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Resolving the Vacuum Fluctuations of an Optomechanical System Using An LETTERS PUBLISHED ONLINE: 15 JUNE 2015 | DOI: 10.1038/NPHYS3365 Resolving the vacuum fluctuations of an optomechanical system using an artificial atom F. Lecocq*, J. D. Teufel, J. Aumentado and R. W. Simmonds Heisenberg’s uncertainty principle results in one of the Here, we go beyond just cQED by introducing cavity strangest quantum behaviours: a mechanical oscillator can optomechanical interactions. Our unique architecture incorporates never truly be at rest. Even at a temperature of absolute an artificial atom—a superconducting qubit22—into a circuit cavity zero, its position and momentum are still subject to quan- electromechanical system23, on a single chip. Here, a low-frequency, tum fluctuations1,2. However, direct energy detection of the high-quality-factor mechanical oscillator strongly interacts with oscillator in its ground state makes it seem motionless1,3, the microwave cavity photons. The qubit–cavity interaction and in linear position measurements detector noise can realizes a non-classical emitter and detector of photons, thus masquerade as mechanical fluctuations4–7. Thus, how can providing an essential nonlinear resource for the deterministic we resolve quantum fluctuations? Here, we parametrically control of long-lived mechanical quantum states. We demonstrate couple a micromechanical oscillator to a microwave cavity the potential of such an architecture by measuring the quantum to prepare the system in its quantum ground state8,9 and vacuum fluctuations inherently present in the motion of a then amplify the remaining vacuum fluctuations into real macroscopic oscillator. energy quanta10. We monitor the photon/phonon-number A microwave cavity is the central element of this architecture distributions using a superconducting qubit11–13, allowing us to (in blue in Fig. 1a). It is a linear inductor–capacitor (LC) res- resolve the quantum vacuum fluctuations of the macroscopic onator formed by a coil inductor and a mechanically compliant oscillator’s motion. Our results further demonstrate the vacuum-gap capacitor23,24. First, the intra-cavity electromagnetic ability to control a long-lived mechanical oscillator using field is coupled by means of radiation pressure to the vibrational a non-Gaussian resource, directly enabling applications in mode of the compliant capacitor (in red in Fig. 1). Second, the quantum information processing and enhanced detection of microwave cavity is capacitively coupled to a phase qubit (in green displacement and forces. in Fig. 1). A phase qubit is formed from a Josephson junction Cavity optomechanical systems have emerged as an ideal in parallel with an LC oscillator, and it behaves like a nonlin- testbed for exploring the quantum limits of linear measurement of ear resonator at the single-quantum level, that is, an artificial macroscopic motion2, as well as a promising new architecture for atom22. To a good approximation the phase qubit can be oper- ! performing quantum computations. In such systems, a light field ated as a two-level system whose transition frequency qb can reflecting off a mechanical oscillator acquires a position-dependent be widely tuned in situ by applying an external flux, such that ! = phase shift and reciprocally, it applies a force onto the mechanical 9GHz≤ qb 2π≤13.5 GHz. The microwave cavity and the funda- oscillator. This effect is enhanced by embedding the oscillator inside mental flexural mode of the capacitor are two harmonic oscillators ! = a high-quality-factor electromagnetic cavity. Numerous physical with resonance frequencies of respectively c 2πD10.188 GHz and Ω = implementations exist, both in the microwave and optical domains, m 2πD15.9 MHz. and have been used to push the manipulation of macroscopic The qubit and the cavity are both electrical circuits with oscillators into the quantum regime, demonstrating laser cooling quantized energy levels, sharing a voltage through the coupling 8,14 ∆ ! ! to the ground state of motion , coherent transfer of itinerant capacitor. On resonance, qb D qb − c D0, the interaction between light fields into mechanical motion9,15, or their entanglement10. the qubit and the cavity is well described by the Jaynes–Cummings . σ †σ / σ σ Thus far, linear position measurements have provided evidence Hamiltonian Hjc D hJN aO OC COa O− . Here, OC ( O−) is the raising for the quantization of light fields through radiation pressure shot (lowering) operator for the qubit, aO † (aO) is the creation (annihilation) noise16,17 and mechanical vacuum fluctuations through motional operator for cavity photons and J is the capacitive coupling strength. 