nanomechanics: a brief overviewindico.ictp.it/event/a12166/session/1/contribution/1/... · 2014. 5....
TRANSCRIPT
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2445-07
Advanced Workshop on Nanomechanics
Florian Marquardt
9 - 13 September 2013
Erlangen (Germany)
Nanomechanics: a brief overview
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Nanomechanics:a brief overview
Florian Marquardt, Erlangen (Germany)
Frontiers of Nanomechanics / Trieste 2013
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Of bending (nano-)beams
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Leonardo da Vinci 1493
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Galileo Galilei 1638
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Leonhard Euler 1744Daniel Bernoulli &
Euler
Elasticity theory &energy approach
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Euler-Bernoulli theory for beam bending
E: elastic modulusI: moment of inertiaF: applied force(doubly clamped beam)
energy: bending energy stretching energy
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Wikipedia
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Elasticity theory still works well on the nanometer scale!
(Weig)
1,000,000 times smaller!
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Elasticity theory still works well on the nanometer scale!
(Weig)
1,000,000 times smaller!
(Weig)
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Mechanical vibrations
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http://tsgphysics.mit.edu/pics/C%20Oscillations/C38%20Chladni_top_tile.jpg
node
s
Eigenmodes of a membrane (“Chladni figures”)
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Frequency (MHz)
174465 174470 1744750
1
2
3
2344950 2345100 23452500
1
2
3
2519400 2519550 25197000.0
0.5
1.0
1.5
fL=174.47 kHz fM=2.3451 MHz fH=2.5195 MHz
0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0
Frequency (kHz) Frequency (MHz) Frequency (MHz)
Am
plitu
de (a
rb. u
nits
)
Am
plitu
de (a
rb. u
nits
)
Am
plitu
de (a
rb. u
nits
)
H :1.1 Hz H :34 Hz M :24 Hz Eigenfrequencies Eigenmodes
(Yamaguchi)
Small vibrations of any mechanical structure described by:
deflection from equilibrium
)
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Each eigenmode is a harmonic oscillator
restoring force(linear) damping
externalforce
displacement field
Linear superposition of vibrations
resp
onse
am
plitu
de
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Mass sensing via a shift of the eigenfrequency
Freq
uenc
y
Time
Silvan Schmid (Friday)
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Usually focus on one mechanical mode...but interesting effects for multiple coupled modes!
f1
f
f2
f
2
fpump ~ f2-f1 ffpumppffff f2ff -f1ff fsignal ~ f2
Parametric drive of coupling:
...leads to “Rabi oscillations”of mechanical energy between the two modes
Hiroshi Yamaguchi (Thursday)
(Yamaguchi)
beam A
beam B
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Quantum-mechanical mechanical harmonic oscillator
n=0
n=1
n=2
n=3
phonon number
mechanical zero-pointfluctuations (ground state width)
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Usually: mechanical modes are harmonic oscillators(typically very good approximation for small vibrations,
e.g. near the single-phonon level)
But: Potential use as qubits if anharmonicity (nonlinearity) can be made strong enough!
Two-level system
Michael Hartmann (Tuesday)
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Mechanical damping
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Damping rate Quality factor
~ number of oscillationsduring damping time
Excitation of ground state(due to thermal fluctuations)
thermal occupation
Mechanical damping
(different for each mode)
...sets limits on quantum coherence!
e.g. 105
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Common sources of mechanical damping
“Clamping losses”: Beam attached to structure
Structural losses; e.g. due to two-level fluctuatorscan be excited by vibrations
Sound waves radiated into structure
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“Phonon shield” (Painter group)Antisymmetric mode (LKB group)
How to prevent...
Structural losses: increase tension (oscillation energy)
Samuel Deleglise (Thursday) Amir Safavi-Naeini (Wednesday)
“Clamping losses”: Engineer mode shape or surroundings
Qualityfactor103
Resonance frequency [MHz]
2.0
1.5
1.0
0.5
0.0
Stress[GPa]
Experiment
250
200
150
100
50
0
12108642
(b)
(Unterreithmeier, Faust, Kotthaus, 2010)
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How to prevent...
Nicolai Kiesel (Thursday)
Jack Harris (Tuesday)
“Clamping losses”: levitate mechanical object!
Levitate drop of superfluid helium(surface waves!)
glass sphere,trapped in standing light wave
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The mechanicalfluctuation spectrum
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Classical equipartition theorem:
•Direct time-resolved detection•Analyze fluctuation spectrum of x
Possibilities:extract
temperature!
Thermal fluctuations of a harmonic oscillator
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The fluctuation spectrum
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The fluctuation spectrum
area yields variance of x:
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susceptibility
for the damped oscillator:
(classical limit)
Fluctuation spectrum from the susceptibility:Fluctuation-dissipation theorem
forceresponse
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Experimental curve:Gigan et al., Nature 2006
T=300 K
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Coupling radiation to a mechanical resonator
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?
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electromagnetic wave
microwaves (GHz)optical (THz)
resonant coupling
optomechanical coupling force ~ E(t)
force ~ E2(t)
radio-frequency (kHz-MHz)
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opticalcavity mechanical
modelaser
Recent Review “Cavity Optomechanics”: M. Aspelmeyer, T. Kippenberg, FM; arXiv 2013
The standard optomechanical setup
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Karrai(Munich)
Mavalvala(MIT)
Aspelmeyer (Vienna)
Bouwmeester(Santa Barbara)
LKB group(Paris)
Vahala (Caltech)Kippenberg (EPFL),
Carmon, ...
