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Irene Sánchez Arribas, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Eva M. Weig

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[Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical Resonator](https://mdr.nims.go.jp/datasets/3ad53e98-cf2c-47b0-9388-ee6503dcc600)

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Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical ResonatorRadiation Pressure Backaction on a Hexagonal Boron NitrideNanomechanical ResonatorIrene Sánchez Arribas, Takashi Taniguchi, Kenji Watanabe, and Eva M. Weig*Cite This: Nano Lett. 2023, 23, 6301−6307 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Hexagonal boron nitride (hBN) is a van der Waalsmaterial with excellent mechanical properties hosting quantumemitters and optically active spin defects, with several of them beingsensitive to strain. Establishing optomechanical control of hBN willenable hybrid quantum devices that combine the spin degree offreedom with the cavity optomechanical toolbox. In this Letter, wereport the first observation of radiation pressure backaction at telecomwavelengths with a hBN drum-head mechanical resonator. Thethermomechanical motion of the resonator is coupled to the opticalmode of a high finesse fiber-based Fabry−Peŕot microcavity in amembrane-in-the-middle configuration. We are able to resolve theoptical spring effect and optomechanical damping with a singlephoton coupling strength of g0/2π = 1200 Hz. Our results pave the way for tailoring the mechanical properties of hBN resonatorswith light.KEYWORDS: optomechanics, microcavity, hexagonal boron nitride, nanomechanical resonators, 2D materialsPart of the current research efforts in the field of cavityoptomechanics1 focuses on implementing nanomechan-ical resonators based on low dimensional materials, such ascarbon nanotubes,2−5 nanowires,6 or van der Waals materi-als.7−10 Their low mass makes them very sensitive andresponsive to external stimuli, and their large zero-pointfluctuations xzpf provide large optomechanical single-photoncouplings g0, necessary to manipulate the mechanical or opticalstates in the quantum regime.11−13Hexagonal boron nitride (hBN) has recently caught theattention of the optomechanics community. Its large in-planeYoung’s modulus of 392 GPa 14 and breaking strain of 12.5% 15together with the recent development of patterning meth-ods16,17 have opened the door to the engineering ofmechanical resonators with high quality factors and tunablefrequencies. This layered crystal is transparent in the visibleand infrared part of the optical spectrum due to its widebandgap of 6 eV 18 and therefore is less prone to photothermalheating than other van der Waals materials like graphene. Sofar, photothermal forces, rather than radiation pressure, wereresponsible for the optomechanical backaction observed inother two-dimensional resonators in the optical regime,limiting their performance.19−21Moreover, perhaps one of the most appealing characteristicsof hexagonal boron nitride is its large variety of single-photonemitters. They span from the UV to the low infrared,22,23 aretunable via strain or electric fields,24−27 and are capable ofoperating at room temperature and up to 800 K.28 Exper-imental works over the past three years29−31 have demon-strated optically detected magnetic resonance in negativelycharged boron vacancy defects (VB−), together with coherentcontrol of the spins.32,33 A recent study on these vacancies hasshown control at room temperature of a protected qubit basis,with a coherence time as high as 0.8 μs.34 These spin defectsare also sensitive to strain,35,36 making hBN a promisingmaterial to develop the field of spin-mechanics and spin-optomechanics.37,38 Indeed, these hybrid systems could enablethe communication between photons and qubits within hBN, anew step toward quantum networks and quantum communi-cation and an alternative system to the leading platform ofnitrogen vacancy centers in diamond.Given these remarkable properties, it is natural to study howto use radiation pressure to control and modify the mechanicalproperties of hBN resonators. However, optomechanicaldynamical backaction has not yet been observed withresonators made of this van der Waals material. Indeed, theattempts to perform cavity optomechanical experiments withhBN resonators are scarce: the first available platforms for hBNcavity optomechanics experiments are mechanically exfoliatedhBN resonators coupled to the near-field of a microdiskReceived: February 10, 2023Revised: June 22, 2023Published: July 17, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society6301https://doi.org/10.1021/acs.nanolett.3c00544Nano Lett. 2023, 23, 6301−6307Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on July 29, 2023 at 01:55:23 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Irene+Sa%CC%81nchez+Arribas"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Eva+M.