Sensing the quantum motion of nanomechanical oscillators Konrad Lehnert Post-docs Tauno Palomaki Joseph Kerckhoff Collaborators John Teufel Cindy Regal Ray Simmonds Kent Irwin Graduate students Jennifer Harlow Reed Andrews Hsiang-Shen Ku William Kindel Adam Reed
Precision measurement tools were once mechanical oscillators Huygens pendulum clock The Cavendish balance for weighing the earth
Modern measurement tools exploit optics and electronics, not mechanics Laser light electricity Image: Cundiff lab JILA Optical and electrical measurement tools: Large dynamic range
Compact, high-q mechanical oscillators are ubiquitous in information technology 1 mm Quartz crystal oscillator: in everything electronic Applications: Timing and filtering Surface acoustic wave filters: In radios, tuners, mobile phones sound speed << light speed Compact and high-q oscillators Q ~ 100,000
Optical probes are ill-suited to directly measuring many interesting systems system 100 nm nuclear spins in a virus 100 nm electrons in an aluminum ring (Harris lab, Yale) Systems with: dense low-energy spectra nanometer length scales weak coupling to light optical or electrical probe
Mechanical oscillators enable measurements of non-atomic systems system Systems with: mechanical intermediary dense low-energy spectra nanometer length scales probe field weak coupling to light
Mechanical oscillators are tools that access the nano-world Atomic Force Microscope 20 µm Perkins lab, JILA Mechanical oscillator nanometer probe universal coupling (senses any force) Optical interferometer detects oscillator motion
Mechanical oscillators form ultrasensitive, mesoscopic magnetometers nanoscale MRI of a single virus S = 0.8 an/hz Rugar Lab, IBM tot 1/2 f
Mechanical oscillators as quantum coherent interfaces between incompatible systems quantum system Cleland group UCSB Nature 464, 697-703 (1 April 2010) γ Mechanical oscillators are classical kt B >> 1 ω m mechanical oscillator ω m Quantum regime state preparation state measurement state manipulation Γ environment kt B bath γ Γ kt B ω m < 1 quantum probe
Cavity optomechanics: Use radiation pressure for state preparation and measurement Fabry-Perot cavity with oscillating mirror Infer motion through optical phase Cool with cavity-retarded radiation force Hˆ ( 1 ) ( 1 aa bb ) = ω + + ω + + Hˆ c 2 m 2 I Hˆ = F = aa + I ˆ xˆ gxzp ( b b) gxzp G ~ 2π 10 Hz Aspelmeyer lab, IOQOI, Vienna
Images of cavity optomechanical systems Caltech, Painter G 2π 1 MHz EPFL, Kippenberg Yale, Harris UCSB: Bouwmeester ENS: Pinard and Heidmann MIT, Mavalvala
Microwave cavity optomechanics
Reduce coupling to the environment by lowering temperature: microwave optomechanics Microwave light in ultralow temperature cryostat coupling m k cavity LC oscillator Fabry-Perot cavity m k Strategy Cool environment to T bath << 1 K High Q mechanical oscillators γ kt B Γ ω bath 1 m <
Superconducting electromechanics used in resonant mass gravitational wave detectors Meter sized superconducting cavity with mechanically compliant element Braginsky, V. B., V. P. Mitrofanov, and V. I. Panov, 1981, Sistemi s maloi dissipatsei (Nauka, Moscow) [English translation: Systems with Small Dissipation (University of Chicago, Chicago, 1985)].
Resonant electromechanics used in surveillance Soviet passive bug hidden in the United States Seal Henry Cabot Lodge, Jr. May 26, 1960 in the UN Images appear in http://www.spybusters.com/great_seal_bug.html
Cavity optomechanical system realized from a nanomechanical wire in a resonant circuit 150 µm G = 2π 0.3 Hz Wire response Q m =300,000 microwave resonant circuit ω c = 7 GHz 2π κ=200 khz drive frequency (MHz) 400 µm
Parallel-plate capacitor geometry enhances microwave mechanics interaction capacitor built with suspended micromechanical membrane* Electrical circuit resonant at 7 GHz 15 µ m *K. Cicak, et al APL 96, 093502 (2010). J. D. Teufel et al arxiv:1011.3067 G 2π 50 Hz
Nanomechanical motion monitored with a microwave Mach-Zehnder interferometer ω ed N / τ phase reference ω c N A 40 φ 1 S 21 2 Infer wire motion from phase shift ω c gx φ = = κ κ 0 2π Phase sensitivity limited by amplifier (HEMT) 1 N A + 2 noise quanta Sφ = = N / τ photon flux φ 0 φ ω c
Thermal motion of beam calibrates interferometer noise (imprecision) ( 2 Hz / Hz ) S ωc T S x 260 mk 147 mk 50 mk frequency (MHz) Determine measurement imprecision C. A. Regal, J. D. Teufel, KWL Nature Phys. (2008) imp S x Minimum imprecision S = 145 ZPE imp x S = 290 SQL imp x Imprecision at the SQL S sql x imp S x = m ωγ m
Amplifier added noise mimics quantum inefficiency η η= 1 2 + 1 N A Excellent microwave amplifier: N A = 40 η = 1.2%
Efficient quantum measurement
Linear amplifiers must add noise X 2 out ( ˆ ) 1 ω ˆ 2 ω V( t) = V X cos t+ X sin t q in X 1 out in V = G( V + N A ) Phase-preserving linear amplifiers at least double quantum noise N A 1 2
A single quadrature amplifier preserves entropy with photon number gain in N A, G out ( ˆ ) 1 ω ˆ 2 ω V( t) = V X cos t+ X sin t q 2 1 X 2 in out 2 4 X 1 Xˆ Xˆ = GXˆ out in 1 1 = 1 G Xˆ out in 2 2 Xˆ Xˆ Xˆ Xˆ out out 1 2 i out out 2 1 = 2 N A 0
Incorporate quantum pre-amplifier into the Mach- Zehnder interferometer JPA HEMT N A = N + JPA N G HEMT JPA Josephson parametric amplifier (JPA) makes more photons without more entropy
Diagram conceals some complexity Dilution refrigerator 50 cm mechanics JPA
Realization of Josephson parametric amplifier pump signal in amplified signal out pump port Kerr medium signal port 30 µm N JPA < 0.1 array of 480 SQUIDs embedded in a CPW resonator M. A. Castellanos-Beltran, K. D Irwin, KWL, et al, Nature Phys. (2008)
Imprecision noise is below the standard quantum limit with the JPA sql Sx / Sx ω 4 Q = 131,500 T m = 131 mk sql x S / S = 0.83 x S = sql x 5.7 fm/ Hz frequency (MHz) J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. Harlow, KWL, Nature Nanotech., 4, 820-823 (2009).
