Optomechanics

Transcription

Optomechanics

Cavity optomechanics:
– interactions between light and
nanomechanical motion
Florian Marquardt
University of Erlangen-Nuremberg, Germany, and
Max-Planck Institute for the Physics of Light (Erlangen)
Radiation pressure
Johannes Kepler
De Cometis, 1619
(Comet Hale-Bopp; by Robert Allevo)
Radiation pressure
Johannes Kepler
De Cometis, 1619
Radiation pressure
Nichols and Hull, 1901
Lebedev, 1901
Nichols and Hull, Physical Review 13, 307 (1901)
Radiation forces
Trapping and cooling
• Optical tweezers
• Optical lattices
...but usually no back-action from motion onto light!
Optomechanics on different
length scales
4 km
LIGO – Laser Interferometer
Gravitational
Wave Observatory
Mirror on cantilever –
Bouwmeester lab, Santa Barbara
(2006)
1014 atoms
Optomechanical Hamiltonian
laser
optical
cavity
mechanical
mode
laser
optical
cavity
mechanical
mode
Review “Cavity Optomechanics”:
M. Aspelmeyer, T. Kippenberg, FM
arXiv:1303.0733
laser
optical
cavity
mechanical
mode
laser detuning optomech.
coupling
...any dielectric moving inside a cavity
generates an optomechanical interaction!
The zoo of optomechanical
(and analogous) systems
Karrai
(Munich)
Bouwmeester
(Santa Barbara)
LKB group
(Paris)
Mavalvala
(MIT)
Vahala (Caltech)
Kippenberg (EPFL),
Carmon, ...
Harris (Yale)
Teufel, Lehnert (Boulder)
Painter (Caltech)
Schwab (Cornell)
Stamper-Kurn (Berkeley)
cold atoms
Aspelmeyer (Vienna)
Optomechanics: general outlook
2
Fundamental tests of quantum
mechanics in a new regime:
entanglement with ‘macroscopic’ objects,
unconventional decoherence?
[e.g.: gravitationally induced?]
Mechanics as a ‘bus’ for connecting
hybrid components: superconducting
qubits, spins, photons, cold atoms, ....
Precision measurements
small displacements, masses, forces, and
accelerations
Painter lab
Tang lab (Yale)
Optomechanical circuits & arrays
Exploit nonlinearities for classical and
quantum information processing, storage,
and amplification; study collective
dynamics in arrays
Towards the quantum regime of
mechanical motion
Schwab and Roukes, Physics Today 2005
nano-electro-mechanical systems
•Superconducting
qubit coupled to nanoresonator: Cleland & Martinis 2010
• optomechanical systems
Ca
IQ
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1x1010
1x109
8
x
1 10
1x107
6
x
1 10
100000
10000
1000
100
10
1
0.1
0.01
0.001
0.0001
0.00001
LKB
phonon number
Laser-cooling towards the ground state
ground state
0.01
0.1
analogy to (cavity-assisted)
laser cooling of atoms
min
i
phomum p
non oss
num ible
ber
1
10
FM et al., PRL 93, 093902 (2007)
Wilson-Rae et al., PRL 99, 093901 (2007)
Optomechanics (Outline)
Displacement detection
Linear optomechanics
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
Quantum theory of cooling
Interesting quantum states
Towards Fock state detection
Hybrid systems: coupling to atoms
Optomechanical crystals & arrays
Optical displacement detection
input laser
optical
cavity
reflection
phase shift
cantilever
Thermal fluctuations of a
harmonic oscillator
Classical equipartition theorem:
Possibilities:
•Direct time-resolved detection
•Analyze fluctuation spectrum of x
extract
temperature!
Fluctuation spectrum
Fluctuation spectrum
Fluctuation-dissipation theorem
General relation between noise spectrum and linear
response susceptibility
susceptibility
(classical limit)
susceptibility
(classical limit)
for the damped oscillator:
susceptibility
(classical limit)
for the damped oscillator:
area yields
variance of x:
...yields
temperature!