+Weig"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c00544&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/14?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/14?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/14?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/14?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00544?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://acsopenscience.org/open-access/licensing-options/cavity.39,40 Shandilya et al.39 were able to measure the thermalmotion of a hBN beam through its optomechanical interactionwith a silicon microdisk cavity in the telecom regime for thefirst time, with a sensitivity of 0.16 pm/ Hz . Nevertheless, nooptomechanical backaction was observed.In this paper, we report the first demonstration of radiationpressure backaction with a hexagonal boron nitride circulardrum-head resonator at room temperature. We achieve this byinserting the nanomechanical resonator in a high finesse fiber-based Fabry−Peŕot microcavity41−44 in a membrane-in-the-middle configuration,1,43,45−48 featuring an optical mode waist8 times smaller than the drum diameter. The correspondingsmall mode volume, intrinsic to fiber cavities, is critical to avoidclipping of the cavity mode by the edges of the drum,maintaining the high finesse of the cavity. It allows reducingthe resonator’s diameter down to some tens of micrometers,which is crucial as large area few-layer flakes are difficult toobtain through mechanical exfoliation.Figure 1 shows the sample used in this work. It consists of acircular resonator made of a mechanically exfoliated hexagonalboron nitride flake. The flake rests on a 40 μm diametercircular hole patterned on a broad 500 × 281 μm2 stripe. Thehole and the stripe are etched from a commercially availablelow stress 200 nm thick SiN membrane (Norcada) via standardphotolithography and reactive ion etching. The crystal istransferred onto the hole through the all-dry viscoelasticmethod49 and cleaned with O2 plasma (300 W, 100 sccm, 90Pa, 3 min). Its thickness is measured with an atomic forcemicroscope in tapping mode, revealing a thickness of 68 nm(Figure 1b, inset). Finally, the 200 μm thick silicon frame ofthe SiN membrane is cleaved along the white dashed line inFigure 1a to allow inserting the sample into the fiber-basedFabry−Peŕot microcavity.We identify the mechanical resonances by systematiccharacterization in a standard Michelson interferometer.Following the work from Jaeger et al.,50 we use theexperimentally determined effective mass to characterize thedegree of mechanical hybridization of the hBN resonator withthe mechanical modes of the SiN stripe supporting the flake(Supporting Information). We observe a series of mechanicalmodes between 1500 kHz and 1700 kHz that are localized inthe circular hBN resonator and possess effective masses morethan 1 order of magnitude below that of pure SiN modes,which we identify as hybridized modes with a strong hBNcharacter. Subsequently, the sample is placed in a high finesseFabry−Peŕot microcavity, operated at λ = 1550 nm. The cavity,illustrated in Figure 2a, consists of two fiber mirrors concavelyshaped by CO2-laser ablation with a radius of curvature of190.8 μm for the input fiber (single mode) and 135.6 μm forthe output fiber (multimode), respectively, separated by alength of Lcav = 41.8 μm. The calculated beam waist is w0 =5.1 μm. The fiber ends are ion beam sputtered with adistributed Bragg reflector (LaserOptik GmbH) to obtain amirror transmission of 10 ppm around λ = 1550 nm. Each ofthe fiber mirrors is glued to a shear piezo that allows tuning ofthe cavity length by ±0.7 μm. By scanning the cavity length, weextract the cavity line width κ/2π = 18.5 MHz and thepolarization mode splitting Δνpol = 133.5 MHz. The free-spectral range and empty cavity finesse are ωFSR/2π = 3.584THz and = 194 000, respectively. More details on the cavitycharacterization methods can be found elsewhere.41 Thesample is placed in a 5-axis positioning system (SmarAct)that allows aligning the sample to the cavity mode axis (z-axisin Figure 2a) and scanning it along the x, y, and z directions.The system is operated at room temperature, in vacuum at apressure below 10−6 mbar, and