Quantum Optics in Wavelength Scale Structures€¦ · Single-photon sources • Optically driven...
Transcript of Quantum Optics in Wavelength Scale Structures€¦ · Single-photon sources • Optically driven...
Quantum Optics in Quantum Optics in
Wavelength Scale Wavelength Scale
StructuresStructures
SFBSFB Summer School Summer School
BlaubeurenBlaubeuren
July 2012July 2012
J. G. RarityJ. G. RarityUniversity of BristolUniversity of Bristol
[email protected]@bristol.ac.uk
Confining light: periodic dielectric structuresPhotonic crystals
From; Photonic Crystals:From; Photonic Crystals: Moulding the Flow of Light, Joannopoulos Moulding the Flow of Light, Joannopoulos
et al, 2008, Princeton University Presset al, 2008, Princeton University Press
Confining light: periodic dielectric structuresPhotonic crystals
Quantum optics in wavelength scale structures
Motivation
More efficient
• single photon sources
• gates, Hybrid QIP.
Content
• 2-level system in a cavity
• Charged quantum dots in cavity
• Spin-photon interface
• Quantum repeater
• Progress towards experiment
True single photon sources
V+
Particle
like Wave-like during propagationParticle
like
Single atom or ion (in a trap)
Single dye molecule
Single colour centre (diamond NV)
Single quantum dot (eg InAs in GaAs)
Key problem: how to get single photons
from source efficiently coupled into
single spatial mode
Single photons from NV- centres
in diamond
Solid immersion lens fabricated on diamond
using focussed ion beam
~5% collection into 0.9NA lens from flat surface
~30% collection into SIL + 0.9NA lens
FDTD simulation
Serendipitous discovery
of single NV centres
under SILs
on Polycrystalline
diamond (E6)
J.P. Haddon et al
APL 97, 241901 2010
QUANTUM DOTS IN MICRO
CAVITIES: SINGLE PHOTON
SOURCES
FIB etching ICP/RIE etching
Pillar microcavities for enhanced out-
coupling of photons from single quantum
dots
Cavity Quantum Electrodynamics (CQED)
Weak coupling
Cavity decay
rate τω
κκ 1==+Q
s
QD dipole decay rate γ
sκκκ
η+
~Efficiency
Purcell Factor ( )effV
nQ
P2
3
4
31~
π
λ+
Weak cavity coupling γκκ ,sg +<<
0 2000000 4000000 6000000 8000000 10000000
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
Ex Field Intensity (a.u.)
Time(ps)
FDTD simulations: 0.50μm
radius micropillar microcavity:
Plane wave resonance=1001 nm
15 mirror pairs on top and 30 bottom
0
10
20
30
40
50
60
70
80
90
100
12 13 14 15 16 17 18 19 200
1500
3000
4500
6000
7500
9000
10500
12000
Q-factor
Number of top mirror pairs (Nt)
Efficiency (%)
Efficiency
Q-factor
Experimental Setup
Hanbury-Brown Twiss measurement
)(
):(~
)()()(
2
)2(
tp
ttp
n
tntng
τττ
+
><
>+<=
Time
Interval
Analyser
Single QD emission and
temperature tuning
962 963 964 965 966 967 968
50K48K46K
44K42K40K38K
36K34K32K
4.3K7K
10K15K
20K22K24K
26K
28K30K
PL Intensity (arb. units)
Wavelength (nm)
3µm×3µm
FIB
0 5 10 15 20 25 30 35 40 45 50 551282
1283
1284
1285
1286
1287
Energy (meV)
Temperature (K)
QD1
QD2
Cavity mode
• Single QD emission can be observed in smaller pillar at low excitation power
• QD emission line shifts faster than cavity mode
Single photon generation in circular pillars
With increasing excitation power
• QD emission saturates
• Cavity mode intensity develops
Single photon generation in circular pillars
( ) 11)()( )2(2)2( +−= τρτ ggb
backgroundcavitysignal
signal
III
I
++=ρ
2)2( 1)0( ρ−=bg
� g(2) (0)=0.05 indicates multi-
photon emission is 20 times
suppressed.
