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ARTICLESPUBLISHED ONLINE: 20 JANUARY 2013 | DOI: 10.1038/NPHYS2527

Slowing, advancing and switching of microwavesignals using circuit nanoelectromechanicsX. Zhou1,2, F. Hocke3, A. Schliesser1,2, A. Marx3, H. Huebl3*, R. Gross3,4 and T. J. Kippenberg1*

The parametric coupling of electromagnetic and mechanical degrees of freedom gives rise to a host of optomechanicalphenomena. Examples include quantum-limited displacement measurements, sideband cooling or amplification of mechanicalmotion. Likewise, this interaction provides mechanically mediated functionality for the processing of electromagneticsignals, such as microwave amplification. Here, we couple a superconducting niobium coplanar waveguide cavity to ananomechanical oscillator, and demonstrate all-microwave field-controlled tunable slowing and advancing of microwavesignals, with millisecond distortion-free delay and negligible losses. This is realized by using electromechanically inducedtransparency, an effect analogous to electromagnetically induced transparency in atomic physics. Moreover, by temporallymodulating the electromechanical coupling and correspondingly the transparency window, switching of microwave signalsis demonstrated and its temporal dynamics investigated. The exquisite temporal control gained over the electromechanicalcoupling provides the basis for realizing advanced protocols for storage of both classical and quantum microwave signals.

Microwave superconducting coplanar waveguide (CPW)resonators are key elements in sensitive astrophysicaldetectors1 and circuit quantum electrodynamics2. In

combination with artificial atoms in the form of superconduct-ing qubits3,4, they now provide a technologically promising andscalable platform for quantum information processing tasks2,5–8.Coupling these circuits, in situ, to other quantum systems, such asmolecules9,10, spin ensembles11,12, quantum dots13 or mechanicaloscillators14,15, has been explored to realize hybrid systems withextended functionality. Coupling of superconducting resonators tonano- and micromechanical oscillators14–17 allows exploring cavityoptomechanical phenomena14,15 and has led to efficient transduc-tion of nanomechanical motion to microwave fields with an impre-cision below the level of the zero-pointmotion18, electromechanicalmicrowave sideband cooling to the quantum ground state17,19, andelectromechanical amplification of microwave signals20. Moreover,the electromechanical coupling modifies the microwave responseleading to the electromechanical equivalent of the phenomenon ofoptomechanically induced transparency21,22. Here we demonstratea class of control phenomena over the microwave field with asuperconducting circuit nanoelectromechanical system. Exploit-ing the coupling of a superconducting microwave cavity to ananomechanical oscillator, we demonstrate a tunable group delay(positive and negative) in microwave pulse propagation, mediatedby the nanomechanical oscillator’s response. The high mechanicalquality factor allows a delay of microwave pulses exceeding 3ms,corresponding to an effective coaxial cable length of hundreds ofkilometres. Importantly, this delay is achieved with negligible lossesand pulse distortion. Moreover, we explore the circuit nanoelec-tromechanical response to a time-dependent control field. Thetemporal modulation of the electromechanical coupling is requiredfor a series of advanced protocols including quantum state transferand storage23,24, fast sideband cooling25, and switching, modulationand routing of classical and quantum microwave signals. To thisend, we demonstrate all-microwave field-controlled switching and

1École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland, 2Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany,3Walther-Meißner-Institut, 85748 Garching, Germany, 4Technische Universität München, 85748 Garching, Germany. *e-mail: hans.huebl@wmi.badw.de;tobias.kippenberg@epfl.ch.

show that counterintuitive regimes can be found in which theswitching time can be much faster than the slow mechanicaloscillator energy decay time of the high-Q oscillator. Finally, wealso demonstratemapping of themechanical (Duffing) nonlinearityinto the microwave domain.

