Towards the transduction of radiofrequency qubits … the transduction of radiofrequency qubits to...

© 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

[email protected]


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]


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


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


Two contributions: 𝑔0 = 𝑔𝑂𝑀,𝑀𝐵+𝑔𝑂𝑀,𝑃𝐸

1. Moving dielectric boundary

2. Photo-elastic effect

Optical field

Mechanical deformation

Ω𝑚 , Γ𝑚


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


𝑔𝑂𝑀,𝑀𝐵 ≈ −5 ∙ 𝑔𝑂𝑀,𝑃𝐸


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


Favored

properties can

be engineered

by design.


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



40nm


SEM images of devices


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



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


??


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


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


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



Optomechanically induced absorption (OMIA)

14

Int

Freq

𝜔𝑜


Power Meter


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


Weis et al., “Optomechanically Induced Transparency,” Science 330, 1520 (2010).


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!


Expected transmission:

Ω𝑚 , Γ𝑚


OMIA – data used for evaluation

N=9 N=10

16Katharina Schneider, [email protected]


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


OMIA

Final results for 1D slotted photonic crystals

© 2016 IBM Corporation18 Katharina Schneider, [email protected]

Advantage of moving

boundary effect

because of wavelength

independence!


Mach-Zehnder interferometer to increase the measured RF power

19


Power Meter


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


no Device


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



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!


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


Ω𝑚 , Γ𝑚


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


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



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]

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