Displacement spectrum
a
b
-29
10
nd=18
-13
10
n d =4,500
n m=27
4
-31
10
nd=280
nd=1,100
nd=4,500
n m=8.5
n m=2.9
c
100
2
-14
10
8
nd=28,000
6
4
nd=89,000
2
n m=0.93
nd=180,000
-15
-32
10
S/Po (1/H z)
10
n d =11,000
n m=22
-30
2
Sx (m /H z)
nd=71
10
10.556
10.558
F requency (M H z)
10.3
Teufel et al., Nature 2011
Measurement noise
Measurement noise
meas
Two contributions to
phase noise of
1. measurement imprecision laser beam (shot
noise limit!)
2. measurement back-action:
fluctuating force on system noisy radiation
pressure force
full noise
(including back-action)
imprecision noise
intrinsic (thermal &
quantum) noise
measured noise (log scale)
“Standard Quantum Limit”
im
pr
ec
isi
on
no
SQL
ise
ba
-a
k
c
n
o
i
ct
n
e
s
i
o
zero-point
fluctuations
laser power (log scale)
Best case allowed by quantum mechanics:
“Standard quantum limit
(SQL) of displacement
detection”
...as if adding the zero-point fluctuations a
second time: “adding half a photon”
Notes on the SQL
“weak measurement”: integrating the signal
over time to suppress the noise
trying to detect slowly varying “quadratures of
motion”:
Heisenberg is the reason for SQL!
no limit for instantaneous
measurement of x(t)!
SQL means: detect
down to
on a
time scale
Impressive:
!
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
oscillating mirror
Basic physics:
Statics
x
radiation
input laser
fixed mirror
Frad
Experimental proof of static bistability:
A. Dorsel, J. D. McCullen, P. Meystre,
E. Vignes and H. Walther:
Phys. Rev. Lett. 51, 1550 (1983)
Frad(x) = 2I(x)/c
λ
2F
pressure
cantilever
λ/2
Vrad(x)
Veff = Vrad + VHO
x
hysteresis
amics: Delayed light
response
Basic physics:
quasistatic
F
dynamics
finite sweep!rate
sweep x
finite
cavity
ring-down
rate γ time
finite
optical
ringdown
⇒ delayed response to cantilever motion
–
delayed response to cantilever motion
F
!
F dx
<0
>0
x
cooling
heating
0
Höhberger-Metzger and Karrai,
(amplification)
Nature 432, 1002 (2004):
C. Höhberger!Metzger and K. Karrai, Nature 432, 1002 (2004)
300K to 17K [photothermal
force]
(with photothermal force instead of radiation pressure)
Equations of motion
input laser
optical
cavity
cantilever
Equations of motion
optical
cavity
input laser
mechanical
frequency
mechanical
damping
equilibrium
position
cavity
detuning
decay
rate
from resonance
cantilever
radiation
pressure
laser
amplitude
Linearized optomechanics
(solve for arbitrary
)
Optomechanical
frequency shift
(“optical spring”)
Effective
optomechanical
damping rate
Linearized dynamics
Effective
optomechanical
damping rate
Optomechanical
frequency shift
laser
detuning
cooling
heating/
amplification
softer
stiffer
Linearized dynamics
Effective
optomechanical
damping rate
Optomechanical
frequency shift
laser
detuning
cooling
heating/
amplification
softer
stiffer
laser
optical
cavity
mechanical
mode
laser detuning optomech.
coupling
Quantum optomechanics:
Linearized Hamiltonian
large amplitude quantum fluctuations
(laser drive)
bilinear interaction
tunable coupling!
Sufficient to explain (almost) all current
optomechanical experiments in the quantum regime
Mechanics & Optics
After linearization: two linearly coupled harmonic oscillators!
mechanical oscillator
driven optical cavity
Different regimes
blue-detuned
cavity
pump
red-detuned
beam-splitter
(cooling)
QND
squeezer
(entanglement)
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
ring-down rate γ
esponse to cantilever motion
Self-induced oscillations
F
!
F dx
<0
>0
x
cooling 0 heating
total
ring-down rate γ
esponse to cantilever motion
Self-induced oscillations
F
!
F dx
<0
>0
x
cooling 0 heating
total
Beyond some laser input power threshold: instability
Cantilever displacement x
Amplitude A
Time t
An optomechanical cell as a Hopf oscillator
amplitude
laser
power
phase
bifurcation
Amplitude fixed, phase undetermined!