We investigate these phenomena in a niobium (Nb) supercon-ducting circuit nanoelectromechanical system (similar in geometryto the ones studied in refs 16,17) consisting of a quarter-wavelengthCPW resonator1 (Fig. 1), parametrically coupled to a nanomechan-ical oscillator, consisting of a stoichiometric, high-stress Si3N4 beamcoated with Nb. The microwave resonator studied in this workexhibits a fundamental resonance frequency of ωc= 2π×6.07GHzand has a linewidth of κ = 2π× 742 kHz of which κex = ηcκ =2π× 338 kHz are due to external coupling to the feedline. TheNb/Si3N4 composite nanomechanical beam has dimensions of60 µm× 140 nm× 200 nm and shows at cryogenic temperaturesvery low dissipation (Qm> 105), with a damping rate of Γm= 2π×9Hz resonating atΩm=2π×1.45MHz. This system thus resides inthe resolved sideband regime as Ωm>κ . The thermal decoherencerate of the mechanical oscillator is Γmnm ∼= 2π× 21 kHz, wherenm is the thermal equilibrium phonon occupancy at the dilutionrefrigerator temperature of approximately 170mK. At an evenlower temperature, of approximately 30mK, we observe an increasein the Q factor to 0.6 × 106 and a reduction of the thermaldecoherence rate to Γmnm∼= 2π×1.18 kHz. These temperatures arefar below the superconducting transition temperature of Nb (9.2 K)and the thermal excitation of the microwave cavity is significantlysuppressed, as hωc/kB = 288mK, where h is the reduced Planckconstant and kB is the Boltzmann constant.

The interaction between the mechanical oscillator and the mi-crowave CPW resonator is formally equivalent to the optomechan-ical interaction14,15 and quantified by the vacuum coupling rate g0(ref. 26) in the corresponding interactionHamiltonian

Hint= hg0(am+ a†m)np (1)

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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS2527

Frequency detuning (Hz)

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Figure 1 | Superconducting circuit nanoelectromechanical system.a, False-colour scanning electron microscopy image of aquarter-wavelength CPW resonator, coupled to a CPW feedline. The 6 µmgaps are patterned by etching through the Nb layer (yellow) down to the Si(green). b, False-colour scanning electron microscopy image (yellow: Nb,green: Si, violet: Si3N4) of a 30 µm long mechanical beam integrated in themicrowave cavity. Note that the beam investigated in this work hasdimensions of 60 µm × 140 nm×200 nm. c,d, A magnified view, showingthe mechanical beam released from the Si substrate. e, Measurementset-up with a frequency-modulated pump tone on cavity resonance withΩmod=Ωm−2π×40 Hz and a modulation index of2π×80 Hz/Ωmod≈ 5.5× 10−5 as the radiofrequency (RF) input, and ahomodyne RF readout after signal amplification at 4 K with a high electronmobility transistor (HEMT). f, Mechanical thermal noise spectrum and thecalibration peak as measured at the Q output of the mixer. g, Calibratedfrequency noise spectral density Sνν (blue dots, ν≡Ω/2π) of themechanical beam, and Lorentzian fit (black). h, The vacuum coupling rateg0 derived from two groups (red and yellow) of measurement, with a 4 dBpower difference in the modulated input tone.

where np is the intracavity photon number operator, and amand a†

m are the ladder operators of the mechanical oscillator.The vacuum coupling rate g 0 in equation (1) is the product ofthe electromechanical frequency pulling parameter G= (dωc/dx),denoting the cavity resonance frequency change onmechanical dis-placement, and the mechanical resonator’s zero-point fluctuationxzpf=

√(h/2meffΩm)≈30 fm, wheremeff≈7 pg is the effective mass

of the beam. The coupling rate g 0 is calibrated by applying a knownfrequency modulation to a microwave tone coupled into the cavity(see Supplementary Information and ref. 26 for details; Fig. 1e). Thespectrum of the homodyne readout is shown in Fig. 1f,g, yieldinga measured coupling rate of g 0 = 2π× (1.26± 0.05)Hz, a valuethat, given the chosen calibration procedure, is independent of themicrowave power reaching the CPW cavity after several stages ofattenuation in the refrigerator.

