towards the transduction of radiofrequency qubits … the transduction of radiofrequency qubits to...
TRANSCRIPT
© 2016 IBM Corporation
Towards the transduction of radiofrequency qubits to optical qubits with slotted photonic crystal cavities
Katharina Schneider
2/2/2016, CQom Workshop, Diavolezza, Switzerland
Katharina Schneider, Paul Seidler
IBM Research – Zurich
© 2016 IBM Corporation
Outline
2
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
Katharina Schneider, [email protected]
© 2016 IBM Corporation
Slotted 1D photonic crystal structures
3
Q = 1.4 x 105 (measured)
V = 0.0096 (l/n)3
⇒ Q/V > 107
Seidler et al., Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode
volume ratio, Opt. Exp., 32483 (2013);
Optical switches/transistors
Ultralow-threshold lasers
Single-photon sources
Entangled photon sources
Electrical or optically driven harmonic
generation/frequency conversion
Active material
Katharina Schneider, [email protected]
Sensing and Metrology
Modulators for communication
Coherent transduction of RF
to optical photons
Foundations of quantum mechanics
Optomechanics
© 2016 IBM Corporation4
𝐻 = 𝜔𝑜 𝑎† 𝑎 + Ω𝑚
𝑏† 𝑏 + 𝑔0 ( 𝑏† + 𝑏) 𝑎† 𝑎
Vacuum optomechanical coupling strength
𝜔𝑜 𝑥 ≈ 𝜔o +𝜕𝜔𝑜
𝜕𝑥𝑥 + ⋯
Mirror displacement
→ Change of the optical cavity mode
𝑔0 =𝜕𝜔o
𝜕𝑥∙ 𝑥𝑧𝑝𝑓
Fundamentals of Optomechanics
Harmonic oscillator + interaction Hamiltonians
𝑥=𝑥𝑧𝑝𝑓 ∙ ( 𝑏† + 𝑏)
laser ,o
optical
mode
mechanical
mode
Katharina Schneider, [email protected]
Two contributions: 𝑔0 = 𝑔𝑂𝑀,𝑀𝐵+𝑔𝑂𝑀,𝑃𝐸
1. Moving dielectric boundary
2. Photo-elastic effect
Optical field
Mechanical deformation
Ω𝑚 , Γ𝑚
© 2016 IBM Corporation
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:
5
Optical field Mechanical deformation
simulated: Q = 1.8 x 106
simulated: Ω𝑚/2π = 3.3 GHz
Katharina Schneider, [email protected]
𝑔𝑂𝑀,𝑀𝐵 ≈ −5 ∙ 𝑔𝑂𝑀,𝑃𝐸
© 2016 IBM Corporation
6
Device structures, that exploit the effect of the slit
Open slit
Slit closed with crossbars
Vertical slit
Horizontal Double slit
Mechanical deformationOptical field
Q = 1.6 x 106
Q = 1.8 x 106
Q = 3.8 x 105
760 MHz
6.1 GHz
3.2 GHz
Katharina Schneider, [email protected]
Favored
properties can
be engineered
by design.
© 2016 IBM Corporation
Fabrication process
7
Si
Siphotoresist
Si
Si
SiO2
Si
Si
SiO2
HSQ
Si
Si (220 nm)
SiO2 (3mm)
HSQ
Si
Si
SiO2
Si
Si
SiO2
100-keV e-beam
exposure/development
HBr/O2
ICP-RIE
UV photo exposure/
development
Buffered HF wet etch
Katharina Schneider, [email protected]
© 2016 IBM Corporation
How to measure the optomechanical coupling strength g0
9
Calibration tone
Gorodetsky et al, “Determination of the vacuum
optomechanical coupling rate using frequency
noise calibration”, OSA (2010)Weis et al., “Optomechanically Induced
Transparency,” Science 330, 1520 (2010).