inside an acoustic isolation boxto damp spurious mechanical vibrations. Figure 2b depicts asimplified version of the setup. To perform dynamicalbackaction experiments, we lock the cavity length to areference laser (NKT Koheras Basik E15, λ = 1550 nm)referred to in the following as lock laser. The lock laser isphase-modulated at ωmod/2π = 30 MHz with an electro-opticmodulator (EOM). The light transmitted through the cavity,recorded by a fast photodetector (PD), is demodulated at thesame frequency and sent to a PI controller that sends thefeedback signal to a piezoelectric converter (PZT) to performthe lock. We use the Y-quadrature of the demodulated signal aserror signal for the lock. The reflected light from the lock laseris equally demodulated and fed to a spectrum analyzer thatrecords the mechanical spectra. We use an additional probeFigure 1. hBN circular membrane. (a) Bright-field microscopy imageof the suspended flake (blue) atop a 40 μm diameter hole patternedon a stripe processed from a commercial SiN membrane (yellow).The frame of the SiN membrane is cleaved along the white dashedline next to the stripe to allow inserting the mechanical resonatorinside the optical cavity. (b) Zoom into the black rectangle from (a).The inset shows the AFM height profile along the white line in thetop-right corner of the micrograph.Figure 2. Representation of the experimental setup. (a) The Fabry−Peŕot cavity is formed by two fiber mirrors (light blue rods) separatedby a length of Lcav = 41.8 μm. The suspended hBN (dark blue) on theSiN membrane (SiN in green, Si frame in gray) is inserted betweenthe mirrors by a positioner stack allowing tilt corrections and positionscans along the x, y, and z directions. (b) The cavity length is fixed byapplying a DC voltage to the top piezo (PZT). The lock laser isphase-modulated at ωmod with an electro-optic modulator (EOM),and its transmission signal is demodulated at ωmod and fed to a PIcontroller. The latter sends the feedback signal to the bottom piezo,stabilizing the cavity length. The reflection photodetector (PD) signalis sent to a spectrum analyzer (SA) to characterize the mechanicalspectra. An additional tunable probe laser is used to measureoptomechanical dynamical backaction effects.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00544Nano Lett. 2023, 23, 6301−63076302https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00544/suppl_file/nl3c00544_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00544?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aslaser (New Focus TLB-6700) to sweep the wavelength acrossthe cavity resonance and exert an optomechanical force. Bothlasers are operated at orthogonal cavity polarizations to avoidinterference effects.The dispersive optomechanical coupling G = ∂ωcav/∂z 48 isobtained by measuring the dependence of the detuning of thecavity resonance frequency Δ(z) as a function of the sampleposition z along the cavity mode axis. To that end, the systemis operated in an open-loop configuration, and both piezos arescanned symmetrically. We use only the lock laser and recordthe cavity transmission and reflection. We observe a sinusoidalpattern of the detuning (blue dots, Figure 3a) that reaches amaximum of Δ/2π = 600 GHz when the sample is placed atthe cavity antinodes. We verify that the cavity detuningoriginated solely from the hBN drum and has no contributionfrom the surrounding SiN by performing the same measure-ment on the second, empty 40 μm diameter hole (SupportingInformation) shown in Figure 1a. G is directly extracted fromthe measurement by performing a numerical derivative (bluedots, Figure 3b). We observe a maximum of |G/2π| = 2.5GHz/nm. As expected for a membrane-in-the-middle system,the quadratic dispersive coupling G(2) = ∂2ωcav/∂z2 reaches amaximum at the cavity nodes and antinodes,47,51 of value |G(2)/2π| = 20 MHz/nm2 for our system (blue dots, Figure 3c).The quadratic coupling is extracted by smoothing the datafrom Figure 3b with a spline and computing its numericalderivative. The measurements are well reproduced by transfermatrix calculations52 (solid lines in Figure 3), with inputparameters of a flake thickness of 58 nm and flake refractiveindex of nhBN = 1.85. The reduced thickness originates from anadditional O2 cleaning step that etched the flake, which wasobserved as a change of color under an optical microscope.Any absorption or scattering from the flake will manifest as amodulation of the cavity line width κ, displayed in Figure 3d.The line width is calculated from the cavity transmission onresonance (see ref 41 for more