In our system, the effective radiation pressure force thatis reflected by the electromechanical interaction Hamiltonian

(F = i[Hint,p]/h) gives rise to amodification of the dynamics of themechanical oscillator. Moreover, it leads to an interaction betweentwomicrowave fields sent simultaneously into the cavity20,27,28. Thislatter phenomenon, which is also referred to as electromechanicallyinduced transparency, arises as the overall radiation pressure of thetwo fields, a strong pump at frequency ωp and a weak probe fieldat frequency ωp+Ω , drives the motion of the mechanical oscillatorat the two fields’ beat frequency Ω . The mechanical oscillation isresonantly enhanced if the frequency difference Ω between the twofields coincides with Ωm. The driven mechanical motion, in turn,generates Stokes- and anti-Stokes sidebands on the pump field,which can interfere with the probe field leading to an inducedtransparency (or amplification for a blue-detuned pump20,22). Theresulting transmission coefficient of the probe field for the presentcavity waveguide geometry is given by

tp≈ 1−ηcκ

2χaa

1+g 20 a2χxxχaa

(2)

where χ−1aa =−i(Ω + ∆)+ (κ/2) is the bare susceptibility of thecavity and χ−1xx = −i(Ω −Ωm)+ (Γm/2) is the bare mechanicalsusceptibility. The approximation in equation (2) is valid when theStokes scattering of the pump field is negligible (see SupplementaryInformation for the complete model). Here, a2= np=〈np〉 denotesthe expectation value of the intracavity pump photon numberand ∆ = ωp − ωc + Gx is the effective detuning of the pumpfield with the static mechanical displacement x . Figure 2 showsthe measured probe transmission in the presence of a red-detuned pump ∆ = −Ωm, resulting in an induced transmissionwindow, which coincides with the microwave-cavity resonance.The width of this window in the weak coupling regime isgiven by the effective mechanical damping rate Γeff ≈ Γm+Γdba,with Γdba = 4g 2

0 np/κ resulting from radiation-pressure-induceddynamical backaction17,19,29–33.

We study this response experimentally using a vector networkanalyser to generate the probe tone, and analyse its directtransmission, in this case without the homodyne interferometer. Amicrowave generator provides the pump tone that is simultaneouslycoupled into the cavity (see Supplementary Information fora more detailed description of the employed measurementset-up). A systematic investigation of the electromechanicaleffective damping as a function of pump detuning and pumpintracavity photon number shows excellent agreement withtheory (Fig. 2c,d). Importantly, these measurements, together withthe independently determined g0, can be used to provide anindependent calibration of the intracavity pump-photon numbernp, and therefore the microwave attenuation in the refrigeratorbefore entering the microwave cavity (62 dB attenuation in thismeasurement set-up).

Interestingly, the nanoelectromechanical system shows signif-icant deviations from the standard electromechanically inducedtransparency behaviour already for moderate pump power (np ≈3.9× 106) if the probe power is increased to more than −91 dBm(Fig. 2e). Strongly asymmetric line shapes of the transmissionwindow are observed. This asymmetry increases with an increasingprobe power—much in contrast to the fully linear theory. Thisnonlinearity is a direct consequence of the fact that the trans-mission window is modified by scattering of photons inducedby the mechanical oscillator. The oscillator exhibits a Duffingnonlinearity34,35 with a critical amplitude of about 2 nm and aDuffing parameter β = 1.2×1012 Nm−3, which is compatible withearlier experiments36. This value is independently determined ina set of measurements, in which the oscillator is driven by alow-frequency a.c. voltage applied externally through the d.c. portof a bias-tee (see Supplementary Information for the details ofthe calibrationmeasurement). The full electromechanical dynamics

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NATURE PHYSICS DOI: 10.1038/NPHYS2527 ARTICLES

