All optical control of electron spins in quantum dot ensembles - - PowerPoint PPT Presentation
All optical control of electron spins in quantum dot ensembles Manfred Bayer Experimentelle Physik II Technische Universitt Dortmund JST-DFG workshop, Aachen, 05.-07.03.2008 Acknowledgements A. Greilich, S. Spatzek, I. Yugova, I. Akimov, D.
JST-DFG workshop, Aachen, 05.-07.03.2008
Research group: „Quantum Optics in Semiconductor Nanostructures“
Borussia Dortmund Fußball heißt das Spiel, Borussia seine Seele!
Prerequisite Availability of high quality quantum hardware: Quantum dots! Prerequisite Availability of high quality quantum hardware: Quantum dots! Potential of quantum information processing: Increase of computational power Realization of new functionalities for communication Reduction of complexity Potential of quantum information processing: Increase of computational power Realization of new functionalities for communication Reduction of complexity
InGaAs GaAs GaAs
Demand: Long living coherence
Spin is efficiently protected by confinement against efficient relaxation mechanisms in higher-dim. systems.
Experiments on QD ensembles!! Single electron per QD!
InGaAs GaAs GaAs
Relaxation times T1 in high magnetic field: TU Delft: gated QDs T1 ~ 10 ms Nature 430, 431 (2004) TU Munich: self-assembled QDs T1 ~ 10 ms Nature 432, 81 (2004) at zero magnetic field: Dortmund: self-assembled QDs T1 ~ 0.3 s PRL 98, 107401 (2007)
Single spin
Single spin
Spin ensemble
Spin ensemble
, 5 µ m
Self-assembled quantum dots
Non-annealed QD geometry: dome-shaped ~ 25 nm diameter ~ 5 nm height large oscillator strength!
Sample
prepare spin polarization
kprobe kpump Δt M pump - probe Faraday rotation Delay time, Δt (ps) θF (mrad) B= 3T M
* 2
F
) t cos( ) T t exp(
* 2
Δ ω Δ − ∝ θF B θF ∝ M • kprobe ∝Mz BIIx
characteristic quantities: T1 relaxation longitudinal relaxation time T2 decoherence transverse relaxation time T2
transverse (T2) 2 / ) | (| ↓〉 ↑〉+ 2 / ) | (| ↓〉 + ↑〉
ϕ i
e
T1
longitudinal (T1)
energy spin-flip B B T2* dephasing ensemble effects (inhomogeneities, measurement variations etc)
500 1000 1500
0T 1T 2T 3T 4T 5T 6T
Faraday rotation(a.u.) time(ps)
7T
BX
z
σ+
y
x B e e
1.38 1.39 1.40 1.41 1.42 0.50 0.52 0.54 0.56 0.58
laser
considerable variation of g-factor
0.24 0.25 0.26 0.27 0.28 0.29
30 60 90 120 150 180 210 240 270 300 330
0.24 0.25 0.26 0.27 0.28 0.29
ωel, fit ωexc fit
ω (ps
0.65 0.54 0.65 ge gX ge,x
500 1000 1500
0T 1T 2T 3T 4T 5T 6T
Faraday rotation(a.u.) time(ps)
7T
BX
z
σ+
y
x B e e
0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 5 6 7 8 9 1 2 3 0,00 0,05 0,10 0,15
T*
2(ns)
B(T)
B (T)
e B e e e
T2*(B=0) > 6ns dephasing in random nuclear magnetic field T2*(B=0) > 6ns dephasing in random nuclear magnetic field
* 2
e B e e e
5 0 0 1 0 0 0 1 5 0 0 2 0 0 0
Faraday rotation tim e (p s)
B= 0T B= 1T B= 6T
BX
z
σ+
y time (ns) pulse 1 pulse 2 pulse 3 pulse 4
* 2 <
2 4 6 8 10 1 2 negative delay positive delay fit, Δge=0.005
Dephasing time T*2 (ns) Magnetic Field (T)
coherence outlasts pulse repetition period & dephasing time.