Attractor diagram
power fed into
the cantilever
1
0
cantilever
energy
100
3
2
1
0
-1
detuning
FM, Harris, Girvin,
PRL 96, 103901 (2006)
Ludwig, Kubala, FM,
NJP 2008
Attractor diagram
power fed into
the cantilever
1
power balance
0
cantilever
energy
100
3
2
1
0
-1
detuning
FM, Harris, Girvin,
PRL 96, 103901 (2006)
Ludwig, Kubala, FM,
NJP 2008
Attractor diagram
power fed into
the cantilever
1
power balance
0
cantilever
energy
100
3
2
1
0
-1
detuning
FM, Harris, Girvin,
PRL 96, 103901 (2006)
Ludwig, Kubala, FM,
NJP 2008
Attractor diagram
15
Oscillation amplitude
10
Höhberger, Karrai, IEEE
proceedings 2004
Carmon, Rokhsari,
Yang, Kippenberg,
Vahala, PRL 2005
5
+
transition
0
FM, Harris, Girvin,
PRL 2006
Metzger et al.,
PRL 2008
ï
0
detuning
Attractor diagram
15
10
proceedings 2004
Carmon, Rokhsari,
Yang, Kippenberg,
Vahala, PRL 2005
5
+
FM, Harris, Girvin,
PRL 2006
0
Metzger et al.,
PRL 2008
ï
0
detuning
Attractor diagram
15
10
proceedings 2004
Carmon, Rokhsari,
Yang, Kippenberg,
Vahala, PRL 2005
5
+
FM, Harris, Girvin,
PRL 2006
0
Metzger et al.,
PRL 2008
ï
0
detuning
Coupled oscillators?
Coupled oscillators?
...
Collective dynamics in an array of
coupled cells?
Phase-locking: synchronization!
Synchronization: Huygens’ observation
(Huygens’ original drawing!)
Coupled pendula synchronize...
...even though frequencies slightly different
mechanical coupling k/mΩ21
Classical nonlinear collective dynamics:
Synchronization in an optomechanical array
two coupled
cells
0.06
0.05
0.04
c
n
sy
0.03
n
o
hr
→
→
0.02
d
e
iz
0
π
n
y
s
un
d
e
z
i
n
o
chr
0.01
-0.91
0.01
0.02
0.0
0.61
0.03
0.04
frequency difference δΩ/Ω1
G. Heinrich et al., Phys. Rev. Lett. 107, 043603 (2011)
##
Experiments (two cells, joint optical mode)
#
laser detuning
Michal Lipson lab, Cornell
Hong Tang lab,Yale
sync
sync
mechanical frequency
(Zhang et al., PRL 2012)
(Bagheri, Poot, FM, Tang; PRL 2013)
Effective Kuramoto model
eff. Kuramoto
model
optomech.
model
Hopf model
eff. Kuramoto
model
optomech.
model
Hopf model
Effective Kuramoto-type model
for coupled Hopf oscillators:
eff. Kuramoto
model
optomech.
model
Hopf model
Effective Kuramoto-type model
for coupled Hopf oscillators:
sin(δϕ)
1
0
-1
0
1
2
3
4
5
6
time tδΩ/2π
0
1
2
3
4
5
time tδΩ/2π
6
Synchronization in optomechanical arrays
Optomechanical arrays
Optomechanical array: Many
coupled optomechanical cells
optical mode
mechanical mode
laser drive
Possible design based on “snowflake” 2D optomechanical crystal (Painter
group), here: with suitable defects forming a superlattice (array of cells)
Pattern formation in optomechanical arrays
work with Christian Brendel, Roland Lauter,
Steve Habrake, Max Ludwig
mechanical phase
6.28319
40
20
Phase vortex
20
40
60
6.28319
transient state
0
(B,A can be calculated from
microscopic parameters)
0
0
6.28319
6.28319
60
60
60
40
40
40
20
20
20
0
0
0
20
40
0
0
60
0
20
40
0
60
40
40
40
20
20
20
0
0
20
40
60
40
60
6.28319
60
0
20
6.28319
60
Spatiotemporal
Chaos
0
0
60
6.28319
steady state
initial state
60
0
0
0
20
40
60
Spiral patterns
0
0
20
40
60
0
e
�b̂† b̂� reaches a finite value. Yet, the expectation value
coherent
mechanical
n
�Transition
b̂� remains smalltowards
and constant
in time. When
increasoscillations
e
ing the intercellular coupling, though, �b̂� suddenly starts
roscillating:
Observation
for strong inter-cell coupling:
t spontaneous time-dependence of phonon field
“order parameter”
r
(“mechanical coherence”)
−iΩ
t
y,
�b̂�(t) = b̄ + re eff .