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effΓ

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Figure 2 | Electromechanical and nanomechanical response. a, Thefrequency of the pump tone is detuned by ∆ from the cavity resonancefrequency. The probe tone has an offset frequency Ω from the pump tone.The probe tone is tuned over the cavity resonance, which has a linewidth ofκ . b, The probe transmission in the presence of a red-detuned pumptone (∆≈−Ωm). Two transparency windows are observed, in thehighlighted red rectangle and shown in the inset, corresponding to thein-plane (mode 1) and out-of-plane (mode 2) mechanical oscillation. Thetwo modes are 38.3 kHz apart in frequency. c, Damping rate versusintracavity pump photon number with pump detuning ∆=−Ωm (blue:in-plane mode, red: out-of-plane mode) together with linear fits (Γeff ∝ np;ref. 31). The probe tone has a power of−99 dBm. The inset shows a typicaltransparency window where the mechanical damping rate Γeff is derived.The two modes have close intrinsic damping rates. The coupling rate g0 ofthe in-plane mode is three times as large as that of the out-of-plane mode,and is chosen to be studied in this work. d, Damping rate versus pumpdetuning (points) and fits (lines) according to the model of dynamicalbackaction. The pump tone has constant powers of−57 dBm (blue),−59 dBm (red) and−64 dBm (purple), which correspond to intracavityphoton numbers of 1.1× 107, 7.2× 106 and 2.3× 106 at the maximumdynamical backaction damping, when the pump tone is optimally detuned(∆opt=−

√Ω2

m+(κ/2)2). The probe tone has a constant power of−109 dBm. e, Electromechanically induced transparency with Duffingresponse. The intracavity pump photon number is 3.9× 106, the values ofthe probe tone power are−99,−95,−91,−87,−83 and−79 dBm,respectively.

(including the Duffing nonlinearity for β 6= 0) are captured by theset of equations in the Fourier domain:

A(−i(Ω+∆)+

κ

2

)=−iag0X/xzpf+

√ηcκ/2 S (3)

meff(Ω 2m−Ω 2

− iΓmΩ)X+3β|X |2X =−2hAag0/xzpf (4)

for the amplitude of the intracavity probe field A and themechanical oscillation X . Here, in equations (3) and (4), weassume the resolved-sideband regime (Ωm κ), as well as alarge mechanical quality factor Qm a/A, so that the dynamic(resonant) response of the mechanical oscillator X ∝ aA is much

larger than the static displacement x ∝ a2 (see the SupplementaryInformation for details). Furthermore, |S|2 denotes the powerof the probe field sent towards the cavity. As seen in Fig. 2e,the Duffing nonlinearity is thus mapped directly onto thetransmission of the probe field, yielding nonlinear behaviour forprobe powers as low as −91 dBm sent towards the cavity. Themechanically resulting bistability of the microwave transmission,as the electrically implemented counterpart37, could be used fornon-volatile memory applications38.

For lower probe powers, the radiation-pressure-induced oscil-lation amplitude of the mechanical mode remains well below thethreshold for nonlinear oscillations. In this regime, the transmissionof the probe field is well described by equation (2). Importantly,the presence of the pump tone does not only induce a strongmodification of the transmission of the probe field, but also leadsat the same time to a fast variation of the phase φ = arg(tp) of thetransmitted probe field across the transmission window. This canlead to significant group delays21,22,39,40, in analogy to that achievedwith the electromagnetically induced transparency in atomic41 andin solid-state media42. The delay is given by

τg=∂φ

∂Ω(5)

for a microwave probe pulse whose centre frequency falls into thetransmission window. In particular, in the resolved-sideband caseand for red-detuned pumping (κ < Ωm = −∆), the group delayin equation (5) is given by (see Supplementary Information fordetails and ref. 22)

τg≈2ηcC

(1+C)(1+C−ηc)Γ−1m (6)

where C =Ω 2c /(κΓm) denotes the electromechanical cooperativity

parameter43 with the coupling rate Ωc = 2g0a and ηc = κex/κ . Thegroup delay in equation (6) reaches its maximum value