� g(2) (0) increases with pump
power due to the cavity mode
Progress outside Bristol
Single-photon sources
• Optically driven with multiphoton emission <2%
• 1.3µm single photons: Quantum Key Distribution demonstrated over 35km
• Electrically driven single-photon sources Single photon LED
• HoM Interference demonstrated between separate photons from the same QD (75% visibility)
Bennett et al, Optics Exp 13, 7778 (2005)
Journal of Optics B 7, 129-136 (2005).
Entangled photon pairs from Biexciton
Exciton cascaded emission
Nature 439, 179-182, PRL 102, 030406 (2009),
Douce et al., Nature 466, 217 (2010)
Biexciton State
Ground State
Exciton States
‘bright’ m=±1
‘dark’ m=±2
Large dot
15nm
Large dot
15nm
On-chip generation and transmission of single-photons
� In-plane emission of single
photons from a semiconductor
QD.
1.38 1.39 1.400
5000
10000
15000
20000
25000
30000
Intensity (counts/s)
Photon energy (eV)
XX
X
-40 -20 0 20 400
20
40
Coincidences
Time (ns)
0.2
0.4
0.6
0.1 1
10000
100000
Counts per second
Excitation power (µµµµW)
g(2) (0)
X peak - Pulsed mode
More details: Appl. Phys. Lett. 99, 261108 (2011)
Hybrid QIP
Linear gates η<0.5 F>0.9
Non-linear optics?
The PROBLEM: many qubits quantum processor
U
NN
g F,η
Unitary transform
N
sη
Single Qubit source
Single 2-level ~ 2-10%
Heralded from pair ~ 80%
N
dη
Detectors
Si 600-800nm ~70% (100%?)
InGaAs 1.3-1.6um ~30%
Superconducting~10-88%
Linear gates η<0.5 F>0.99
Non-linear optics η~1 F>0.9?
Throughput~ RFfNg
Nd
Ns ).(.ηηη
Spin photon interface using charged
quantum dots in microcavities
C.Y. Hu, A. Young, J. L. O’Brien, W.J. Munro, J. G. Rarity, Phys. Rev. B 78,
085307 (08)
C.Y. Hu, W.J. Munro, J. G. Rarity, Phys. Rev. B 78, 125318 (08)
C.Y. Hu, W.J. Munro, J. L. O’Brien , J. G. Rarity, Arxiv: 0901.3964(09)
C.Y. Hu, J. G. Rarity, Arxiv: 1005.5545, PRB XX, XXX (2011)
Cavity Quantum Electrodynamics (CQED)
eff
2
0
2
4 mV
feg
r
πεπε
h=
QD-cavity
interaction
Cavity decay
rate Q
s
ωκκ
h=+
QD dipole decay rate γ
Strong
coupling
f=oscillator strength
m= electron
effective mass
V= cavity volume
To optimise g/κ
Maximise Q/V1/2
4
sgκκ +
>
Reflection coefficient
Giant optical Faraday rotation
Phase shift gate
Single-sided cavity
( )↓↓⊗+↑↑⊗∆=∆
RRLLieU
ϕϕ )(ˆ
( )
1)~( ,
2tan2)( 1)( 0 1
0
=>>
−+±=== −
c
c
rg
rg
ωωγκκωω
πωϕωCold Cavity
Hot cavity
C.Y. Hu, Rarity et al, Phys. Rev. B 78, 085307 (08)
C.Y. Hu, Rarity et al, Phys. Rev. B 78, 125318 (08)
� Electron spin ↑, L-light feels a hot cavity and R-light feels a cold cavity
� Electron spin ↓, R-light feels a hot cavity and L-light feels a cold cavity
� By suitable detuning can arrange orthogonal, Giant Faraday rotation angle
2 45
2
00 πϕθ
ϕϕθ >∆=−=
−= ↓↑
FF
Giant optical Faraday rotation
Achievable with
1 5.1)(
1~ 1.0)(
>>>+
>+
ss
ss
g
g
κκ
κκ
κκ
κκLow efficiency
High efficiency
Quantum non-demolition detection of a single electron spin
Input light )(2
1LRH +=
Spin up
↑+ →↑⊗ 0)2/(45
2
1πUH
&
Spin down
↓− →↓⊗ 0)2/(45
2
1πUH
&
Spin superposition state ↓+↑ βα
{ }↓−+↑+→↓+↑⊗ 00 45452
1)( βαβαH
C.Y. Hu, et al, Phys. Rev. B 78, 085307 (08)
A photon spin
entangler!