(4)
s
r
Our more detailed analysis (see below) indicates that
coheren
ce
1
0
mechanical
0.5
0
optical
coherence
0.25
inter-cell coupling
0.5
quantum mean-field
result
Mechanical quantum states
Incoherent mechan. oscillations (weak inter-cell coupling)
15
5
Mechanical Wigner density
shows incoherent mixture of
all possible oscillation phases
0
0
0
15
-5
-5
0
5
Coherent mechan. oscillations (strong inter-cell coupling)
Mechanical Wigner density
shows preferred phase
(coherent state) –
spontaneous symmetry
breaking!
15
5
0
0
0
15
-5
-5
0
5
b̂� remains small and constant in time. When increastowards
ng the Transition
intercellular coupling,
though,coherent
�b̂� suddenly mechanical
starts
oscillations
scillating:
�b̂�(t) = b̄ + re−iΩeff t .
“order parameter”
(“mechanical coherence”)
(4)
Our more detailed
analysis
(see below)
indicates that
mechanical
coherence
(color-coded)
0.25
0
-1.5
coherent
onset of self-oscillations
mechancial inter-cell coupling
0.5
1.5
1
incoherent
0.5
0
-1
-0.5
0
0.5
1
laser detuning
Max Ludwig, FM, PRL 111, 073603 (2013):Quantum many-body dynamics in optomechanical arrays
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
Cooling with light
input laser
optical
cavity
cantilever
Current goal in the field: ground state of
mechanical motion of a macroscopic cantilever
Classical theory:
Pioneering theory and
experiments: Braginsky
(since 1960s )
optomechanical damping rate
Cooling with light
input laser
optical
cavity
cantilever
Current goal in the field: ground state of
mechanical motion of a macroscopic cantilever
Classical theory:
Pioneering theory and
experiments: Braginsky
(since 1960s )
quantum limit?
shot noise!
optomechanical damping rate
Cooling with light
input laser
optical
cavity
cantilever
Quantum picture: Raman scattering – sideband cooling
Original idea:
Sideband cooling in ion traps – Hänsch, Schawlow / Wineland, Dehmelt 1975
Similar ideas proposed for nanomechanics:
cantilever + quantum dot – Wilson-Rae, Zoller, Imamoglu 2004
cantilever + Cooper-pair box – Martin Shnirman, Tian, Zoller 2004
cantilever + ion – Tian, Zoller 2004
cantilever + supercond. SET – Clerk, Bennett / Blencowe, Imbers, Armour 2005,
Naik et al. (Schwab group) 2006
Quantum noise approach
System
(cantilever)
Bath
(radiation field
in cavity)
spectrum
spectrum
bath provides
energy
transition
rate
bath absorbs
energy
Quantum theory of
optomechanical cooling
Spectrum of radiation pressure fluctuations
radiation
pressure
force
photon number
photon shot noise spectrum
ation pressure force:
F̂ =
n̂
L theory of
Quantum
e spectrum for photon number:
optomechanical cooling
# +∞
κ
(ω) =
dt e (#n̂(t)n̂(0)$−n̄ ) = n̄
Spectrum
of radiation pressure (ω
fluctuations
+ ∆)2 + (κ/2
−∞
iωt
2
SF F (ω) [norm.]
ning laser/cavity resonance: ∆ = ωL − ωR
Cavity decay rat
detuning :
−∆
κ
cavity linewidth
cavity emits energy / absorbs energy
dt eiωt(#n̂(t)n̂(0)$−n̄2) = n̄
SF F (ω) [norm.]