4–7 sideband asymmetries . However, the use of only classical and Hjc describes the exchange of a single quantum between the qubit linear tools has restricted most optomechanical experiments to the and the cavity at a rate 2J. In the strong-coupling regime, when the γ manipulation of Gaussian states. coupling strength J overcomes the decoherence rates of the qubit qb κ >(γ κ/ The addition of a strong nonlinearity, such as an atom, has and the cavity , that is, J qb, , the system hybridizes, leading to fostered tremendous progress towards exquisite control over non- the well-known vacuum Rabi splitting, measured spectroscopically Gaussian quantum states of light fields and atomic motion11,12. in Fig. 1e. The qubit–cavity interaction can be effectively turned off First developed in the context of cavity quantum electrodynamics by detuning the qubit. (cQED), these techniques are now widely applied to engineered The position of the mechanical oscillator modulates the cavity systems, such as superconducting quantum bits (qubits) and resonance frequency and thus, the energy stored in the cavity. As microwave resonant circuits13,18–21. In a pioneering cQED-type a result, the microwave photons apply a force on the mechanical experiment, a qubit resonantly coupled to a high-frequency oscillator. This interaction is described by the radiation pressure 3 2 ! = † mechanical oscillator allowed for the control of a single-phonon Hamiltonian Hrp DhGN nO cxO, where GDd c dx, nO c DOa aO is the cavity .O† O/ Fock state. However, short energy lifetimes of the mechanical photon number and xO Dxzpf b Cb is the oscillator's position. Here, O† O oscillator and the qubit have slowed any further progress. xzpf is the oscillator's zero-point fluctuation and b (b) is the creation National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA. *e-mail: fl[email protected] NATURE PHYSICS | VOL 11 | AUGUST 2015 | www.nature.com/naturephysics 635 © 2015 Macmillan Publishers Limited. All rights reserved LETTERS NATURE PHYSICS DOI: 10.1038/NPHYS3365 a b 100 μm d Cavity drive Qubit bias ω c d ωqb ω d p Qubit Pump drive 2 μm c b c Circuit Microwave QED optomechanics Phase Microwave Mechanical qubit cavity oscillator J g ω ω Ω T = 25 mK qb c m 2 μm f e Drive frequency, (GHz) 10.28 2 10.190 Pe |R| (dB) 0.0 0.1 0.2 −1.0 −0.5 0.0 π 10.189 /2 10.22 qb d ω ω /2π J/π c g/π 10.188 ω d c 10.16 /2 π Ω π − m /2 10.187 Drive frequency, (GHz) 10.10 80 40 0 −40 −80 −17 −16 −15 −14 ω ω ω ω π Qubit detuning, ( qb − c ) /2 π (MHz) Pump detuning, ( p − c )/2 (MHz) Figure 1 | Device description and strong-coupling regime. a, False-colour optical micrograph of the device. Aluminium is in grey and sapphire in light blue. The phase qubit is in green; the microwave cavity in blue; and the mechanically compliant capacitor in red. b,c, False-colour scanning electron micrograph of the qubit’s Josephson junction and of the mechanical oscillator, respectively. d, Equivalent circuit diagram. e, Qubit–cavity vacuum Rabi splitting. Population of the qubit’s excited state Pe, in green, as a function of the drive frequency and of the qubit detuning with respect to the microwave cavity. The avoided crossing is a clear signature of the single-photon strong-coupling regime. From a fit with theory we extract the qubit/cavity coupling rate J=2πD12.5 MHz. f, Cavity–oscillator normal-mode splitting. Reflected power in blue as a function of the drive and pump frequencies. The drive is applied 5 near the cavity resonance and the pump is applied near ∆p D−Ωm. Here, the pump strength is set to np ≈5×10 . The normal-mode splitting observed in the cavity-driven response corresponds to the hybridization of the cavity and mechanical modes in the driven strong-coupling regime. From a fit with theory we extract κ=2πD163 kHz, Γm=2πD150 Hz and gD2π×242kHz>( nNmΓm,κ), where nNm ≈32 at T ≈25 mK. (annihilation) operator for mechanical phonons. The force applied the cavity lifetime, 1/κ ≈ 1 µs, this device is in the quantum- by a single photon onto the mechanical oscillator is typically weak, coherent regime15. Γ κ/ with g0 D Gxzpf nN m m, , where nN m is the equilibrium thermal Measurements in the frequency domain provide an extensive Γ occupancy of the oscillator and m is its intrinsic relaxation rate. characterization of the device's parameters; however, they probe However, the total force increases significantly with the intensity only the steady state of the system, in equilibrium with the of the intra-cavity field. In the presence of a strong coherent thermal environment. In the next two paragraphs, we will show ! microwave pump of frequency p, the optomechanical interaction that time-domain protocols enable: the preparation of non-classical is linearized and takes two different forms depending on the cavity states and the measurement of the intra-cavity photon- ∆ ! ! 11–13 pump–cavity detuning p D p − c (Supplementary Information). number distribution ; and coherent state transfer by frequency ∆ Ω When p D − m, the annihilation of a mechanical phonon can conversion and entanglement by parametric amplification between up-convert a pump photon into a cavity photon, mediating a the microwave cavity and the mechanical oscillator25,26.
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