flap-ping ( j¼ b) and optically dark breathing ( j¼ d) mechanicalmodes. k represents the internal mechanical coupling betweenthe two modes. Equation (5), together with the three externalactuation forces (optical, squeeze-film and thermal in nature),leads to the following equations of motion for the two mechanicalmodes:

d2xbdt2þ Gmb

dxbdtþV2mbxb þ

k

mbxd ¼

Fbmbþ Fo

mbð6Þ

d2xddt2þ Gmd

dxddtþV2mdxd þ

k

mdxb ¼

Fdmd

ð7Þ

where Fj ( j¼ b,d) represents the thermal Langevin forces and we haveincorporated the squeeze-film damping into Gmb for the opticallybright differential motion. Equations (6) and (7) lead to a spectral

10 12 14 16 1886 0Frequency (MHz) Frequency (MHz) Δ0/Γt

Pow

er s

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ensi

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0 dB

/div

)

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ensi

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0 dB

/div

)

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pect

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ensi

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0 dB

/div

)

10 12 14 16 18 386 2

hg

f

168 10 12 14Frequency (MHz)

18 168 10 12 14 18 168 10 12 14Frequency (MHz)Frequency (MHz)

18

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−75

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er s

pect

ral

dens

ity (d

Bm H

z−1 )

−85

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ity (d

Bm H

z−1 )

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−75

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er s

pect

ral

dens

ity (d

Bm H

z−1 )

−85

−95

c d e

f g h

a b

1

Figure 3 | Coherent mechanical mode mixing in the double-disk cavity. a,b, FEM simulated mechanical motion of the differential flapping mode (a) and the

common breathing mode (b), with simulated frequencies of 7.95 and 14.2 MHz. The colour map indicates the relative magnitude (exaggerated) of the

mechanical displacement. c, Recorded power spectral density (PSD) of the cavity transmission for the double-disk, with an input power of 315mW. Eachcurve corresponds to a normalized laser-cavity frequency detuning, D0/Gt, indicated in e. For display purposes, each curve is relatively shifted by 10 dB in the

vertical axis. d, The corresponding theoretical PSD. e–h, Detailed PSD at three frequency detunings (f–h) indicated by the arrows in e, with the experimental

and theoretical spectra in blue and red, respectively.





intensity for xb of (see Supplementary Information)

SxbðVÞ ¼2kBT

mb

h4Gmd þ GmbjLdðVÞj2

jLbðVÞLdðVÞ � h4j2 ð8Þ

where h4 ; k2/(mbmd) represents the mechanical coupling coeffi-cient, Lb(V)¼Vmb2 2V2 2 iGmbV 2 fo(V)/mb , and Ld(V)¼Vmd

2 2 V2 2 iGmdV. As discussed in more detail in ref. 23 and inthe Supplementary Information, the parameters for the double-disk are mb¼ 264 pg, gOM/2p¼ 33 GHz nm21, and Gt/2p¼280 MHz. The power spectral density of the cavity transmission,which we measure optically, is linearly proportional to Sxb(V). Asshown in Fig. 3d, the theoretical model (with fitting parameterh/2p¼ 3.32 MHz) provides an excellent description of theobserved phenomena. As presented in the SupplementaryInformation, similar coherent mode-mixing involving two opticallydark modes and a single optically bright mode occurs in thezipper cavity.

The mechanical response given by equation (8) is directly analo-gous to the atomic response in EIT38. Just as in EIT, one can under-stand the resulting Fano lineshape in two different ways. The firstperspective considers the interference associated with multiple exci-tation pathways. In the optomechanical system, the mechanicalmotion of the flapping mode is thermally excited along two differentpathways, either directly into the broadband (lossy) flapping mode,or indirectly, through the flapping mode, into the long-lived breath-ing mode, and then back again into the flapping mode. The twoexcitation pathways interfere with each other, resulting in theFano-like resonance in the spectral response of the opticallybright flapping mode. An alternative, but perfectly equivalent viewof the coupled optomechanical system considers the dressed statesresulting from the internal mechanical coupling. In this picture

the internal mechanical coupling renormalizes the broadbandflapping mode and the narrowband breathing mode into twodressed mechanical modes, both broadband and optically bright.In particular, when the flapping and breathing mechanical frequen-cies coincide, the two dressed modes are excited with equal ampli-tude and opposite phase at the centre frequency between the splitdressed states. Destructive interference results, suppressing exci-tation of the mechanical system at the line centre. Consequently,the mechanical motion becomes purely a trapped mechanicallydark state, transparent to external excitation. As shown in Fig. 4c,this induced mechanical transparency is a direct analogue to EITin atomic systems2,38–40, in which the quantum interferencebetween the transition pathways to the dressed states of theexcited electronic state, through either j1l $ jþ l or j1l $ j 2l,leads to an induced spectral window of optical transparency.