details) and reaches a minimumvalue of κ/2π ≃ 40 MHz when the sample is placed at thecavity nodes. hBN has a negligible absorption coefficient attelecom wavelengths,53,54 and therefore the large cavity linewidths we observe cannot be attributed to optical absorption.Performing the same measurements shown in Figure 3d on theSiN membrane results in modulations of the same magnitude(Supporting Information) that cannot be explained consider-ing the absorption coefficient of SiN. This suggests that thelosses in our system are dominated by scattering to higherorder optical modes of the cavity originated by a samplemisalignment with respect to the cavity mode axis47,51 and notby remaining impurities from the transfer process. Thehypothesis is also consistent with the dips observed at theantinodes and the small scale variations (z < λ) of the cavityline width.47 The line width modulation translates into thedissipative coupling Gz= (Figure 3e) that we extract bysmoothing the data in Figure 3d and performing a numericalderivative. We highlight that dissipative coupling is more than3 orders of magnitude smaller than the dispersive coupling andis therefore negligible in our system.To perform dynamical backaction experiments, we place thehBN drum Δz = 13 nm away from the cavity node. From thecavity transmission, we obtain a loaded cavity line width of κ/2π = 39.8(2) MHz, yielding a loaded cavity finesse of =90 000. This sample position corresponds to a value of G/2π =330 MHz/nm and Gκ/2π = 0.19 MHz/nm, extracted from themeasurements in Figure 3. We lock the cavity length with alock power of Pl = 34.5 μW and at a frequency ωcav detunedfrom the lock laser frequency ωl by Δl/2π = (ωl − ωcav)/2π =−50 MHz. We choose this value as a compromise betweenhaving a good signal in reflection and minimizing thebackaction from the lock. To transform the measured powerspectral densities SV in volts into displacement power spectradensities Sx, we use as reference the thermomechanical spectraof a well characterized SiN mode at 164.0 kHz of knowneffective mass meff = 2.3 μg when probed at the center of thedrum-head, following the calibration procedure described in ref55. This mode is suitable for calibration because it does notshow optomechanical coupling. The conversion factor betweendisplacement and voltage is 3 pm/mV. Figure 4 shows thespectrum of the SiN mode used for calibration, together withthe spectrum of the hBN mode used to perform backactionexperiments. The solid lines are fits using the displacementpower spectral density formulaSk Tm( )4(( ) )x0 Beff 02 2 202 2=+ (1)where T is the bath temperature, kB is the Boltzmann constant,and the only fit parameters are the mechanical resonanceFigure 3. Static optomechanical couplings. (a) Cavity detuning (dots) vs sample position z along the cavity mode axis. The coordinate z = 0corresponds to the sample sitting in an optical field node. (b) Dispersive and (c) quadratic dispersive coupling. The solid lines in (a), (b), and (c)are the result of transfer matrix calculations. (d) Cavity line width modulation and (e) corresponding dissipative coupling.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00544Nano Lett. 2023, 23, 6301−63076303https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00544/suppl_file/nl3c00544_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00544/suppl_file/nl3c00544_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00544/suppl_file/nl3c00544_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00544?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asfrequency Ω0, the mechanical line width Γ0, the effective massmeff, and an additional constant noise floor. The fit yields,assuming the sample is thermalized with the environment, Ω0/2π = 1592.671(4) kHz, Γ0/2π = 525(10) Hz, quality factor Q= 3000(50), and meff = 1.2(1) ng for the hBN mode. Theinferred zero-point fluctuations are xzpf = m/(2 )eff 0 =2.1(1) fm which lead to a single-photon coupling strength ofg0/2π = Gxzpf/2π = 330 MHz/nm × 2.1 fm = 693 Hz. Since theeffective mass was measured with the lock red detuned, thecalculated value of g0 is a lower limit to the real value. Finally,from the noise floor level we obtain a sensitivity of 15 fm/Hz .The mechanical resonator will experience an optomechan-ical force when the frequency of the probe laser ωp is sweptacross the cavity resonance, with Δp = ωp − ωcav the probedetuning. This leads to the optical spring effect, a shift of themechanical frequency Ωm2 = Ω02 + δ(Ω2) that, whenneglecting the dissipative coupling, is given by48g( ) 2( ) ( /2)( ) ( /2)202 0 p0 p2 20 