Schneider Diavolezza 2016

Transcription

Katharina Schneider
2/2/2016, CQom Workshop, Diavolezza, Switzerland
Towards the transduction of radiofrequency
qubits to optical qubits with slotted photonic
crystal cavities
Katharina Schneider, Paul Seidler
IBM Research – Zurich
ksc@zurich.ibm.com
© 2016 IBM Corporation
Outline
1. Optomechanics with 1D slotted photonic crystals
High optomechanical coupling rate based primarily
on the moving boundary effect.
2. Piezoelectric actuation of a 1D photonic crystal
Towards the coherent conversion of radiofrequency
photons to optical photons
2
Katharina Schneider, ksc@zurich.ibm.com
Slotted 1D photonic crystal structures
Q = 1.4 x 105 (measured)
V = 0.0096 (l/n)3
⇒ Q/V > 107
Active material
Seidler et al., Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode
volume ratio, Opt. Exp., 32483 (2013);
Optomechanics
Sensing and Metrology
Modulators for communication
Coherent transduction of RF
to optical photons
Foundations of quantum mechanics
3
Optical switches/transistors
Ultralow-threshold lasers
Single-photon sources
Entangled photon sources
Electrical or optically driven harmonic
generation/frequency conversion
Fundamentals of Optomechanics
mechanical
mode
Ω𝑚 , Γ𝑚
optical
mode
Mirror displacement
→ Change of the optical cavity mode
𝜕𝜔𝑜
𝜔𝑜 𝑥 ≈ 𝜔o +
𝑥+⋯
𝜕𝑥
laser
o , 
Vacuum optomechanical coupling strength
𝜕𝜔o
𝑔0 =
∙ 𝑥𝑧𝑝𝑓
𝜕𝑥
𝑥=𝑥𝑧𝑝𝑓 ∙ (𝑏 † + 𝑏)
Optical field
Harmonic oscillator + interaction Hamiltonians
𝐻 = 𝜔𝑜 𝑎† 𝑎 + Ω𝑚 𝑏 † 𝑏 + 𝑔0 (𝑏 † + 𝑏) 𝑎† 𝑎
Two contributions: 𝑔0 = 𝑔𝑂𝑀,𝑀𝐵 +𝑔𝑂𝑀,𝑃𝐸
Mechanical deformation
1. Moving dielectric boundary
2. Photo-elastic effect
4
Optimization of the slottes photonic crystal for optomechanics
 Electric field is concentrated in the air region at the high index contrast boundary
 Small contribution of photo-elastic effect
 Moving dielectric boundary effect dominates
 Optimization of F = Q ∙ 𝑔0 with COMSOL and Matlab
 Coupling can be increased by making the slit narrower
 Challenge: maintain the high mechanical resonance frequency
Achieved structure from simulation:
Optical field
simulated: Ω𝑚 /2π = 3.3 GHz
simulated: Q = 1.8 x 106
5
𝑔𝑂𝑀,𝑀𝐵 ≈ −5 ∙ 𝑔𝑂𝑀,𝑃𝐸
Device structures, that exploit the effect of the slit
Optical field
Open slit
760 MHz
Q = 1.6 x 106
Slit closed with crossbars
3.2 GHz
Q = 1.8 x 106
Vertical slit
6.1 GHz
Favored
properties can
be engineered
by design.
Q = 3.8 x 105
Horizontal Double slit
6
Fabrication process
HSQ
Si (220 nm)
SiO2 (3mm)
100-keV
e-beam
exposure/
development
Si
Si
Buffered HF
wet etch
Si
7
HSQ
Si
SiO2
HBr/O2
ICP-RIE
Si
SiO2
Si
Si
Si
photoresist
Si
SiO2
Si
UV photo
exposure/
development
SiO2
Si
SEM images of devices
40nm
8
How to measure the optomechanical coupling strength g0
Optomechanically induced
transparency and absorption
Calibration tone
Gorodetsky et al, “Determination of the vacuum
optomechanical coupling rate using frequency
noise calibration”, OSA (2010)
9
Weis et al., “Optomechanically Induced
Transparency,” Science 330, 1520 (2010).