τmaxg = 2(1−

√1−ηc)2/ηcΓm (7)

as the cooperativity approaches C =√1−ηc. To experimentally

explore this predicted behaviour, microwave probe pulses aregenerated by modulating the amplitude of a weak (−108 dBm)probe tone derived from a microwave generator. The Gaussian-shaped envelope functions (full-width at half-maximum duration83ms) are generated with an arbitrary waveform generator. Theemission of a probe pulse is synchronized with the acquisition ofthe transmitted probe field. Simultaneously, a continuous-wavepump tone is sent to the cavity (see Supplementary Information fordetails). Figure 3 shows the results of these measurements. A delayof the probe pulses can be observed when the power of the pump isvaried. As shown in Fig. 3a,b, the maximum group delay achievedwith negligible losses is 3.5 ms, which agrees with equation (7).The demonstrated delay is achieved without pulse distortion, asit fulfils the condition that the pulse bandwidth is narrower thanthe transparency window width (we discuss the pulse distortion inmore detail in the Supplementary Information).

In the case of a slightly detuned probe tone, δ=Ω−Ωm 6= 0, agood approximation of the group delay is given by

τg≈−

2ηc1−ηc

CΓm

4δ2+ (1+C)2Γ 2m·4δ2−α(1+C)Γ 2

m

4δ2+α2Γ 2m

(8)

where α=1+C(1−ηc). This allows for a negative group delay, thatis the advancing of the microwave pulses, with sufficient detuning

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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS2527

¬10 0

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plitude

Figure 3 |Delayed and advanced microwave pulse propagation in a circuit electromechanical system in the presence of electromechanically inducedtransparency at 200 mK. a, Normalized transmitted amplitude of probe pulses, for various different pump powers between−89 and−49 dBm and tunedto the red sideband (−∆=Ω) and with a frequency detuning |δ| = |Ω−Ωm| = 2π×1.2 Hz. The inset shows the Gaussian pulse readout. b, Extracted groupdelay for pump powers between−89 and−49 dBm, with various detunings |δ| = 2π×(1.2 Hz(1), 5.4 Hz(2), 10 Hz(3),44 Hz(4)). The measured groupdelays are plotted (red data points) versus the input power together with the fittings from the full model (black). c, Group delay for different detunings δ.The pump tone has a constant power of−66 dBm. d, Maximum delay achievable for a given frequency detuning δ and optimum cooperativity Copt.

such that |δ|>Γm/2. The probe delay measured when both pumptone power and probe tone detuning are varied reveals an excellentagreementwith the full theory given in equation (8) (Fig. 3b–d).

For a number of advanced optomechanical protocols forboth quantum and classical applications23–25, it is necessary todynamically tune the coupling rate

Ωc(t )= 2g0a(t ) (9)

For switching applications, the response of the system can be limitedboth by the dynamics of the mechanical mode amplitude (X(t ))as well as the pump field (a(t )). In the following, we explore thesedynamics experimentally. To this end, the pump tone is tuned to thered sideband (∆=−Ωm). The probe tone, tuned in resonance withthe cavity (Ω+ωp=ωc), is constantly on. The probe transmissionand its anti-Stoke scattering at the blue sideband (∆ = Ωm) arerecorded (Fig. 4a). On switching on the pump field, the intracavitypump power rings up on a timescale κ−1≈0.2 µs. The transmissionof the probe power builds up on a much slower timescale Γ−1eff , thetimescale at which the mechanical oscillation amplitude convergestowards its steady-state value. Figure 4a shows the typical ring-upof the probe transmission. The characteristic timescales extractedfrom the data are shown in Fig. 4b as a function of pump power. Onswitching off the pump field, the probe transmission immediatelydrops, as the pump field (giving rise to destructive interference)decays from the cavity on a fast timescale of κ−1. So doesthe corresponding field-enhanced electromechanical coupling rateΩc(t ) given in equation (9). The mechanical oscillation howeverstill prevails. The power of the anti-Stokes scattered probe fielddecays with a constant time constant 1/Γm, shown in Fig. 4b, inthe absence of the pump tone (see Supplementary Information fora quantitative analysis).

On the basis of this study of the on–off dynamics, we firstprepare the mechanics to its steady-state amplitude by applyingsimultaneously a pump and a probe tone for a sufficiently long time.Next, a series of pump pulses is applied with a period T =Ton+Toff.