Optomechanically induced
transparency and absorption
Katharina Schneider, [email protected]
© 2016 IBM Corporation
Calibration tone measurement
10
Tunable Infrared Laser
Power Meter
Fiber Polarization Controller
99:1 Fiber Optic Splitter
TunableBandpass
Filter
EDFA
Optical Receiver
Electrical SpectrumAnalyzer
• The cavity transduces laser frequency
fluctuations and cavity frequency fluctuations
in the same way: 𝑆𝑉 Ω = GV,ω Ω2∙ 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.
Phase modulator
Katharina Schneider, [email protected]
??
© 2016 IBM Corporation
Calibration tone measurement
11
Integrated area beneath the
thermomechanical noise peak:
𝑉2𝑚 = 2𝑔0
2 𝑛𝑡ℎ GV,ω Ω𝑚2
Integrated area beneath calibration
tone:
𝑉2𝑐𝑎𝑙 =
1
2Ω𝑐𝑎𝑙2 𝛽2 GV,ω Ω𝑐𝑎𝑙
2
Comparison leads to
𝑔0 =𝛽Ω𝑐𝑎𝑙
2
1
𝑛𝑡ℎ
𝑉2𝑚
𝑉2𝑐𝑎𝑙
GV,ω Ω𝑐𝑎𝑙
GV,ω Ω𝑚N g0/2π
9 310 ± 47 kHz
10 181 ± 29 kHzKatharina Schneider, [email protected]
Gorodetsky et al, “Determination of the vacuum optomechanical
coupling rate using frequency noise calibration”, OSA (2010)
mechanical
resonance
calibration
tone
© 2016 IBM Corporation
Comparison to existing designs
12 Katharina Schneider, [email protected]
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)
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 11.5 MHz
Rick Leijssen and Ewold Verhagen; Strong
optomechanical interactions in a sliced photonic crystal
nanobeam, Scientific reports 5, 15974 (2012)
*simulation
© 2016 IBM Corporation
How to measure the optomechanical coupling strength g0
13
Calibration tone
Gorodetsky et al, “Determination of the vacuum
optomechanical coupling rate using frequency
noise calibration”, OSA (2010)Weis et al., “Optomechanically Induced
Transparency,” Science 330, 1520 (2010).
Optomechanically induced
transparency and absorption
Katharina Schneider, [email protected]
© 2016 IBM Corporation
Optomechanically induced absorption (OMIA)
14
Int
Freq
𝜔𝑜
Tunable Infrared Laser
Power Meter
Fiber Polarization Controller
EOM
99:1 Fiber Optic
Splitter
TunableBandpass
Filter
EDFA
Optical ReceiverVector
Network Analyzer
Constructive interference of the lower
sideband and the intracavity probe field
Enhanced transparency window
for the probe beam
Katharina Schneider, [email protected]
Weis et al., “Optomechanically Induced Transparency,” Science 330, 1520 (2010).
© 2016 IBM Corporation
laser ,o
optical
mode
mechanical
mode
𝜅𝑒
𝜅𝑖
optomechanical coupling
rate 𝐺 can be measured
G = 𝑔0 ∙ 𝑛𝑐𝑎𝑣
𝑡 ΔO𝐶 =𝜅𝑒/2
𝜅/2 +𝐺2
𝑖 Ω𝑚 − Δ𝑂𝐶 + Γ𝑚/2
Inferring the optomechanical vacuum coupling rate g0
The intracavity photon number 𝑛𝑐𝑎𝑣can be determined from the power
leaving the cavity.
H.Haus, “Waves and fields in optoelectronics,” , Prentice-
Hall, (1984)
Quite a number of uncertainties in
this calculation!
Katharina Schneider, [email protected]
Expected transmission:
Ω𝑚 , Γ𝑚
© 2016 IBM Corporation
OMIA – data used for evaluation
N=9 N=10
16Katharina Schneider, [email protected]
© 2016 IBM Corporation17
N g0/2π [kHz]
9 600 ± 300
10 900 ± 600
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.
g0/2π [kHz]
310 ± 47
181 ± 29
calibration tone
g0/2π [kHz]
342
simulation
N 𝜅/2π [GHz] Ω𝑚/2π [GHz]
9 4.01 2.69
10 1.70 2.68
Katharina Schneider, [email protected]
OMIA
Final results for 1D slotted photonic crystals
© 2016 IBM Corporation18 Katharina Schneider, [email protected]
Advantage of moving
boundary effect
because of wavelength
independence!