Despite the intriguing similarities between the optomechanicalsystem studied here and EIT in atomic media, there are some impor-tant, subtle differences. For instance, in the optomechanical system,rather than the linear dipole transition of EIT, the interaction corre-sponds to a second-order transition. The dynamic back-actionbetween the cavity field and mechanical motion creates Stokesand anti-Stokes optical sidebands, the beating of which with thefundamental optical wave resonates with the mechanical motionto create/annihilate phonons (Fig. 4d). Functionally, this is likecoherent Stokes and anti-Stokes Raman scattering, albeit with unba-lanced scattering amplitudes resulting from the colouring of theelectromagnetic density of states by the optical cavity (seeSupplementary Information). Therefore, in analogy to EIT, it isthe modulation signal carried by the incident optical wave (RFor microwave photons) that fundamentally probes/excites themechanical motion and to which the trapped mechanically darkstate becomes transparent. Moreover, rather than tuning the Rabisplitting through the intensity of a control beam resonant with

Input Output

|1

|3

|1

|2

|−

|+

Probe

Control

|3

|2

RF/microwavephoton

Coupling

StokesPump

Anti-stokes

Pump

d

a

c

b

Γ2

Γ3

γ3

γ2

mb

κmd

xb

xdkd

kb

Input Output

2

1

Coupling

Figure 4 | Illustration of the analogue to atomic and coupled-resonator systems. a, Schematic of an equivalent Fabry–Perot cavity system showing

mechanical mode mixing. The mechanical motion of the cavity mirror (mb, equivalent to the optically bright flapping mode) is primarily actuated by thespring kb and the optical force. It is internally coupled to a second mass spring system (md, equivalent to the breathing mode) actuated by the spring kd,which is decoupled from the optical wave. The two masses are internally coupled via spring k. b, A photonic analogue to the optomechanical system

involving coupled resonators. Microcavity 1 is directly coupled to the external optical waveguide (equivalent to the optically bright flapping mode) and also

internally coupled to the narrowband cavity 2 (equivalent to the optically dark breathing mode). The red arrows indicate the propagation direction of light.

c, State diagram of an EIT-like medium. The excited state (j2l) is split by the optical control beam into two broadband dressed states (jþ l and j2 l). Thedipole transition between ground states j1l and j3l is forbidden. d, The state diagram corresponding to the optomechanical system of a, where j1l is thephonon vacuum state, and j2l and j3l correspond to the flapping and breathing modes, respectively.





the j3l $ j2l electronic transition (Fig. 4c), this optically inducedmechanical transparency is controlled by means of optical springtuning of the resonance frequency of the optically bright flappingmechanical mode. Perhaps the most apt analogy to the optomecha-nical system can be made to the photonic resonator system shown inFig. 4b. The interference in this case is between the two optical path-ways composed of the waveguide-coupled low-Q optical resonator 1,and the waveguide-decoupled high-Q resonator 2. This interferenceagain leads to a Fano-like resonance, or what has been termedcoupled-resonator-induced transparency, in the optical cavitytransmission9–12.

Although the studies considered here involve thermal excitationof the optomechanical system, the same phenomena can be excitedmore efficiently, and with greater control, using external opticalmeans (see Supplementary Information). As such, beyond the inter-esting physics of these devices, exciting applications inRF/microwave photonics and quantum optomechanics exist.Similar to the information storage realized through EIT38,41,42,optical information can be stored and buffered in the dark mechan-ical degree of freedom in the demonstrated NOMS. This can be rea-lized through a procedure similar to that recently proposed forcoupled optical resonators43,44 in which dynamic, adiabatic tuningof optical resonances is used to slow, store and retrieve opticalpulses. The corresponding optomechanical system would consistof an array of double-disk resonators, all coupled to a commonoptical bus waveguide into which an optical signal carryingRF/microwave information would be launched. In this scheme, asecond control optical beam would adiabatically tune the frequencyof the optically bright flapping mode of each resonator, allowing forthe RF/microwave signal to be coherently stored in (released from)the long-lived breathing mode through adiabatic compression(expansion) of the mechanical bandwidth43,44. In comparison tothe all-photonic system, optomechanical systems have severaladvantages, primarily related to the attainable lifetime of the darkmechanical state. For example, the radial breathing mechanicalmode of a similar whispering-gallery cavity has been shown toexhibit a lifetime of more than 2 ms (ref. 45), a timescale morethan seven orders of magnitude longer than that in demonstratedphotonic coupled-resonator systems46 and comparable with EITmedia41,42. Moreover, mechanical lifetimes of more than one secondhave recently been demonstrated using stressed silicon nitride nano-beam47 and nanomembrane48 mechanical resonators operating inthe megahertz frequency regime. In the quantum realm, such asystem operating in the good cavity or sideband-resolved regime (byincreasing either the optical Q factor49 or the mechanical frequency)would reduce the simultaneous creation and annihilation of Stokesand anti-Stokes photons, thus allowing single-channel transferbetween the photonic and phononic states (Fig. 4d). By maintainingthe system in a cryogenic environment to prevent coherence degra-dation induced by thermal heating of the optically bright flappingmode, the strong optomechanical coupling in our system, togetherwith the internal coupling between the two mechanical modes, canefficiently convert a singe-photon state with high fidelity back andforth to a single-phonon state in the long-lived optically dark breath-ing mode, through a similar procedure describe above. This schemethus shows great potential for efficient information storage and retrie-val at the single quantum level, suitable for quantum state transfer.

