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

Imag

e: C

undi

ff la

b JI

LA

Laser light electricity

Optical and electrical measurement tools: Large dynamic range

Compact, high-Q mechanical oscillators are ubiquitous in information technology

Quartz crystal oscillator: in everything electronic

Surface acoustic wave filters: In radios, tuners, mobile phones

Applications: Timing and filtering

1 mm

Q ~ 100,000

sound speed << light speed Compact and high-Q oscillators

system

optical or electrical probe

Optical probes are ill-suited to directly measuring many interesting systems

100 nm 100 nm

Systems with:

dense low-energy spectra

nanometer length scales

weak coupling to light

nuclear spins in a virus

electrons in an aluminum ring (Harris lab, Yale)

probe field

mechanical intermediary

Mechanical oscillators enable measurements of non-atomic systems

Systems with:

dense low-energy spectra

nanometer length scales

weak coupling to light

system

Mechanical oscillators are tools that access the nano-world

Mechanical oscillator nanometer probe universal coupling (senses any force)

Optical interferometer detects oscillator motion

Perkins lab, JILA

20 µm

Atomic Force Microscope

nanoscale MRI of a single virus Rugar Lab, IBM

Mechanical oscillators form ultrasensitive, mesoscopic magnetometers

tot 1/20.8 aN/HzfS =

mechanical oscillator

environment

quantum system

Mechanical oscillators as quantum coherent interfaces between incompatible systems

γ

bathBk T

mω

quantum probe

Γ

1B

m

k T>>

ω

Mechanical oscillators are classical

Quantum regime •state preparation •state measurement •state manipulation

1B

m

k Tγ < Γ ω

Cleland group UCSB Nature 464, 697-703 (1 April 2010)

Cavity optomechanics: Use radiation pressure for state preparation and measurement

Fabry-Perot cavity with oscillating mirror

( ) ( )† 12

† 12

ˆ ˆc m IH Ha a b b= + ω ++ +ω

† †ˆ ˆˆ ( )I zpH F a ax x bg b= ⋅ = +

Infer motion through optical phase Cool with cavity-retarded radiation force

Aspelmeyer lab, IOQOI, Vienna

~ 2 10 Hzzpgx G≡ π×

Images of cavity optomechanical systems

UCSB: Bouwmeester

ENS: Pinard and Heidmann

Caltech, Painter

EPFL, Kippenberg

Yale, Harris

MIT, Mavalvala

2 1 MHzG ≈ π×

Microwave cavity optomechanics

coupling

cavity

Fabry-Perot cavity LC oscillator

Strategy

Cool environment to Tbath << 1 K

High Q mechanical oscillators

mk

mk

Reduce coupling to the environment by lowering temperature: microwave optomechanics

Microwave “light” in ultralow temperature cryostat

bath 1B

m

k Tγ < Γ ω

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)].

Superconducting electromechanics used in resonant mass gravitational wave detectors

Meter sized superconducting cavity with mechanically compliant element

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

Wire response

drive frequency (MHz)

Cavity optomechanical system realized from a nanomechanical wire in a resonant circuit

Qm=300,000

400 µm

microwave resonant circuit

7 GHz2

cω=

π

150 µm

2 0.3 HzG = π×

200 kHzκ =

Parallel-plate capacitor geometry enhances microwave—mechanics interaction

capacitor built with suspended micromechanical membrane*

15 mµ

*K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067

Electrical circuit resonant at 7 GHz

2 50 HzG ≈ π×

Nanomechanical motion monitored with a microwave Mach-Zehnder interferometer

φ

0

2π

1

0

cω

221S

∆φ

c gx∆ω= =

κ∆φ

κ

Infer wire motion from phase shift

phase reference

12 noise quanta

/ photon fluxAS

NN

φ

+= =

τ

Phase sensitivity limited by amplifier (HEMT)

40AN ≈

/N τeω

cω

φ

ωd

frequency (MHz)

260 mK 147 mK

Thermal motion of beam calibrates interferometer noise (imprecision)

50 mK

C. A. Regal, J. D. Teufel, KWL Nature Phys. (2008)

impxS

Determine measurement imprecision

TxS

impxS

()

2H

z/H

zc

S ω

imp 290 SQLxS = ×

Minimum imprecision

sqlx

m

Sm

=ω γ

Imprecision at the SQL

imp 145 ZPExS =

Amplifier added noise mimics quantum inefficiency

η

12 1AN

η =+

NA = 40 η = 1.2%

Excellent microwave amplifier:

Efficient quantum measurement

Linear amplifiers must add noise

Phase-preserving linear amplifiers at least double quantum noise

12AN ≥

( )1 2ˆ ˆ( ) cos sinqV t V X t X tω ω= +

1X

2X

in )( iout n

AVV G N+=

out

A single quadrature amplifier preserves entropy with photon number gain

1X

2X

1 2 2 1ˆ ˆ ˆ ˆ

2out out out out iX X X X− =

1 1

2 2

ˆ ˆ

1ˆ ˆ

out in

out in

X GX

X XG

=

=

0AN ≥

2 4

2 1

in out

NA , G in out

( )1 2ˆ ˆ( ) cos sinqV t V X t X tω ω= +

JPA HEMT

Incorporate quantum pre-amplifier into the Mach-Zehnder interferometer

HEMTJPA

JPAA

NN NG

= +

Josephson parametric amplifier (JPA) makes more photons without more entropy

Diagram conceals some complexity

50 cm

mechanics

JPA

Dilution refrigerator

signal port Kerr medium pump port

pump signal in

amplified signal out

Realization of Josephson parametric amplifier

array of 480 SQUIDs embedded in a CPW resonator

30 µm

M. A. Castellanos-Beltran, K. D Irwin, KWL, et al, Nature Phys. (2008)

JPA 0.1N <

Imprecision noise is below the standard quantum limit with the JPA

frequency (MHz)

Q 131,500131 mK

m

T=

=

sql

/x

xS

S

sql/ 0.83x xS S =sql 5.7 fm/ HzxS =

4ω

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. Harlow, KWL, Nature Nanotech., 4, 820-823 (2009).

Frequency (MHz)

S x (f

m2 /H

z)

efficient interferometer (JPA)

HEMT only

resolve n = 0.1 •10 minutes with JPA •1 week with HEMT

Detecting near ground state motion requires a quantum efficient interferometer

Radiation pressure cooling

cavity lineshape D.O.S.

ωm

ωc

ωd

ω

( )† ††ˆI zp aH g babx a a= +

Radiation pressure can cool the beam to ground state in the resolved sideband limit

24 dGNΓ =

κ

Nd cavity photons from cooling drive

( )† †ˆdI bH G a bN a+=

linearized interaction around strong cooling drive

Radiation pressure changes the wire’s damping rate and resonance frequency

detuning

ωdω

cω

γ

detuning (MHz)

cooling damping

amplifying driving

m∆ω

Mechanical response measures antisymmetric force noise

2

2 [ ( ) ( )]zpf m f m

xS SΓ = ω − −ω

F. Marquardt et al., PRL 99 093902 (2007)

†f Ga a= 2 0.1 HzG = π×

Coupling to radiation is too weak to cool wire to motional ground state

2(p

m/H

z)xS

Frequency (MHz)

140B

m

k T=

ω

P = 0.008

P = 1.3

J. D. Teufel, J. W. Harlow, C. A. Regal, KWL Phys. Rev. Lett. 101, 197203 (2008).

Tbath = 50 mK 700B

m

k T=

ω

Nd

Use parallel-plate capacitor geometry to enhance coupling in microwave optomechanics

capacitor built with suspended micromechanical membrane*

15 mµ

*K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067

Electrical circuit resonant at 7 GHz

m 2 10.5 MHz2 30 Hz

ω πγ π

= ×= ×

c 2 7.5 GHz2 250 kHz

ω πκ π

= ×= ×

S x (f

m2 /H

z)

Frequency (MHz)

Thermal motion reveals large coupling

50 HzG =

2B s

m m

k xk Tnω ω

= =

n os

cilla

tor p

hono

ns

Tbath refrigerator temperature (mK)

Cooling mechanics to motional ground state

n = 22

S x (f

m2 /H

z)

n = 0.93

n = 8.5

n = 2.9

n = 27

Frequency (MHz)

Increasing strength of measurement and cooling

Nd

Cooling mechanics to motional ground state S c

(rad

2 /Hz)

n = 0.36

n = 0.55

n = 0.93

Frequency (MHz)

G / π ground state and strong coupling

n = 0.38

n = 0.42

J. D. Teufel, T. Donner, KWL et al Nature, 475, 359–363 (2011).

Manipulating mechanics with

microwave

Strong coupling enables coherent control of mechanics

time (µs)

swap states of cavity and mechanics

κ

V out

(mV

)

dG N > κ

dG N

Agile state control provided by extreme resolved sideband limit

ω

mω

cavity preparation

cavity – mechanics interaction Nd (t)

κ/ 50mω κ =

cω

cavi

ty

resp

onse

linearized phonon – photon interaction • beam splitter • time dependent

( )† †ˆ ( )dIH G tN ab ba+=

Mechanical oscillators are long-lived coherent memories

( )c mP ω − ω

( )cP ωprepare swap measure

intt

time (µs)

V out

(mV

)

220 π × κ

Mechanical oscillators are long-lived coherent memories

( )c mP ω − ω

( )cP ωprepare swap measure

intt

time (µs)

V out

(mV

)

220 π × κ

Mechanical oscillators are long-lived coherent memories

int ( )t sµ

V out

(mV

)

Ramsey like oscillation in coupled microwave-mechanical system

Quantum states of the micro-drum harmonic oscillator are long-lived

1 6.1 nsT = 1

1 bath

100 s1/T

T n≈ µ

= γCleland 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

Si3N4 membrane

(0,0)

(1,1)

Mechanics and optics couple to different antinodes

GHz

MHz

L C

λ

metal dielectric

Membrane in free-space cavity Superconducting LC circuit

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