0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 1.37 1.38 1.39 1.40 1.41 1.42 1.43
Energy (eV) QD emission laser electron g-factor
QD ensemble offers broad distribution of g-factors further selection: phase synchronization of spin subsets by laser
R R B e e
g-factor precession frequency laser pulse separation: TR = 13.2ns laser pulse separation: TR = 13.2ns
TR
pump pulses probe
time N=8 N=6 N=4 mode out of phase phase synchronization condition
R e
precession frequency N N+1 N-1 N+2 N-2 N+3 N-3
µs T . 3
2 =
R e
T N π ω 2 ⋅ =
decay time gives single dot coherence time T2 = 3.0 μs four orders of magnitude longer than ensemble dephasing T2*=0.4ns at B=6T!
0.2 0.4 0.6 0.8 1.0 50 100 150 200
B = 6 T T = 2 K
T2 = 3.0 μs
Faraday rotation amplitude Pulse repetition period, TR (μs)
laser repetition period TR varied by pulse-picker from 13.2 to 990 ns
500 1000 1500
B = 6 T
Faraday rotation amplitude
Time (ps)
TR = 13.2 ns
1000 2000 3000 4000
B= 6T two-pulse experiment: pump-pulse split into two beams with variable time delay in between two-pulse experiment: pump-pulse split into two beams with variable time delay in between
1000 2000 3000 4000
TD= 1.8ns B= 6T
TR / TD = 7
1000 2000 3000 4000
both pumps are on
B= 6T TD= 1.8ns
+1 burst
TR / TD = 7
⇒ spins echoes every TD
D e
redistribution
precession frequencies
D R e
2 0 0 0 4 0 0 0 6 0 0 0
Faraday rotation t i m e ( p s )
TR TD
+1 burst +2 burst
pump 1
TR
pump 2
µs T . 3
2 =
R e
T N π ω 2 ⋅ =
0,0 0,2
Aneg no nuclei model
A
Apos
0,0 0,2 0,4
with nuclei model
B
Faraday rotation amplitude
0,0 0,5 1,0 1,5
C
(arb. units) Time (ns)
experiment
explanation for similar FR amplitudes before and after pump pulse arrival nuclei create magnetic field such that all electron spins in the ensemble contribute to mode-locking
N B e R e
how do electrons and nuclei communicate? hyperfine interaction
2 α α α α
electron spin
nuclear spins
~ 100.000 nuclei per QD N VB CB HF N VB CB HF change
nuclear field
h / ) ( 2
N B e R e
B B g T N + = = μ π ω
Random walk until mode-locking is fulfilled!
1 2 3 4 5
16 m in 12.3 m in 7.2 m in
pump 1 pump 2 burst 0 burst 2
Faraday rotation amplitude Time (ns)
T
D
T
R-T D
T
R= 13.2 ns
pum p 1 only pum p 1 + 2 pum p 1 (after two-pulse exposition)
B = 6 T T = 6 K
pum p pulses
1 2 1 2
burst 1
2.6 m in
Do the long-living nuclear spins show up in the FR studies?
5 10 15 20
FR amplitude Time (min)
pump 1 on 4 min completely dark delay 1.857 ns
FR decay only for system under illumination! FR amplitude constant over an hour time scale, when system is held in darkness!
300 305 310 315 320 1 10 100 electron precession frequency ωe (GHz)
single pump two pumps
background of unlocked dots is removed! broad spin precession distribution is transferred to comb-like distribution! focussing drastically enhances density at the positions
300 305 310 315 320 1 2 3 4 5
single pump two pumps
B
Density of states
300 305 310 315 320 0,00 0,05 0,10 0,15
no nuclei
Precession frequency, ωe (GHz)
C
Density of states
important: change of precession frequency comparable to mode locking spacing
~million inhomogeneous electrons focussed
Quantum effects will play a key role in the next generation
EXCITONS coherence time: ~ns manipulation time: ~ps sufficient for quantum communication! EXCITONS coherence time: ~ns manipulation time: ~ps sufficient for quantum communication! ELECTRON SPINS coherence time: ~µs (manipulation time: ~ps) sufficient for simple processors! ELECTRON SPINS coherence time: ~µs (manipulation time: ~ps) sufficient for simple processors!
Further submitted papers