The transmission of the probe follows the pump modulation,determined by the decay time κ−1 of the microwave cavity (Fig. 4e).These observations reveal the counterintuitive regime that theswitching time can be substantially faster than the slowest timescalein the problem (that is, the inverse effective mechanical dampingrate, Γ−1eff ) and is limited only by the microwave cavity decay timeκ−1. When the pump is off, the mechanical oscillation relaxestowards its equilibrium position at the rate of the intrinsic dampingrate Γm; when the pump is on, the mechanical oscillation is drivenback towards its steady state at a rate of the effective dampingrate Γeff, leading to a recovery to a finite probe transmission.Consequently, continuous switching is possible if the loss in themechanical amplitude due to damping between the successivepump pulses is compensated within the switching period, that is,κ−1<Toff< (Γeff/Γm)Ton.

In the on state, the transparency window amplitude dependssignificantly on the mechanical oscillation amplitude (Fig. 4c,d). Incontrast, in the off state, the cavity transmission modulation isnegligible in the absence of coherent driving from the pump tone,hence allowing a high on–off contrast. Note, this modulation of thecavity transmission (in the absence of the pump tone) is due to thefinite residual amplitude of themechanical oscillator and is given by1|tp|2/|tp|2≈O(ε2), with ε=g0x/xzpfΩm and x being the amplitudeof motion. For the amplitudes concerned in this work, ε is typicallyat the level of <1% (see Supplementary Information for details),and hence the cavity transmission is only weakly modified. Note,in the above electromechanical-switching experiments the pumptone is modulated and the probe tone remains stationary. Using thedemonstrated temporal control in conjunction with probe pulsesallows storage of the probe field through conversion into a coherentexcitation of the mechanical oscillator44–49.

To summarize, we have demonstrated that electromechanicallyinduced transparency can be used in electromechanical systemsto manipulate the transmission and delay of a microwavesignal in a fully integrated architecture without the need ofphoton detection and regeneration. Interestingly, the switching

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NATURE PHYSICS DOI: 10.1038/NPHYS2527 ARTICLES

Prob

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c d

ω ωΩ Ωω

Figure 4 | Switching dynamics. a, Measurement scheme (see text fordetails). The pump tone is red-detuned (in red); the probe transmissionreadout is on resonance (in yellow); and the anti-Stokes scattering of theprobe field is read out blue-detuned (in blue). b, Time constants of thering-up (yellow dots) and ring-down (blue squares) of the individual pulseas a function of pump power. The curve (black) shows the calculation forthe ring-up constant with Γm= 2π× 12 Hz. Note the time constant tcon isextracted from the voltage readout, and tcon= 2/Γeff. c,d, A train ofred-detuned (∆=−Ωm) pulses is sent into the cavity, with a period ofTon= Toff= 100 µs that is shorter than 1/Γeff (c) and Ton= Toff= 10 msthat is on the same order of 1/Γeff (d), with a power descending from−63 dBm (green) to−79 dBm (blue) in steps of 4 dB. A weak probe tone(−99 dBm) is present on cavity resonance. Probe transmission on cavityresonance (ωc) measured with a spectrum analyser in zero-span mode isplotted versus time, showing the dynamics of electromechanically inducedtransparency on cavity resonance.

can be faster than the timescale of the mechanical oscillator’senergy decay. Using electromechanically induced transparency,classical microwave signals can be switched, or routed50 througharrays of electromechanical systems, and synchronized by theassociated tunable positive and negative delays. The employedmicrofabrication techniques offer in this context a far-reachingflexibility in the design of both mechanical and microwaveproperties—including carrier frequencies and bandwidth—as wellas the overall architecture of complex networks. The delay andadvancing of pulses may also be extended to single microwavephoton pulses5. The prerequisite for preserving the single-photonstate is that the thermal decoherence time (1/Γmnm) is longcompared with the photon delay/advance time. The pulse duration(that is, bandwidth of the pulses) is limited by the width of thetransparency window (Γeff) to avoid pulse distortion, implyingthat the condition Γeff nmΓm needs to be satisfied. In theweak coupling limit (Ωc < κ), this condition is equivalent to acooperativityC exceeding the thermal occupation nm.

