Sensing the quantum motion of nanomechanical oscillators

Konrad Lehnert

Post-docs Graduate students Tauno Palomaki Jennifer Harlow Joseph Kerckhoff Reed Andrews Hsiang-Shen Ku Collaborators William Kindel John Teufel Adam Reed Cindy Regal Ray Simmonds Kent Irwin Precision measurement tools were once mechanical oscillators

The Cavendish balance Huygens pendulum clock for weighing the earth Modern measurement tools exploit optics and electronics, not mechanics Laser light electricity

Image: Cundiff JILA lab Cundiff Image:

Optical and electrical measurement tools: Large dynamic range Compact, high-Q mechanical oscillators are ubiquitous in information technology

1 mm

Quartz crystal oscillator: Surface acoustic wave filters: in everything electronic In radios, tuners, mobile phones

Applications: sound speed << light speed Timing and filtering Compact and high-Q oscillators

Q ~ 100,000 Optical probes are ill-suited to directly measuring many interesting systems

system 100 nm 100 nm

nuclear spins electrons in an in a virus aluminum ring (Harris lab, Yale)

Systems with: dense low-energy spectra optical or electrical nanometer length scales probe weak coupling to light Mechanical oscillators enable measurements of non-atomic systems

system

mechanical intermediary Systems with: dense low-energy spectra probe field nanometer length scales 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 tot 1/2 Rugar Lab, IBM S f = 0.8 aN/Hz Mechanical oscillators as quantum coherent interfaces between incompatible systems

Mechanical oscillators are classical quantum kT system B >> 1 Quantum regime ωm •state preparation •state measurement Cleland group UCSB •state manipulation Nature 464, 697-703 (1 April 2010) mechanical oscillator γ ωm Γ

quantum environment γ kT B < 1 probe kTB bath  Γω m 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

ˆˆ† 1 † 1 HH= ωc (aa+ 2 ) + ω+m (bb 2 ) + I

ˆ ˆ † † HI = F ⋅=xˆ  aag xbzp ()+ b

gxzp ≡G ~ 2 π× 10 Hz Aspelmeyer lab, IOQOI, Vienna Images of cavity optomechanical systems

Caltech, Painter G ≈2 π× 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 cavity k LC oscillator Fabry-Perot cavity m k

Strategy Cool environment to T << 1 K γ kT bath B bath <1 Γω High Q mechanical oscillators  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 =2 π× 0.3 Hz Wire response microwave resonant circuit Qm=300,000 ω c = 7 GHz 2π κ=200 kHz

400 µm drive frequency (MHz) Parallel-plate capacitor geometry enhances microwave—mechanics interaction

capacitor built with suspended Electrical circuit micromechanical membrane* resonant at 7 GHz

15 µm

G ≈2 π× 50 Hz *K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067 Nanomechanical motion monitored with a microwave Mach-Zehnder interferometer

phase reference φ N / τ 1 ωωed ωc N A ≈ 40 2 S21

0 2π ∆φ φ Infer wire motion from phase shift ∆ω gx ∆φ =c = 0 κ κ ωc Phase sensitivity limited by amplifier (HEMT) N + 1 noise quanta S =A 2 = φ N /τ photon flux Thermal motion of beam calibrates interferometer noise (imprecision)

260 mK Minimum imprecision

) 147 mK imp Sx =145 ZPE 50 mK imp 2 S =290 × SQL T x Hz / Hz

( S imp

c x ω S Imprecision at the SQL S x

sql  Sx = mωγm frequency (MHz) Determine measurement imprecision imp Sx

C. A. Regal, J. D. Teufel, KWL Nature Phys. (2008) Amplifier added noise mimics quantum inefficiency

η

1 η= 21N A +

Excellent microwave amplifier:

NA = 40 η = 1.2% Efficient quantum measurement Linear amplifiers must add noise

Vt( )= V Xˆˆ cosωω t+ X sin t out q ( 12) X 2 in out in V = G(V + N A ) X1

1 Phase-preserving linear amplifiers at least N A ≥ 2 double quantum noise

A single quadrature amplifier preserves entropy with photon number gain

in NA , G out ˆˆ Vt( )= Vq ( X12 cosωω t+ X sin t)