Calibration tone measurement
Power
Meter
99:1 Fiber Optic
Splitter
Fiber Polarization
Controller
Phase
modulator
EDFA
Electrical
Spectrum
Analyzer
Tunable Infrared
Laser
•
The cavity transduces laser frequency
fluctuations and cavity frequency fluctuations
in the same way: 𝑆𝑉 Ω = GV,ω Ω
•
•
10
Optical
Receiver
Tunable
Bandpass
Filter
2
∙ 𝑆𝜔 Ω
Phase-modulate the laser field with a known
modulation depth 𝛽 at frequency Ω𝑐𝑎𝑙 .
?
?
Compare the calibration tone signal with the
thermomechanical frequency noise.
Calibration tone measurement
mechanical
resonance
calibration
tone
Integrated area beneath the
thermomechanical noise peak:
𝑉2
𝑚
= 2𝑔02 𝑛𝑡ℎ GV,ω Ω𝑚
2
Integrated area beneath calibration
tone:
𝑉2
𝑐𝑎𝑙
1 2 2
= Ω𝑐𝑎𝑙 𝛽 GV,ω Ω𝑐𝑎𝑙
2
2
Comparison leads to
N
g0/2π
9
960 ± 50 kHz
10
560 ± 20 kHz
𝛽Ω𝑐𝑎𝑙 1 𝑉 2 𝑚 GV,ω Ω𝑐𝑎𝑙
𝑔0 =
2
𝑛𝑡ℎ 𝑉 2 𝑐𝑎𝑙 GV,ω Ω𝑚
Gorodetsky et al, “Determination of the vacuum optomechanical
coupling rate using frequency noise calibration”, OSA (2010)
11
Comparison to existing designs
Jasper Chan, Amir H. Safavi-Naeni, Jeff T.Hill. Seán
Meenehan, and Oskar Painter; Optimized optomechanical
crystal with acoustic radiation shield, Appl. Phys. Lett. 101
081115 (2012)
12
Rick Leijssen and Ewold Verhagen; Strong
optomechanical interactions in a sliced photonic crystal
nanobeam, Scientific reports 5, 15974 (2012)
Chan et al.
Leijssen et al.
𝜔0 /2π
194 THz
186.7 THz
Q0
1.2·106
400
𝜔M/2π
5.1 GHz
5.8 MHz
QM
6.8·105
200 (free space)
𝑔𝑂𝑀,𝑃𝐸 /2π
950 kHz *
𝑔𝑂𝑀,𝑀𝐵 /2π
-90 kHz *
𝑔0 /2π
1.1 MHz
*simulation
11.5 MHz
How to measure the optomechanical coupling strength g0
Optomechanically induced
transparency and absorption
Calibration tone
Gorodetsky et al, “Determination of the vacuum
optomechanical coupling rate using frequency
noise calibration”, OSA (2010)
13
Weis et al., “Optomechanically Induced
Transparency,” Science 330, 1520 (2010).
Optomechanically induced absorption (OMIA)
Power
Meter
Int
99:1 Fiber
Optic
Splitter
Fiber
Polarization
Controller
𝜔𝑜
EDFA
EOM
Vector
Network
Analyzer
Optical
Receiver
Tunable
Bandpass
Filter
Tunable
Infrared
Laser
Freq
Constructive interference of the lower
sideband and the intracavity probe field
 Enhanced transparency window
for the probe beam
Weis et al., “Optomechanically Induced Transparency,” Science 330, 1520 (2010).
14
Inferring the optomechanical vacuum coupling rate g0
Expected transmission:
𝜅𝑒 /2
𝑡 ΔO𝐶 =
𝐺2
𝜅/2 +
𝑖 Ω𝑚 − Δ𝑂𝐶 + Γ𝑚 /2
 optomechanical coupling
rate 𝐺 can be measured
G = 𝑔0 ∙ 𝑛𝑐𝑎𝑣
𝜅𝑒
laser
optical
mode
o , 
𝜅𝑖
Ω𝑚 , Γ𝑚
mechanical
mode
The intracavity photon number 𝑛𝑐𝑎𝑣
can be determined from the power
leaving the cavity.
H.Haus, “Waves and fields in optoelectronics,” , PrenticeHall, (1984)
 Quite a number of uncertainties in
this calculation!
OMIA – data used for evaluation
N=9
16
N=10
Final results for 1D slotted photonic crystals
simulation
calibration tone
OMIA
N
g0/2π [kHz]
g0/2π [kHz]
9
700 ± 400
970 ± 70
10
500 ± 300
560 ± 70
g0/2π [kHz]
967
The slotted photonic crystal devices…
• show a high vacuum optomechanical
coupling strength.