(ω + ∆)2 + theory
(κ/2)2
Quantum
of
Cavity decay rate: κ
ωR
ty resonance: ∆ = ωL −
optomechanical
cooling
Cooling rate
−∆
κ
Quantum limit for
cantilever phonon number
cavity emits energy / absorbs energy
FM, Chen, Clerk, Girvin,
PRL 93, 093902 (2007)
also: Wilson-Rae, Nooshi, Zwerger,
Kippenberg, PRL 99, 093901 (2007);
Genes et al, PRA 2008
experiment with
Kippenberg group 2007
Ground-state cooling
needs: high optical finesse /
large mechanical frequency
01
1
r2
de
ul
Bo
Ca
lte
ch
20
11
IQ
OQ
I
MP
Q
JIL
A
Yal
e
MIT
1x1010
1x109
8
x
1 10
1x107
6
x
1 10
100000
10000
1000
100
10
1
0.1
0.01
0.001
0.0001
0.00001
LKB
phonon number
Laser-cooling towards the ground state
ground state
0.01
0.1
analogy to (cavity-assisted)
laser cooling of atoms
min
i
phomum p
non oss
num ible
ber
1
10
FM et al., PRL 93, 093902 (2007)
Wilson-Rae et al., PRL 99, 093901 (2007)
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
Squeezed states
Squeezing the mechanical oscillator state
Squeezed states
Squeezed states
Squeezed states
t
x
Squeezed states
t
x
Periodic modulation of spring constant:
Parametric amplification
Squeezed states
t
x
Squeezed states
t
x
Squeezed states
t
x
Measuring quadratures
(“beating the SQL”)
Clerk, Marquardt, Jacobs; NJP 10, 095010 (2008)
amplitude-modulated input field
(similar to stroboscopic
measurement)
measure only one quadrature, back-action noise affects
only the other one....need:
measurement)
p
reconstruct
mechanical
Wigner density
(quantum state tomography)
x
measurement)
p
reconstruct
mechanical
Wigner density
x
measurement)
p
reconstruct
mechanical
Wigner density
x
Optomechanical entanglement
Bose, Jacobs, Knight 1997; Mancini et al. 1997
n=0
n=1
n=2
n=3
coherent mechanical state
entangled state
(light field/mechanics)
Proposed optomechanical which-path
experiment and quantum eraser
p
x
Recover photon
coherence if interaction
time equals a multiple of
the mechanical period!
cf. Haroche experiments in 90s
Marshall, Simon, Penrose, Bouwmeester, PRL 91, 130401 (2003)
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
optical frequency
“Membrane in the middle” setup
Thompson, Zwickl, Jayich, Marquardt,
Girvin, Harris, Nature 72, 452 (2008)
“Membrane in the middle” setup
frequency
optical frequency
membrane
transmission
membrane displacement
Experiment (Harris group, Yale)
50 nm SiN membrane
Mechanical frequency:
ωM=2π⋅134 kHz
Mechanical quality factor:
6
7
Q=10 ÷10
Optomechanical cooling
from 300K to 7mK
Towards Fock state detection of
a macroscopic object
Detection of displacement x: not what we need!
frequency
membrane
transmission
frequency
membrane
transmission
frequency
membrane
transmission
phase shift of measurement beam:
frequency
membrane
transmission
phase shift of measurement beam:
(Time-average over
cavity ring-down time)
QND measurement
of phonon number!
simulated phase shift
(phonon number)
Time
(phonon number)
Time
(phonon number)
Time
(phonon number)
Time
(phonon number)
Signal-to-noise
ratio:
Optical freq. shift
per phonon:
Noise power of
freq. measurement:
Ground state lifetime:
Time
(phonon number)
y
r
e
v
c
ll e
a
h
n
i
g
n
!
g
Signal-to-noise
ratio:
Optical freq. shift
per phonon:
Noise power of
freq. measurement:
Ground state lifetime:
Time
Ideal single-sided cavity: Can observe only
phase of reflected light, i.e. x2: good
Two-sided cavity: Can also observe transmitted
vs. reflected intensity: linear in x!
- need to go back to two-mode Hamiltonian!
- transitions between Fock states!
Single-sided cavity, but with losses: same story
Detailed analysis (Yanbei Chen’s group, PRL 2009)
shows: need
absorptive part of photon
decay (or 2nd mirror)
Miao, H., S. Danilishin, T. Corbitt, and Y. Chen, 2009, PRL 103, 100402
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
Atom-membrane coupling
Note: Existing works simulate
optomechanical effects using cold atoms
K. W. Murch, K. L. Moore, S. Gupta, and
D. M. Stamper-Kurn,
Nature Phys. 4, 561 (2008).