Photon-spin quantum interface
(a)
State transfer from photon to spin
(b)
State transfer from spin to photon
• Deterministic
• High fidelity
• Two sided cavity makes an entangling
beamsplitter (Phys Rev B 80, 205326, 2009)
Quantum Repeater: arXiv1005.5545
Quantum Repeater: arXiv1005.5545
Experiments
• Strong coupling seen in resonant reflection
experiment
• Phase shift between resonant and non-
resonant case ~0.2 radians
• Young, Rarity et al arXiv 1011.384, PRB
2011
Reflection spectroscopyConditional phase shift interferometer
)(sin ωφ=×
−
HV
AD
Empty cavity
-0.10 -0.05 0.00 0.05 0.100.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
|r(ω)|
Detuning (meV)
κs=0
κs=κ/5
κs=3κ
-0.10 -0.05 0.00 0.05 0.10-4
-3
-2
-1
0
1
2
3
4
φ (rad)
Detuning (meV)
κs=0
κs=κ/5
κs=3κ
Resonant reflection spectra of an empty 4µ pillar
(Q~84000)
902.01 902.02 902.03 902.04 902.05 902.06
180000
200000
220000
240000
260000
280000
300000
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Intensity (counts)
Wavelength(nm)
Reflected intensity
Lorentzian fit
Phase
Phase Radians
-0.2 -0.1 0.0 0.1 0.2-4
-3
-2
-1
0
1
2
3
4
g=5k κs=κ/5
g=5k κs=3κ
g=k κs=κ/5
g=k κs=3κ
φ (rad)
Detuning (meV)
Strongly coupled cavity on
resonance
-0.2 -0.1 0.0 0.1 0.2
0.5
0.6
0.7
0.8
0.9
1.0
|r(ω)|
Detuning (meV)
g=5k κs=κ/5
g=5k κs=3κ
g=k κs=κ/5
g=k κs=3κ
Resonant reflection spectra of a 2.5µ pillar containing a single dot:
temperature tuning to resonance (Q~54000)
Comparing PL and resonant spectroscopy
Conditional phase seen between a
dot on and off-resonance with cavity
g~9.4ueV κ+ κs ~ 26ueV γ~5ueV
g> (κ+ κs + γ)/4 ∆φ~0.05 rad
(0.12rad)
21K
22K
21K
22K
Attojoule switch
Input a few photons
Input enough photons (1 in principle) to saturate the
dot and return to weak coupling.
Change phase of reflection, modulate D and A
All optical switch (1 photon ~0.1 attojoule)
Future:
• Improve coupling and reduce losses to achieve phase shift > pi/2
• Establish strong coupling with charged dots.• modulation doped
• electrically charged
• Investigate dynamics of spin via Faraday rotation• We cool the spin by measurement
• Creating spin superposition states (hard)
• Rotating spin around equator for spin echo (easy=U(φ))
• Spin coherence times (of microseconds?)
• Nuclear ‘calming’ to extend coherence times
Approaches to 3D cavities
With Daniel Ho
Z
XY
Y
XZ
Y
XZ
Top view of
central 2D
Photonic
Defect
Layer
Top view
1D Photonic Defect in 3D Inverted Structure
FCC array of spherical holes in Silicon
The finite difference time domain method FDTD
λres= 536.65 nm, Eymode
3.000000E+02
Y
XZ
(c)
Preliminary calculations of cavity volume and Q-
factor: inverse FCC in n=3.5 material ‘silicon’.
• Veff~ 9e-5µm3 =0.19(λ/2n)3
• Q = 80856
• Q/V = 2.84E8
• Q/(V)0.5 = 4.8E6 For NV centres
κ/2π ~ 6 GHz
γ/2π ~ 3-10 MHz (ZPL)
g/2π ~ 20 GHz
3D Two-photon Lithography
5µm
67µm
6µm
100µm
2µm
10µm
100 nm
200 nm
100µm
45
Summary and Outlook
• Interaction between light and matter in wavelength scale optical structures
• Quantum dots in nanocavities, • 1D systems such as pillar microcavities
• Diamond based microstructures• Solid immersion lenses
• suspended waveguide photonic crystal cavities
• Strong coupling leading to gates• Attojoule classical switches
• Spin photon interface
• Quantum ‘repeater’
• Modelling 3D systems capable of showing strong coupling