• exploit optomechanical coupling based
primarily on the moving boundary effect.
• achieve the resolved sideband regime.
17
N
𝜅/2π [GHz]
Ω𝑚 /2π [GHz]
9
4.01
2.69
10
1.70
2.68
Advantage of moving
boundary effect
because of wavelength
independence!
18
Mach-Zehnder interferometer to increase the measured RF power
Power
Meter
𝐼𝜔𝑚 ∝ 𝐸1 𝐸2 ∙ 𝑇 𝜔𝑐 + 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚 𝑡 + Δ𝜑
99:1 Fiber
Optic
Splitter
Fiber
Polarization
Controller
+ 𝐸1 𝐸2 ∙ 𝑇 𝜔𝑐 − 𝜔𝑚 ∙ 𝛽 ∙ cos −𝜔𝑚 𝑡 + Δ𝜑
EDFA
Electrical
Spectrum
Analyzer
Optical
Receiver
+ 𝐸22 ∙ 𝑇 𝜔𝑐 ∙ 𝑇 𝜔𝑐 − 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚 𝑡
Tunable
Bandpass
Filter
+ 𝐸22 ∙ 𝑇 𝜔𝑐 ∙ 𝑇 𝜔𝑐 + 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚 𝑡
Tunable
Infrared
Laser
9:1
1:1
no Device
19
Outline
1. Optomechanics with 1D slotted photonic crystals
High optomechanical coupling rate based primarily
on the moving boundary effect.
2. Piezoelectric actuation of a 1D photonic crystal
Towards the coherent conversion of radiofrequency
photons to optical photons
20
Microwave quantum computer interfaces
Stefan Filip, IBM Research, Zurich:
Quantum information processing
with superconducting circuits
CLIENT
Blind
Quantum
Computing
Quantum
computation
without access
to client data
Prepare and
receive
optical states
Typical qubit frequency: 5-10 GHz
How to communicate with a
quantum computer over long
distances?
Quantum
Optical
Communication
Channel
Use optical qubits to reduce
decoherence!
300 K
10 mK
Enable secure, remote interaction
with quantum computers
21
slide adapted from J.Orcutt, IBM Research Yorktown
Alternatives for RF/microwave to optical conversion
optical
mode
laser
mechanical
mode
Ω𝑚 , Γ𝑚
Γ𝜇
𝜇𝑚
𝑔0
Γ𝑚
𝑔0𝑜𝑚
𝜅
𝑛𝑐𝑎𝑣
o , 
Ω𝜇
Compute
Electrostatic actuation
Ω𝑚
𝜔0
Freq
Transmit
Piezoelectric actuation
C
C
d33
L
L
R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W.
Simmonds, C. A. Regal and K. W. Lehnert, “Bidirectional and efficient
conversion between microwave and optical light,” Nature Physics 10,
321-326 (2014).
22
J. Bochmann, A. Vainsencher, D. D. Awschalom and A. N. Cleland.,
Nanomechanical Coupling between microwave and optical photons,
Nat. Phys. Lett. 2478 (2013)
Frequency conversion in the quantum regime with an
intermediate mechanical resonator
Efficient coupling into
and out of the cavities.
Couplings greater than
relaxation rates:
2𝑔0 𝑛𝑐𝑎𝑣 ≫ Γ𝑚 , 𝜅
Requirements
The transducer should
not add any noise.
23
Bandwidth:
FWHM of the
mechanical oscillator in
presence of the drives
F. Lecocq et al., Mechanically mediated microwave frequency conversion in the quantum regime, arxiv: 1512.00078v1
Summary
Optomechanics with 1D slotted photonic crystals
•
Resolved sideband regime
•
High optomechanical
coupling strength of 960 kHz
•
Based primarily on the
moving boundary effect
Towards the coherent conversion of radiofrequency photons to
optical photons
Quantum Optical
Communication
Channel
superconducting
metal electrodes
24
Special thanks to…
• Prof. Kippenberg and the k-Lab
• Bert Offrein and the IBM
photonics group
• Antonis Olziersky
Thanks for your
attention!
25

Schneider Diavolezza 2016

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