Stamper-Kurn (Berkeley)
cold atoms
F. Brennecke, S. Ritter, T. Donner, and T.
Esslinger, Science 322, 235 (2008).
...profit from small mass of atomic cloud
Here: Coupling a single atom to a
macroscopic mechanical object
Challenge: huge mass ratio
Strong atom-membrane coupling
via the light field
existing experiments on “optomechanics
with cold atoms”: labs of Dan-Stamper Kurn
(Berkeley) and Tilman Esslinger (ETH)
collaboration:
LMU (M. Ludwig, FM, P. Treutlein),
Innsbruck (K. Hammerer, C. Genes, M. Wallquist, P. Zoller),
Boulder (J.Ye), Caltech (H. J. Kimble)
Hammerer et al., PRL 2009
Goal:
atom
membrane
atom-membrane coupling
0
100
System
3
2
1
0
-1
Bath
Nonlinear dynamics
Many modes
mechanical
mode
optical
mode
8
Scaling down
cm
usual optical cavities
10 µm
LKB, Aspelmeyer, Harris,
Bouwmeester, ....
Scaling down
cm
50 µm
microtoroids
Vahala, Kippenberg, Carmon, ...
10 µm
Bouwmeester, ....
Scaling down
cm
50 µm
10 µm
Bouwmeester, ....
microtoroids
optomechanics in
photonic circuits
5 µm
H. Tang et al.,Yale
Vahala, Kippenberg, Carmon, ...
optomechanical crystals
O. Painter et al., Caltech
10 µm
Optomechanical crystals
free-standing photonic crystal structures
optical modes
advantages:
tight vibrational confinement:
high frequencies, small mass
(stronger quantum effects)
tight optical confinement:
vibrational modes large optomechanical coupling
(100 GHz/nm)
integrated on a chip
from: M. Eichenfield et al., Optics Express 17, 20078 (2009), Painter group, Caltech
Optomechanical arrays
l a se
cel
r dr
ive
l1
optical mode
mechanical mode
cel
l2
...
collective nonlinear dynamics:
classical / quantum
cf. Josephson arrays
Dynamics in optomechanical arrays
Outlook
• 2D geometries
• Quantum or classical information processing and
storage (continuous variables)
• Dissipative quantum many-body dynamics
(quantum simulations)
• Hybrid devices: interfacing GHz qubits with light
Photon-phonon translator
(concept: Painter group, Caltech)
strong optical “pump”
1
photon
2
phonon
Superconducting qubit coupled
to nanomechanical resonator
Josephson
phase
qubit
2010: Celand & Martinis labs
piezoelectric nanomechanical resonator
(GHz @ 20 mK: ground state!)
swap excitation between qubit and
mechanical resonator in a few ns!
Conversion of quantum information
phonon-photon
translation
Josephson
phase
qubit
nanomechanical
resonator
light
Recent trends
• Ground-state cooling: success! (spring 2011)
[Teufel et al. in microwave circuit;
Painter group in optical regime]
• Optomechanical (photonic) crystals
• Multiple mechanical/optical modes
• Option: build arrays or ‘optomechanical circuits’
• Strong improvements in coupling
• Possibly soon: ultrastrong coupling (resolve single photonphonon coupling)
• Hybrid systems: Convert GHz quantum information
(superconducting qubit) to photons
• Hybrid systems: atom/mechanics [e.g. Treutlein group]
• Levitating spheres: weak decoherence!
[Barker/ Chang et al./ Romero-Isart et al.]
Optomechanics: general outlook
Bouwmeester
(Santa Barbara/Leiden)
Fundamental tests of quantum
mechanics in a new regime:
entanglement with ‘macroscopic’ objects,
unconventional decoherence?
[e.g.: gravitationally induced?]
Mechanics as a ‘bus’ for connecting
hybrid components: superconducting
qubits, spins, photons, cold atoms, ....
Kapitulnik lab (Stanford)
Tang lab (Yale)
[e.g. testing deviations from Newtonian
gravity due to extra dimensions]
Optomechanical circuits & arrays
Exploit nonlinearities for classical and
quantum information processing, storage,
and amplification; study collective
dynamics in arrays
Parameters of Optomechanical Systems
Mechanical damping rate
rate of energy loss,
linewidth in mechanical spectrum
rate of re-thermalization,
ground state decoherence rate
Mechanical quality factor,
number of oscillations during damping
time
Optomechanical coupling strength
bilinear interaction
tunable coupling!