X 2 ˆˆout in X11= GX 1 2 XXˆˆout = in in 22 1 out G i X XXˆˆout out−= XX ˆˆ out out 2 4 1 1 2 21 2

N A ≥ 0 Incorporate quantum pre-amplifier into the Mach- Zehnder interferometer

JPA HEMT

N HEMT NNA =JPA + GJPA

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

signal in pump amplified signal out

pump port Kerr medium signal port

30 µm

NJPA < 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 Qm = 131,500 SSxx/= 0.83 T =131 mK sql sql Sx = 5.7 fm/ Hz

/ ω xx

SS 4

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

/Hz) 2 resolve n = 0.1 (fm

x •10 minutes with JPA S •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

ωd ωm Nd cavity photons from cooling drive cavity lineshape D.O.S. ˆ † † † HgI=  x zp (a ab + aab)

ω ωc

linearized interaction around strong cooling drive

† † 2 ˆ = + 4Nd G HGI  Nd ( ab a b) Γ= κ Radiation pressure changes the wire’s damping rate and resonance frequency

ωc detuning amplifying driving γ

cooling ω damping ωd Mechanical response measures

antisymmetric force noise ∆ω 2 m xzp Γ =[SSfm ( ω ) − f ( −ω m )] 2

† f=  Ga a G =2 π× 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

P = 0.008 Tbath = 50 mK kT B = 700 ωm 2

(pm /Hz) N

x d S

kT B =140 P = 1.3 ωm

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 µm

*K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067 ωπm =2 × 10.5 MHz γπ=2 × 30 Hz

ωπ=2 × 7.5 GHz

/Hz) c 2 (fm

κπ=2 × 250 kHz x S

Frequency (MHz) Thermal motion reveals large coupling

G = 50 Hz oscillator phonons phonons oscillator n 2 kT kxs n =B = ωωmm

Tbath refrigerator temperature (mK) Cooling mechanics to motional ground state

n = 27

n = 22 /Hz) 2 n = 8.5 Nd (fm

x

S n = 2.9

n = 0.93 Increasing strength of measurement and cooling Frequency (MHz) Cooling mechanics to motional ground state

n = 0.93

n = 0.55 /Hz) 2 n = 0.36 (rad

c

S n = 0.38 G / π n = 0.42 ground state and strong coupling Frequency (MHz)

J. D. Teufel, T. Donner, KWL et al Nature, 475, 359–363 (2011). Manipulating mechanics with microwave Strong coupling enables coherent control of mechanics

GNd κ

swap states of cavity and mechanics (mV)

out V GNd >κ

time (µs) Agile state control provided by extreme resolved sideband limit

ωc ωm / κ= 50 ωm κ

cavity cavity response ω

cavity preparation

cavity – mechanics interaction Nd (t) ˆ † † HGI =  Nd () t(ab + a b)

linearized phonon – photon interaction • beam splitter • time dependent Mechanical oscillators are long-lived coherent memories prepare swap measure

P()ωc

tint P()ωcm −ω

2π 20×

κ (mV)

out V

time (µs) Mechanical oscillators are long-lived coherent memories prepare swap measure

P()ωc

tint P()ωcm −ω

2π 20×

κ (mV)

out V

time (µs) Mechanical oscillators are long-lived coherent memories

(mV)

out V

tsint ()µ Ramsey like oscillation in coupled microwave-mechanical system Quantum states of the micro-drum harmonic oscillator are long-lived

= T1 6.1 ns T1 ≈µ100 s 1/Tn= γ Cleland group UCSB 1 bath 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 Si3N4 membrane

(0,0) MHz

(1,1) metal dielectric Membrane in free-space cavity Mechanics and optics Superconducting LC circuit 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/Hz1/2

• Microwave Mach-Zehnder interferometer quantum efficiency 30%

Funding: NSF, NIST, DARPA QuEST, DARPA QuASR, NASA