© 2016 IBM Corporation
Mach-Zehnder interferometer to increase the measured RF power
19
Tunable Infrared Laser
Power Meter
Fiber Polarization Controller
99:1 Fiber Optic
Splitter
TunableBandpass
Filter
EDFA
Optical ReceiverElectrical
SpectrumAnalyzer
𝐼𝜔𝑚∝ 𝐸1𝐸2 ∙ 𝑇 𝜔𝑐 + 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚𝑡 + Δ𝜑
+ 𝐸1𝐸2 ∙ 𝑇 𝜔𝑐 − 𝜔𝑚 ∙ 𝛽 ∙ cos −𝜔𝑚𝑡 + Δ𝜑
+ 𝐸22 ∙ 𝑇 𝜔𝑐 ∙ 𝑇 𝜔𝑐 − 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚𝑡
+ 𝐸22 ∙ 𝑇 𝜔𝑐 ∙ 𝑇 𝜔𝑐 + 𝜔𝑚 ∙ 𝛽 ∙ cos 𝜔𝑚𝑡
9:1 1:1
Katharina Schneider, [email protected]
no Device
© 2016 IBM Corporation
Outline
20
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
Katharina Schneider, [email protected]
© 2016 IBM Corporation
Microwave quantum computer interfaces
Enable secure, remote interaction
with quantum computers
slide adapted from J.Orcutt, IBM Research Yorktown21
Stefan Filip, IBM Research, Zurich:
Quantum information processing
with superconducting circuits
CLIENT
Prepare and
receive
optical states
Quantum
Optical
Communication
Channel
Quantum
computation
without access
to client data
300 K 10 mK
Blind
Quantum
Computing
Typical qubit frequency: 5-10 GHz
How to communicate with a
quantum computer over long
distances?
Use optical qubits to reduce
decoherence!
© 2016 IBM Corporation
Alternatives for RF/microwave to optical conversion
22
C
LL
d33
C
Electrostatic actuation Piezoelectric actuation
Compute TransmitFreq
𝑔0𝜇𝑚 𝑔0
𝑜𝑚
Γ𝑚 𝜅Γ𝜇
𝜔0Ω𝑚Ω𝜇
J. Bochmann, A. Vainsencher, D. D. Awschalom and A. N. Cleland.,
Nanomechanical Coupling between microwave and optical photons,
Nat. Phys. Lett. 2478 (2013)
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).
𝑛𝑐𝑎𝑣
laser ,o
optical
mode
mechanical
mode
Katharina Schneider, [email protected]
Ω𝑚 , Γ𝑚
© 2016 IBM Corporation
Frequency conversion in the quantum regime with an intermediate mechanical resonator
23
Efficient coupling into and out of the cavities.
Couplings greater than relaxation rates:
2𝑔0 𝑛𝑐𝑎𝑣 ≫ Γ𝑚, 𝜅
The transducer should not add any noise.
Bandwidth:
FWHM of the mechanical oscillator in presence of the drives
Requirements
F. Lecocq et al., Mechanically mediated microwave frequency conversion in the quantum regime, arxiv: 1512.00078v1
© 2016 IBM Corporation
Summary
superconducting
metal electrodes
Optomechanics with 1D slotted photonic crystals
Towards the coherent conversion of radiofrequency photons to
optical photons
Quantum Optical
Communication
Channel
• Resolved sideband regime
• High optomechanical
coupling strength of 342 kHz
• Based primarily on the
moving boundary effect
Katharina Schneider, [email protected]
© 2016 IBM Corporation
Special thanks to…
• Prof. Kippenberg and the k-Lab
• Bert Offrein and the IBM
photonics group
• Antonis Olziersky
Thanks for your attention!
25 Katharina Schneider, [email protected]