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Quantum Dots in Photonic Structures
Lecture 11: QD-microcavity in strong coupling
regime
Jan Suffczyński
Wednesdays, 17.00, SDT
Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego
Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki
Plan for today
1.
Extended
Reminder
2.
QD-Cavity Mode
in the strong
coupling regime
– introduction
3. QD-Cavity Mode in
the strong coupling regime
in Photoluminescence
and reflectivity
Quality factor of a planar cavity
The reflectivity of a DBR consisting of m mirror pairs
(n0 equals 1 for the top mirror and
n0 = nGaAs for the bottom mirror)
AlAs/GaAs planar
microcavity sample with
20/24 mirror pairs in
the upper/lower DBR
From 1D to 3D photonic crystal
Planar
microcavity =
1D confinement
of the light
Pillar microcavity=
3D confinement of
the light
DBR made of ZnSSe and MgS/ZnCdSe supperlattices
Lohmeyer et al.
Photoluminescence - Micropillar eigenmodes
Experiment
Simulation
Extended transfer matrix method:
•
•
Material absorption included
Equal emission intensity of each line assumed
(a)
d = 2.9 m
(b)
PL Intensity (arb. units)
PL Intensity (arb. units)
(a)
d = 2.9 m
d = 1.9 m
(c)
d = 1.4 m
(d)
d = 0.9 m
(e)
d = 0.7 m
2040
2050
2070
2080
d = 1.9 m
(c)
d = 1.4 m
(d)
d = 0.9 m
(e)
d = 0.7 m
Experiment
Simulation
2060
(b)
2090
Photon Energy (meV)
2100
2110
2040
2050
Simulation
Simulation (absorption considered)
2060
2070
2080
2090
2100
2110
Photon Energy (meV)
T. Jakubczyk et al.
Quality factor of the micropillar: loss sources
1
𝑄
~
Top view
Photon
Escape 
Rate
1
𝑄(𝑟)
=
„Planar”
losses
1
+
+
„Sidewall”
losses
1
𝑄𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 (𝑟) 𝑄𝑎𝑏𝑠
+
1
𝑄𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 (𝑟)
r dr
dr: typically ~ 10 nm
Scattering losses proportional to the transverse mode intensity at
the microresonator edge:
𝐽0 2 (𝑐𝑜𝑛𝑠𝑡 ∗ 𝑟)
1
|𝐸 𝑟 |2
~
~ϵ
𝑄𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 (𝑟)
𝑟
𝑟
Sidewall roughness
GaAs/AlAs DBRs
Roughness
of the order of tens of nm
Purcell factor vs diameter
• Pillar diameter D decreases - > V decreases, but also Q decreases
• Fp ~ Q/V
• Nonmonotnic dependence of Fp on the pillar diameter
Q factor oscillations
Oscillations attributed to a
coupling of the fundamental mode
to higher-order pillar modes
Basic idea:
+
+
Decay time measurements
XX on resonance with mode
XX out of resonance with mode
T = 40 K
Time
T = 10 K
M
XC
XX
M
X
XC
Photon Energy
XX
X
Decay rate as a function of detuning
Temperature (K)
389 ps
3
21
65
500
91 ps
450
63 ps
Decay Time (ps)
Photon Counts (arb. units)
400
75 ps
300
250
200
150
100
50
0
Detuning (meV):
s
-2
2.8
0.6
0.0
-0.7
-200
350
0
200
Time (ps)
-1
0
1
2
3
4
Detuning (meV)
400
600
• Strong enhancement of the
decay rate at zero-detuning
Directing of the emission
Bragg
mirrors
• Not only
acceleration of the
emission thanks to
the mode
Directing of the emission
• Not only
acceleration of the
emission thanks to
the mode, but also
directing of the
emission!
Coupling coefficient to the mode
b= FP/(FP+1)
Deterministic QD-Cavity Mode matching
Deterministic QD-Cavity Mode matching
Signal
Photoresist
exposured
Resist development
Nickel mask deposition
Etching:
Lift-off
Pillar with a QD placed in
the mode maximum
Microdisc microcavities production techhnology
Resist deposition +
Negative
electrolithography
GaAs/AlGaAs QD
AlGaAs (Al rich region)
Substrate GaAs
Microdisc microcavities production techhnology
Resist deposition +
Negative
electrolithography
Non-selective
wet etching
GaAs/AlGaAs QD
AlGaAs (Al rich region)
Substrate GaAs
Microdisc microcavities production techhnology
Resist deposition +
Negative
electrolithography
GaAs/AlGaAs QD
AlGaAs (Al rich region)
Substrate GaAs
Non-selective
wet etching
Removing of the resist
(acetone)
Selective
wet
etching
The idea:
The realization:
Reitzenstein et al.