p0 p2 2ikjjjjjjy{zzzzzz=++ ++ (2)where g = n gp 0 is the dispersive optomechanical couplingstrength, np is the circulating probe photon number inside thecavity, and g0 = Gxzpf the single-photon coupling strength. Themechanical line width experiences a shift as well, Γm = Γ0 +Γopt, with Γopt the optomechanical damping. Consideringnegligible dissipative coupling, the latter reads48g21( ) ( /2)1( ) ( /2)opt20 p2 20 p2 2ikjjjjjjy{zzzzzz=+ ++ (3)In Figure 5 we demonstrate dynamical backaction bymeasuring the optical spring effect (Figure 5b) andoptomechanical damping (Figure 5c) of the hBN mechanicalmode in Figure 4. We scan the probe frequency across thecavity resonance using a constant probe power of Pp = 11 μW.For each probe detuning, we extract the circulating probephoton number np inside the cavity from its transmission andmeasure the thermomechanical spectrum. We obtain theeffective mechanical resonance frequency Ωm and effective linewidth Γm by fitting eq 1 to the spectra. The circulating probephoton number (Figure 5a) appears to be nonlinear and isasymmetric with respect to probe detuning. Starting frompositive detunings, the photon number increases in aLorentzian fashion until Δp/2π = 35 MHz. Then, it increasesalmost linearly until reaching its maximum at Δp/2π = 0. Afterthat, it drops with decreasing detuning, according to aLorentzian trend. This behavior indicates the presence of anonlinearity in the system that we will discuss in the nextparagraphs.The backaction of the probe leads to a softening (stiffening)of the mechanical frequency for negative (positive) detunings(Figure 5b, red dots), with a maximum frequency shift of |δΩ/2π| = 3 kHz for negative detunings. In addition, the naturalfrequency has a slight negative slope stemming from drifts inthe lock that originate from changes of the sample position dueto slow temperature drifts in the laboratory. The solid line is afit to the optical spring using eq 2 together with a linearbackground. For the fit, we exclude the data points where thephoton number shows a nonlinear response (0 < Δp/2π < 35MHz, gray shaded area in Figure 5b and Figure 5c). We alsoassume negligible dissipative coupling and feed the equationwith the experimentally measured probe photon number np.The only free parameters for the fit are g0 and the cavity linewidth κ. The best fit yields g0/2π = 1200(20) Hz and κ/2π =54(1) MHz. The data show an asymmetry around the probedetuning that is not predicted by the linear cavityoptomechanics theory (eqs 2 and 3). We discard the possibilityof an asymmetry induced by the dissipative coupling becauseof the small value of the single-photon dissipative couplingstrength, g0,κ/2π = Gκxzpf/2π = 0.4 Hz. The asymmetry in theoptical spring could be attributed to nonlinearities in thesystem given the large photon number reached in theexperiments (np > 105). Indeed, a cavity optomechanicalFigure 4. Displacement power spectral density (PSD) measured withthe locked cavity. Two SiN modes are shown in the lower frequencyrange. The left one at 164.0 kHz, of known effective mass meff =2.3 μg, is used to calibrate the spectra. The higher frequency rangeshows the hBN mode used for dynamical backaction experiments.Solid lines are theoretical fits using eq 1 with an additional constantnoise floor.Figure 5. Radiation pressure backaction. (a) Experimental probephoton number np vs probe detuning Δp. (b) Optical spring effect(red dots) and theoretical regression (solid line). The gray regioncorresponds to the regime where the photon number shows anonlinear response and its data are excluded in the fit. (c) Mechanicaldamping (orange dots) and theory calculation (solid line) with theparameters from the fit in (b). The error bars for Ωm and Γm,generated from the fits to eq 1, are omitted because they are notappreciable in the figure.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00544Nano Lett. 2023, 23, 6301−63076304https://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544?fig=fig5&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00544?