Single-photon optomechanical coupling rate
nonclassical mechanical quantum states, ....
Linearized (driving-enhanced)
optomechanical coupling rate
optomechanical damping rate, state transfer rate, ...
single-photon coupling rate g0 / S [Hz]
10
6
10
4
10
1
=
/N
2
g0
2
microwave
photonic crystals
nanoobjects
microresonators
mirrors
cold atoms
-2
10
0
1
=
N
/
g0
0
31
-4
10
0
1
=
N
/
g0
-2
1
10
-4
10
1
10
3
10
5
10
7
10
9
cavity decay rate NS [Hz]
10
11
Cooperativities
Linearized (driving-enhanced) cooperativity
Optomechanically induced transparency,
instability towards optomech. oscillations
Linearized (driving-enhanced) quantum cooperativity
ground state cooling, state transfer,
entanglement, squeezing of light, ...
Single-photon cooperativity
Single-photon “quantum” cooperativity
single-photon cooperativity C 0
10
4
10
2
10
0
10
-2
10
-4
10
-6
10
-8
10
-10
10
-12
10
-14
10
-16
10
-18
10
T=3
T=3
0mK
K
5
1
4
2
31
3
microwave
photonic crystals
nanoobjects
microresonators
mirrors
cold atoms
1
10
3
10
5
10
7
10
mechanical frequency :mS [Hz]
9
10
11
Photon interaction
photon blockade, photon QND measurement, ...
photon blockade parameter D
10
2
10
-2
10
-6
5
10
-10
1
10
-14
10
-18
10
-22
10
31
microwave
photonic crystals
nanoobjects
microresonators
mirrors
cold atoms
-6
10
-4
2 4
3
10
-2
10
0
sideband resolution :mN
10
2
Text
Linear Optomechanics
Optical Spring
Cooling & Amplification
Two-tone drive: “Optomechanically
induced transparency”
State transfer, pulsed operation
Wavelength conversion
Radiation Pressure Shot Noise
Squeezing of Light
Squeezing of Mechanics
Entanglement
Optomechanical Circuits
Bandstructure in arrays
Synchronization/patterns in arrays
Transport & pulses in arrays
Nonlinear Optomechanics
Self-induced mechanical oscillations
Synchronization of oscillations
Chaos
Nonlinear Quantum
Optomechanics
Phonon number detection
Phonon shot noise
Photon blockade
Optomechanical “which-way”
experiment
Nonclassical mechanical q. states
Nonlinear OMIT
Noncl. via Conditional Detection
Single-photon sources
Coupling to other two-level
systems
Note:
Yesterday’s red is today’s green!
Linear Optomechanics
Optical Spring
Cooling & Amplification
Two-tone drive: “Optomechanically induced
transparency”
Ground state cooling
State transfer, pulsed operation
Wavelength conversion
Radiation Pressure Shot Noise
Squeezing of Light
Squeezing of Mechanics
Light-Mechanics Entanglement
Accelerometers
Single-quadrature detection, Wigner density
Optomechanics with an active medium
Measure gravity or other small forces
Mechanics-Mechanics entanglement
Pulsed measurement
Quantum Feedback
Rotational Optomechanics
Multimode
Mechanical information processing
Bandstructure in arrays
Synchronization/patterns in arrays
Transport & pulses in arrays
Nonlinear Optomechanics
Self-induced mechanical oscillations
Attractor diagram?
Synchronization of oscillations
Chaos
White: yet unknown challenges/goals
Nonlinear Quantum
Optomechanics
QND Phonon number detection
Phonon shot noise
Photon blockade
Optomechanical
“which-way” experiment
Nonclassical mechanical q. states
Nonlinear OMIT
Noncl. via Conditional Detection
Single-photon sources
Coupling to other two-level systems
Optomechanical Matter-Wave Interferometry
Optomechanics
Review “Cavity Optomechanics”:
M.Aspelmeyer, T. Kippenberg, FM
arXiv:1303.0733

Optomechanics

Transcription

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