The results:
• Temperature tuning of X energy
• Q factor of 13.000
• Electrically pumped
The idea:
Purcell effect in an electrically tunable
QD-cavity system
The realization:
Laucht et al., 2009
Purcell effect in an electrically tunable
QD-cavity system
The results:
Purcell effect in an electrically
tunable QD-cavity system
Laucht et al., 2009
QD- Cavity Mode in the strong
coupling regime
Energy
Light-matter interaction : Strong coupling
S1
Emitter
S2
Cavity Mode
Optical Modes
outside the cavity
When S1 > S2 and Emitter in resonance with the Cavity Mode:
Photon preserved in the cavity „for long”
Reabsorption and reemission of the photon by the mitter
Strong coupling –Rabi splitting
Out of the resonence:
|1,0> :
Excited
emitter
Empty cavity
Strong coupling –Rabi splitting
Out of the resonence:
|1,0> :
Excited
emitter
Empty cavity
|0,1> :
Photon
Emitter
in ground state inside cavity
Strong coupling –Rabi splitting
In resonance:
|1,0> :
Excited
emitter
Empty cavity
Energy
Out of the resonence:
(|0,1>  |1,0>)/2
Rabbi
Splitting DR
|0,1> :
Photon
Emitter
in ground state inside cavity
(|0,1> + |1,0>)/2
Eigenstates :
Entengled states
emitter-photon
Oscillations |0,1> ↔ |1,0>
with Rabi frequency  = DR / h
Weak vs strong coupling
Out of
the cavity
Weak vs strong coupling
Out of
the cavity
Conditions for the strong coupling regime
Decisive factors:
Emitter decay rate:
QD ~ 1/τQD
Cavity decay rate:
C ~ 1/τC
Coupling constant QD-Cavity mode:
Conditions for the strong coupling regime
Decisive factors:
Emitter decay rate:
QD ~ 1/τQD
Cavity decay rate:
C ~ 1/τC
Coupling constant QD-Cavity mode:
Condition for the strong coupling:
Rabi splitting
On QD-Cavity
resonance:
g> M/2, QD
D Rabi  g 2  ( QD   M ) 2 4
Strong
coupling
regime
D Rabi  g 2  ( QD   M ) 2 4
Energy levels versus
detuning:
QD– Cavity mode detuning
• At resonance QD- Cavity mode: anticrossing of the levels!
Rabi splitting:
D Rabi  g  ( QD   M ) 4
2
2
Conditions of the strong coupling
Rabi splitting:
D Rabi  g  ( QD   M ) 4
2
2
Desired:
• Large g, thus small V and large oscillator strength f
• Small M, this high Quality factor of the Cavity Q
Q=
𝐸𝑀
M
Weak coupling vs strong coupling
Anticrossing/
no anticrossing
Reithmaier et al.,
Nature (2004)
Weak coupling vs strong coupling
Exchange of
linewidths/
no lw exchange
Reithmaier et al.,
Nature (2004)
Weak coupling vs strong coupling
Anticrossing/
no anticrossing
Exchange of
linewidths/
no lw exchange
Equal intensity
at resonance/
X intensity
increased at
resonance
Reithmaier et al., Nature (2004)
QD-Cavity strong coupling : beginnings
Strong coupling in a single quantum
dot–semiconductor microcavity system
Reithmaier et al.,
Nature (2004)
Vacuum Rabi splitting with a single
quantum dot in a photonic crystal
nanocavity
T. Yoshie et al.,
Nature (2004)
Exciton-Photon Strong-Coupling
Regime for a Single Quantum Dot
Embedded in a Microcavity
E. Peter et al.,
Phys. Rev. Lett. (2005)
QD-Cavity strong coupling : beginnings
Yoshie et al.,
Nature 2004
Reithmaier et
al.,
Nature 2004
V= 0.04 µm3
V= 0.3 µm3
Peter et al.,
PRL 2005
Henessy et al
Suisse
Nature 2007
Englund et al,
US
Nature 2007
Srinivasan &
Painter
US
Nature 2007
V = 0.07 µm3
Dot in a well
InAs :
f = 10
Ω/ γ ~1.3
In0.6Ga0.4As :
f = 50
GaAs : f=100
Ω/ γ ~1.0
Ω/ γ ~2.2
InAs QDs
f10
InGaAs QD
Ω/ γ ~2
Ω/ γ ~1.0
InAs QD
InGaAs QW
Ω/ γ ~1.7
Etat de l’art : Couplage fort pour une boîte quantique unique en cavité
Yoshie et al.,
Nature 2004
Reithmaier et
al., Germany
Nature 2004
V= 0.04 µm3
V=0.3 µm3
USA
Peter et
al.,France
PRL 2005
Henessy et al
Suisse
Nature 2007
Englund et al,
US
Nature 2007
Srinivasan &
Painter
US
Nature 2007
V=0.07 µm3
Dot in a well
InAs :
f = 10
Ω/ γ ~1.3
In0.6Ga0.4As :
f = 50
GaAs : f=100
Ω/ γ ~1.0
Ω/ γ ~2.2
InAs QDs
f10
InGaAs QD
Ω/ γ ~2
Ω/ γ ~1.0
InAs QD
InGaAs QW
Ω/ γ ~1.7
Strong coupling in micropillars with an
elliptic cross-section
Quality Factor
70000
Quality factor vs
diameter
60000
50000
32 layers
40000
30000
in-situ 1
20000
in-situ 2
10000
0
0.5
36 layers
e-beam
1.0
1.5
2.0
2.5
3.0
3.5
micropillar radius (µm)
+ improved etching
4.0
 Higher Q factor of
the micropillars
Strong coupling in micropillars with an elliptic cross-section
37K
Data34_C17
Data27_C19
Data30_C17
Data32_C17
Data28_C17
Energy (meV)
Intensity (arb.units)
1324.1
36K
1323.9
1323.8 Mb
DRb = 32 eV
Qb = 15500
1323.6
34K
34K
Qa = 22500
DRa = 35 eV
1324.0 Ma
1323.7
35K
X
Mb
Ma X
1323.8 1324 1324.2
Energy (meV)
36K
38K
Temperature (K)
40K
 Anticrossing X – Mode, DRabi = 35 eV
(A. Dousse, JS et al., 2008)
QD-cavity strong coupling evidenced in
reflectivity
Reflectivity with use of finely tunable laser
QD-cavity strong coupling evidenced in
reflectivity
• Very high spectral
resolution
• Resonant excitation
Loo et al., 2012
Electrically controlled strong coupling
QD-cavity mode
• No need of
temperature tuning
• Rabi splitting of 121μeV
Laucht et al., 2009