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-assystem incorporating a negative Kerr nonlinearity canreproduce the asymmetries we observe.56 Additional experi-ments should be conducted in the future to clarify the origin ofthe nonlinearity in the system. This could be due to, forexample, the radiation pressure force itself57 or to thermaleffects given the absorption of the mirrors’ coating.42Figure 5c shows the effective line width Γm (orange dots) asa function of the probe detuning. The solid line is the result ofeq 3 using the parameters obtained from the fit of the opticalspring. We observe a larger broadening (optomechanicalcooling) than what is predicted by the theory for negativedetunings, whereas the narrowing (optomechanical heating)found for positive detunings is less pronounced compared tothe theoretical model. This behavior also matches the one of acavity optomechanical system with a negative Kerr non-linearity,56 which supports the hypothesis of a nonlinearitypresent in the system. In addition, the measured line widths arebroadened due to unavoidable mechanical fluctuations of thepositioning system and the fiber mirrors. The fluctuationstranslate into cavity length noise, which directly affects thedetuning and therefore turns into mechanical frequencynoise.41,43 Because each experimental mechanical spectrum isthe average of the mechanical response during the acquisitiontime of the spectrum analyzer, the experimental resonancefrequency matches on average the theoretical value, besides theasymmetry already discussed. The mechanical line width(Figure 5c), however, is broadened especially for detunings atwhich Ωm depends strongly on the detuning. The positioningsystem’s mechanical fluctuations are also the limiting factor ofthis experiment and the reason we are unable to successfullylock the cavity at sample positions with a larger coupling G.To conclude, we have demonstrated radiation pressurebackaction on an hBN resonator at telecom wavelengths. Themechanical performance of our sample was limited by thehybridization to the modes of the low stress SiN membraneresonator and the mechanical imperfections originating fromthe dry transfer process. The former can be improved by usinghigh stress Si3N4 as a support for the hBN drums, pushing theSi3N4 resonances to higher frequencies and allowing resolutionof the distinct mode shapes, the latter by using more gentletransfer mechanisms like a wet transfer.50 The setup presentedin this work is very versatile: a careful design of the mirrorcoatings would enable the incorporation of several wave-lengths, enabling photoluminescence experiments on-site. Thiswill open the door to new ways of studying the straindependence of hBN defects with an additional control of themechanical properties through light and a new step forwardtoward the realization of spin-optomechanics with this van derWaals material.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00544.Evidence of sample bulging, optical losses introduced bythe circular frame, mechanical modes characterization,influence of the SiN membrane on the optomechanicalcouplings, and characterization of the dispersiveoptomechanical coupling of additional hBN devices(PDF)■ AUTHOR INFORMATIONCorresponding AuthorEva M. Weig − Department of Electrical Engineering, School ofComputation, Information and Technology, TechnicalUniversity of Munich, 85748 Garching, Germany; MunichCenter for Quantum Science and Technology (MCQST),80799 Munich, Germany; TUM Center for QuantumEngineering (ZQE), 85748 Garching, Germany;Email: eva.weig@tum.deAuthorsIrene Sánchez Arribas − Department of Electrical Engineering,School of Computation, Information and Technology,Technical University of Munich, 85748 Garching, Germany;orcid.org/0000-0003-1903-1678Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba, Ibaraki 305-0044, Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba, Ibaraki305-0044, Japan; orcid.org/0000-0003-3701-8119Complete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c00544Author ContributionsI.S.A. fabricated the samples, constructed the setup, and carriedout all the experiments. I.S.A. and E.M.W. analyzed andinterpreted the data. T.T. and K.W. grew the hBN crystals.I.S.A. and E.M.W. contributed to writing the manuscript.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSWe are grateful to Avishek Chowdhury, Francesco Fogliano,and Felix Rochau for useful discussions. We also thank DavidHunger for his assistance in the fabrication of the fiber mirrors.I.S.A. acknowledges support from the European Union’sHorizon 2020 research and innovation program under theMarie Sklodowska-Curie Grant Agreement 722923 (OMT).I.S.A. and E.M.W. acknowledge the Bavarian State Ministry ofScience and Arts via the project EQAP. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grants19H05790, 20H00354, and 21H05233).■ REFERENCES(1) Aspelmeyer, M.; Kippenberg, T. J.; Marquardt, F. CavityOptomechanics. Rev. Mod. Phys. 2014, 86, 1391−1452.(2) Favero, I.; Karrai, K. Cavity Cooling of a NanomechanicalResonator by Light Scattering. New J. 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