Detecting near ground state motion requires a quantum efficient interferometer HEMT only S x (fm 2 /Hz) resolve n = 0.1 10 minutes with JPA 1 week with HEMT efficient interferometer (JPA) Frequency (MHz)
Radiation pressure cooling
Radiation pressure can cool the beam to ground state in the resolved sideband limit ω d cavity lineshape D.O.S. ω m N d cavity photons from cooling drive Hˆ I = gx zp a + b ( ab aa ) ω c ω linearized interaction around strong cooling drive Hˆ = G N a b I d ( b + a ) Γ= 2 4N d G κ
Radiation pressure changes the wire s damping rate and resonance frequency ω c detuning γ amplifying driving ω d ω Mechanical response measures antisymmetric force noise cooling damping 2 xzp Γ = [ S ( ) ( )] 2 f ωm Sf ωm ω m f = Ga a G = 2π 0.1 Hz detuning (MHz) F. Marquardt et al., PRL 99 093902 (2007)
Coupling to radiation is too weak to cool wire to motional ground state T bath = 50 mk P = 0.008 kt B = ω m 700 2 S x (pm /Hz) N d P = 1.3 kt B = 140 ω m Frequency (MHz) J. D. Teufel, J. W. Harlow, C. A. Regal, KWL Phys. Rev. Lett. 101, 197203 (2008).
Use parallel-plate capacitor geometry to enhance coupling in microwave optomechanics capacitor built with suspended micromechanical membrane* Electrical circuit resonant at 7 GHz 15 µ m *K. Cicak, et al APL 96, 093502 (2010). J. D. Teufel et al arxiv:1011.3067
ωm = 2π 10.5 MHz γ = 2π 30 Hz S x (fm 2 /Hz) ω = 2π 7.5 GHz c κ = 2π 250 khz Frequency (MHz)
Thermal motion reveals large coupling n oscillator phonons G = 50 Hz n kt ω B = = m k s x ω 2 m T bath refrigerator temperature (mk)
Cooling mechanics to motional ground state S x (fm 2 /Hz) n = 27 n = 22 n = 8.5 n = 2.9 N d n = 0.93 Frequency (MHz) Increasing strength of measurement and cooling
Cooling mechanics to motional ground state n = 0.93 S c (rad 2 /Hz) n = 0.55 n = 0.36 n = 0.38 G / π n = 0.42 Frequency (MHz) ground state and strong coupling J. D. Teufel, T. Donner, KWL et al Nature, 475, 359 363 (2011).
Manipulating mechanics with microwave
Strong coupling enables coherent control of mechanics G N d κ V out (mv) swap states of cavity and mechanics G N d >κ time (µs)
Agile state control provided by extreme resolved sideband limit cavity response ω m Hˆ = G N () t ab b I d ( + a ) ω c κ ω ω / κ= 50 cavity preparation cavity mechanics interaction N d (t) linearized phonon photon interaction beam splitter time dependent m
Mechanical oscillators are long-lived coherent memories ( ) P ω c prepare swap measure P( ω ω ) c m t int V out (mv) 2π 20 κ time (µs)
Mechanical oscillators are long-lived coherent memories ( ) P ω c prepare swap measure P( ω ω ) c m t int V out (mv) 2π 20 κ time (µs)
Mechanical oscillators are long-lived coherent memories V out (mv) t ( µ s) int Ramsey like oscillation in coupled microwave-mechanical system
Quantum states of the micro-drum harmonic oscillator are long-lived T 1 = 6.1 ns T1 100 µ s 1/ T1 = nbathγ Cleland group UCSB Nature 464, 697-703 (1 April 2010)
Microwave to optical quantum state transfer Hofheinz Martinis, Cleland, Nature (2009) Microwaves: Arbitrary quantum states Require ultralow temperatures Optics: Communication and storage
Ingredients for two cavities coupled to one oscillator GHz λ L C MHz (0,0) Si 3 N 4 membrane metal dielectric Membrane in free-space cavity Superconducting LC circuit (1,1) Mechanics and optics couple to different antinodes
Conclusions Measure, cool, and manipulate nanomechanical elements with microwaves Optomechanical performance: in quantum regime! cooling: 0.35 phonons imprecision: 0.83 X SQL force: 0.5 an/hz 1/2 Microwave Mach-Zehnder interferometer quantum efficiency 30% Funding: NSF, NIST, DARPA QuEST, DARPA QuASR, NASA