Painter (Caltech)
Schwab (Cornell)
Harris (Yale)
Teufel, Lehnert (Boulder)
Stamper-Kurn (Berkeley)
cold atoms
Sillanpää (Aalto U)
Optomechanical experiments (selection)
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Amir Safavi-Naeini (Wednesday)
Photonic crystals: Very strong coupling between localized vibrational and optical modes
Isabelle Robert (Thursday)
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Nano-Optomechanics: Nanowire in a light field
• Ultra-sensitive nano-optomechanical detection of a bi-dimensional nanomechanical degree of freedom
•Topological structure of the radiation force in a focused laser beam
Pierre Verlot (Friday)
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Coupling to atoms
Samuel Deleglise (Thursday)
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Measuring mechanical motion
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input laseropticalcavity mechanical
resonator
reflection phase shift
Optical detection of mechanical motion
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meas
Two contributions to 1. measurement imprecision2. measurement back-action: fluctuating force on system
phase noise oflaser beam (shot
noise limit!)
noisy radiation pressure force
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true spectrum
+ imprecisionnoise
+ backactionnoise
(measured)(measured)
coupling to detector(intensity of measurement beam)
imprecisionnoise bac
kactio
n
noise
intrinsic fluctuations
full noise
Best case allowed by quantum mechanics:“Standard quantum limit (SQL) of displacement detection”
“Standard quantum limit” of displacement detection
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1.5561.5521.548
Weak
Measurem
entStrong
Measurem
ent
Challenge: Reach optimal regime (where backaction becomes important)
Recent experimental results:
Thomas Purdy (Monday)
Solid state:Membraneresonator
Cold atoms
Sydney Schreppler (Tuesday)
(Berkeley group)
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Strong backaction induces squeezing of radiation field!
Input: laser field with fluctuating intensity
Output: reduced (“squeezed”) noise
Optomechanical system:Intensity-dependent optical resonance (=Kerr medium)
Amir Safavi-Naeini (Wednesday)
Thomas Purdy (Monday)
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Measuring x2 instead of x(Ultimate goal: phonon number detection)
left mode
right mode
)membrane
Membrane position
Lase
r detu
ning
Jack Harris (Tuesday)
Shift in membrane frequency per intracavity photon
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here: use feedback to optimizesqueezing of a thermal mechanical state
Menno Poot (Friday)
100 um
V
10 um
general trick: time-dependent modulation of spring constant produces squeezing
Sensitive measurement can be usedfor feedback!
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Mechanical resonators from carbon
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=carbon
nanotube
Adrian Bachtold (Wednesday)
thermal motion of a carbon nanotube
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Gary Steele (Wednesday)
criti
cal
curr
ent
force
SQUID
carbon nanotube motion coupled to a superconducting circuit (SQUID)
Carbon nanotubes: very low mass, strong quantum zero-point fluctuations – couple to other quantum devices!
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Carbon nanotubes or diamond in photonic circuits
Diamond nanophotonic circuits Waveguide integrated carbon nanotubes
Wolfram Pernice (Tuesday)
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The Quantum Regime(still mostly theory, but first experiments exist)
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Schwab and Roukes, Physics Today 2005
• nano-electro-mechanical systems
• optomechanical systems
Superconducting qubit coupled to nanoresonator: Cleland & Martinis 2010
Laser-cooled to ground state: Teufel et al in microwave circuit 2011, Painter group in photonic crystal 2011
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two-level
system (qubit)
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piezoelectric nanomechanical resonator
Josephsonphase qubit
(GHz @ 20 mK: ground state!)swap excitation between qubit and mechanical resonator in a few ns!
Andrew Cleland (Tuesday, ICTP Coll.)
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(Rabl)
Mikhail Lukin (Tuesday)
Nanomechanical resonator coupled to spin
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Dprobe quantum superpositions of a macroscopic resonator via multiple Ramsey measurements:
Correlations between subsequent measurementoutcomes violate the Leggett-Garg inequality
and can be used for other fundamental tests of quantum mechanics !
Two-level system as a probe of a mechanical resonator
Peter Rabl (Tuesday)
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53
(b)
David Vitali (Monday)
Nonclassical mechanical statesWigner phase space density:
pnega
tive
valu
es!
density matrix of quantum state
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Π Π
Φ
�Φ� �
Π Π
Φ
�Φ� �
Π Π
Φ
�Φ� �
Π Π
Φ�Φ� �
Synchronization between multiple resonators in the
quantum regime
Andreas Nunnenkamp (Thursday)
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Optomechanical control & entanglement with light pulses
Klemens Hammerer (Friday)
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microwave field
optical fieldGHz
100 THz
A quantum interface:Taking quantum information from
microwave to optical
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Mechanical mode connects resonators with different frequencies
Connect different parts of a hybrid quantum networkAchieve quantum operations through the mechanical mode
Optical cavity
Microwave cavity
Mechanical mode
Lin Tian (Wednesday)
Andrew Cleland (Monday)Experiment:
Theory:
(Lin Tian)
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Summary
nanomechanical resonators
sensitivereadout
coupling tospins, qubits, atoms,
quantum dots, SQUIDs etc.:“hybrid systems”
build quantum interfaces
interestingmechanical
quantum states
couple several
couple to radiation field