MethodsThe zipper cavity was formed from a thin film (400 nm) of tensile-stressed,stoichiometric Si3N4 deposited by low-pressure chemical vapour deposition on asilicon substrate. Electron beam lithography, followed by a series of plasma and wetchemical etches, was used to form the released nanobeam structure. The double-diskstructure was formed from a 158-nm sacrifical amorphous silicon layer sandwichedbetween two 340-nm-thick silica glass layers, all of which were deposited by meansof plasma-enhanced chemical vapour deposition. A high-temperature (1,050 K)thermal anneal was used to improve the optical quality of the as-deposited silica

layers. The microdisk pattern was fabricated by reactive ion etching, and thesandwiched a-Si layer was undercut by 6 mm from the disk edge using a sulphurhexafluoride dry release etch. This etch simultaneously undercut the silicon substrateto form the underlying silicon pedestal. The size of the final air gap between the silicadisks was measured to be 138 nm due to shrinkage of the amorphous silicon layerduring annealing.

A fibre-taper optical coupling technique was used to couple in and couple outlight from the zipper and double-disk cavities. The fibre taper, which had extremelylow loss (88% transmission efficiency), was put into contact with the substrate nearthe cavities to mechanically anchor it during all measurements (thus avoidingpower-dependent movement of the taper due to thermal and/or optical forces). Anoptical fibre polarization controller, consisting of a series of circular loops of fibre,was used to selectively excite the TE polarized optical modes of both cavities.

RF spectra was measured by direct detection of the optical power transmittedthrough the cavities using a 125 MHz bandwidth photoreceiver (noise equivalentpower, NEP¼ 2.5 pW Hz21/2 from 0–10 MHz and 22.5 pW Hz21/2 from10–200 MHz, responsivity R¼ 1 A W21, trans-impedance gain G¼ 4� 104 V A21)and a high-speed oscilloscope (2 Gs s21 sampling rate and 1 GHz bandwidth). Apair of ‘duelling’ calibrated optical attenuators were used before and after the cavitiesto vary the input power to the cavity while keeping the detected optical power levelconstant. The measured electrical noise floor was set by the circuit noise of thephotodetector for the optical power levels considered in this work, corresponding to2125 dBm Hz21 near 10 MHz.

Received 12 October 2009; accepted 6 January 2010;published online 7 February 2010

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AcknowledgementsThe authors would like to thank T. Johnson and R. Perahia for their help with deviceprocessing, and T. Alegre for helpful discussions. This work was supported by the NationalScience Foundation (EMT grant no. 0622246 and CIAN grant no. EEC-0812072 throughthe University of Arizona) and through a seedling program from the Defense AdvancedResearch Projects Agency (grant no. HR0011-08-0002).

Author contributionsQ.L., J.R., R.C. and M.E. performed the majority of the fabrication and testing of devices.Q.L., J.R. and D.C. performed the bulk of the analysis, along with optical and mechanicalmodelling. O.P. and K.J.V. contributed to the planning of the measurements. All authorsworked together to write the manuscript.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper at www.nature.com/naturephotonics. Reprints and permissioninformation is available online at http://npg.nature.com/reprintsandpermissions/.Correspondence and requests for materials should be addressed to O.P.



www.nature.com/naturephotonicshttp://npg.nature.com/reprintsandpermissions/mailto:[email protected]://www.nature.com/doifinder/10.1038/nphoton.2010.5www.nature.com/naturephotonics

Coherent mixing of mechanical excitations in nano-optomechanical structuresMethodsFigure 1 Illustration of the double-disk and zipper nano-optomechanical structures.Figure 2 Optical renormalization of mechanical vibrations in the zipper cavity.Figure 3 Coherent mechanical mode mixing in the double-disk cavity.Figure 4 Illustration of the analogue to atomic and coupled-resonator systems.ReferencesAcknowledgementsAuthor contributionsAdditional information

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Coherent mixing of mechanical excitations in nano … · Qiang Lin, Jessie Rosenberg, Darrick Chang, Ryan Camacho, Matt Eichenﬁeld, Kerry J. Vahala and Oskar Painter* The combination