Our system already reaches coupling rates exceeding themechanical decoherence rate Ωc ∼

> nmΓm even at a moderatecryogenic temperature. The estimated decoherence rate of nmΓm

∼=

2π× 1.18 kHz due to a mechanical dissipation of 2π× 2.56Hzat a lower temperature (33mK) brings the system in the regimeof Ωc nmΓm, which overcomes the main obstacle of quantumcoherent manipulation. A larger g0 (refs 23,28), or a simpleimprovement in the measurement set-up, allowing a larger pumpfield (sustainable by the employed Nb cavities) would in principlealready be sufficient for the system to reside in the coherentquantum coupling regime Ωc > (nmΓm,κ). Combining the systemwith the powerful advances in the generation and detection ofsingle microwave photons5 may allow for the control over thepropagation of non-classical states using the electromechanicalarchitecture. Moreover, it provides the basis for the completestorage and retrieval of a microwave quantum state in long-livedmechanical excitations.

MethodsNanoelectromechanically coupled system. For theCPWstructures a characteristicimpedance of Z0 ≈ 50Ω is realized with a 10-µm-wide centre stripline separatedby a gap of 6 µm from the ground plane (Fig. 1). The one-sided cavity with a typicallength of 5.3mm is capacitively coupled to a CPW feedline on one end, and shortedon the other end. This CPW cavity is patterned into a Nb thin film deposited ontop of a Si substrate. Frequency multiplexing is realized by embedding on a singlechip several cavities of different length coupled to a single CPW feedline. Thenanomechanical object integrated in the cavity is a high-aspect-ratio beam, 60 µmlong, 140 nm wide and has a thickness of 200 nm, which consists of 130-nm-thickNb on top of 70-nm-thick tensile-stressed Si3N4. The high tensile stress of Si3N4

overcomes the compressive stress of Nb.

Low-temperature measurement set-up. All experiments have been performedin a dilution refrigerator at around 200mK. In the dilution refrigerator there arethree signal lines: two coaxial-cable lines connecting the two ends of the samplefeedline for the microwave input and output signal, and a low-frequency line tocarry a drive signal (<5MHz) that provides additional means of resonant excitationof the nanomechanical beam through Coulomb force. A sample of dimension10mm×6mm is mounted in a gold-plated copper box. An SMA coaxial connectorat each end is silver-glued to the CPW feedline, transmits signals to/from thesample. Thermal noise from the tones at room temperature is suppressed usingattenuators at successive temperature stages, and by the inertial attenuation of thecoaxial cable. The d.c.-block filter beside the sample prevents the d.c. current in theoverall transmission loop. A high electron mobility transistor amplifier is anchoredat 4 K and is isolated from the sample output by a circulator. For more details of theindividual measurements, see Supplementary Information.

Received 26 June 2012; accepted 5 December 2012;published online 20 January 2013

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AcknowledgementsT.J.K. acknowledges support by the NCCR of Quantum Engineering, an ERC StartingGrant (SiMP) and the Swiss National Science Foundation (SNF). Financial supportfrom the German Excellence Initiative through the Nanosystems Initiative Munich(NIM) is gratefully acknowledged. Samples were grown and fabricated at the Centerof MicroNanotechnology (CMi) at EPFL. The authors acknowledge the assistance ofS. Weis, T. Niemczyk and H. Chibani in fabrication, and P. Hakonen and P. Lähteenmäkifor measurement in the early phase of the project.

Author contributionsX.Z. designed and fabricated the samples. The cryogenic measurement set-up wasimplemented by F.H. and H.H. F.H., X.Z., H.H. and A.S. performed the experiments.X.Z. and A.S. performed theoretical modelling and analysis of the data. X.Z. wrotethe paper with guidance from A.S. and T.J.K. All authors discussed the results andcontributed to the final version of the manuscript.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Correspondenceand requests for materials should be addressed to T.J.K.

Competing financial interestsThe authors declare no competing financial interests.

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