Deterministic Coherent Writing and Control of the Dark ... · Deterministic Coherent Writing and...
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Deterministic Coherent Writing and Control of the Dark Exciton Spin using Short Single Optical Pulses
The Physics Department and the Solid State Institute, Technion – Israel Institute of Technology
Haifa, Israel
Frisno 13, March 21, 2015, Aussois, France
Ido Schwartz, Dan Cogan, Emma Schmidgall, Liron Gantz, Yaroslav Don and David Gershoni
Technion Israel Institute of Technology
Overview • Three main experimental results:
1. Deterministic, all-optical excitation of a quantum-dot confined dark exciton (DE)
2. Coherent “writing” of its spin state using single polarized picosecond pulse.
3. Coherent control of the DE spin state using a picosecond optical pulse
• This talk: – Qubits in quantum dots – Deterministic DE generation and spin writing – DE life and coherence times – Coherent control of the DE spin state
Schwartz et al. Phys Rev X 5, 011009 (2015). Featured in Nature Materials 14, 260 (2015).
Semiconductor Quantum Dots self assembled dots
• Live forever
• Easily incorporated into microcavities and devices
• Easily accessed optically and electronically
• Level separation compatible with fast optics (picoseconds)
• Can be easily charged and discharged
• Disadvantages:
– Every dot is different (size, structure, location)
– Coupled to their solid state environment (phonons)
Advantages of Quantum Dots
Conduction band Empty of electrons
Valence band full of electrons
)no holes(
Orbital angular momentum )±1( and spin (±1/2) aligned :±3/2
Discrete set of energy levels
Photon emission Due to
recombination of e-h pair σ −
12
+
32
−
Orbital angular momentum )0 ( and spin (1/2)
σ +
Photon Polarization ↔ Exciton Spin State
Non
-Res
onan
t Exc
itatio
n
Dark Exciton |+2⟩ Dark Exciton |−2⟩ Benny et al. PRL (2011). Randomized carrier spin Photon does not alter electon spin.
σ −
⇓
⇑
Resonant Excitation
↑
From Spin to Polarization
Bright Exciton
Dark Exciton
Isotropic electron-hole
exchange
Anisotropic electron-hole
exchange a
as
sΔ0 ≈ 300μeV
Δ1 ≈ 34μeV
Δ2 ≈ 1.4μeV
Non interacting
3 12 2 2+ = 3 1
2 2 2− − = −
3 12 2 1− + = −3 1
2 2 1− =
σ + σ −
σ σ−+ −
σ σ++ −
V
H
Ener
gy
Dark Excitons in Quantum Dots
A long-lived two-level system. A qubit? Poem et al. Nature Physics 6, 993-997 (2010).
DiVincenzo criteria for QIP: Fortschr. Phys. 48 77 (2000)
– We need to find some quantum property of a scalable physical system in
which to encode our bit of information (qubit). It should Live long enough
to enable performing computation.
– Initial state preparation. Setting the state of the qubits to zero before each new computation.
– Isolation from the environment to maintain the quantum nature of the qubit - reducing the effects of decoherence.
– Gate implementation. Manipulation of the states of individual qubits with reasonable precision, and inducing interactions between them in a controlled way. The gate operation time must be much shorter than the decoherence time (allow error corrections)
– Readout. It must be possible to measure the final state of our qubits once the computation is finished, to obtain the output of the computation.
Other Quantum Dot Qubits
System Lifetime Coherence Time Initalization
No Field B Field No Field B Field
Electron Spin <1µs1 10s of ms1 1-10 ns1 Few µs1 Optical pumping (ns)
Hole Spin 1 µs2 Few ms2 1-20 ns2 10s of µs2 Optical pumping (ns)
Bright Exciton 1 ns3 Same >10 ns3 Same Polarized pulse (ps)
Dark Exciton >1µs4 >100 ns4 Polarized pulse (ps)
1See Bracker et al. PRL (2005), Press et al. Nature (2008), Berezovski et al. Science (2008) ,Greilich et al. Nat. Phys. (2009 ) and others. 2 See De Greve et al. Nat. Phys. (2011), Godden et al. PRL (2012), Fras et al. PRB (2011) and others. 3See Benny et al. PRL (2011) and others. 4See Schwartz et al. PRX (2015)
Charged qubits: Sensitive to electrostatic fluctuations. Optically active: Short lifetime
The Dark Exciton Bloch Sphere
( ) / 2a = ⇑↑ − ⇓↓
A s B aψ = +
( ) i tt s e aωψ = +
2
2
1.3 eV2 / / 3.1nsT h
µπ ω
∆ ≈= = ∆ ≈
( ) / 2A = ⇑↑ − ⇓↓I. Schwartz et al. Phys Rev X 5, 011009 (2015).
t
I(t)
σ −σ +
Absorption Resonance Biexciton Emission No absorption. No biexciton emission.
Heralding and Probing the DE Spin State
( ) / 2S = ⇑↑ + ⇓↓
|-2> |+2>
CO
CROSS
Low intensity
Spectroscopy of the DE
M. Zielinski et al. Phys Rev B 91 085403 (2015).
|g>
|e> |g> |e>
e
g+e g-e
g
|g> |g>
0ω0 0δ ω ω= − =
Pulse Area A=π0 0
Pulse Area A=2δ ω ω
π= − =
Rabi Oscillations and Spin Rotation
ie π
Rabi oscillations: |g> = empty dot |e> = DE Change pulse area by varying laser intensity
|a>
|s>
|a>
0 0Pulse Area A=2δ ω ω
π= − ≠
Rabi Oscillations
| |ia e sϕ> + >
Spin rotation: Direction determined by polarization Angle determined by detuning
Y. Kodriano et al. PRB 85, 241304(R) (2012). S. Economou and T. Reinecke PRL 99, 217401 (2007)
2 2s = + −
2 2a = − −
2+2−
Life and Coherence Time of the Dark Exciton
Lifetime
Coherence
Autocorrelation of the biexciton emission line under D-polarized CW resonant excitation
Coin
cide
nces
Co
inci
denc
es
*2 100nsecT ≈
Coherence of the Dark Exciton
Detector Start
Detector
Stop
polarizer
polarizer
Timer Rep rate 76MHz
Controlling the DE Spin State
( ) / 2⇑↑ + ⇓↓
( ) / 2⇑↑ − ⇓↓
↑⇑
↓⇓
t
I(t)
Pump
Control (ps) |0⟩
↑⇑ − ↓⇓
↑↓ ⇑ ⇑
Probe
Bloch Sphere Pulse Sequence
Controlling the Dark Exciton Spin
Pump (H)
Control (ps, H)
Control (ps, R)
Probe (R)
( ) / 2⇑↑ − ⇓↓
( ) / 2⇑↑ + ⇓↓
↑⇑
↓⇓
Energy (eV)
X0 Poincare sphere Bloch sphere
( )↑⇓+↓⇑2
1
( )↑⇓−↓⇑2i( )L-R
2iV = R
Writing the spin of the bright exciton by one short optical pulse
0X ∆=34µev |V>
|H>
|V>
|H>
H V 122psT = =∆
( )LR2
1H +=
Poincare sphere Bloch sphere
LR ⋅+⋅ βα
‘Writing’ the spin of the bright exciton with one optical pulse
∆=34µev
Energy (eV)
X0 H V
). 2011, (040504, 106. Lett. Rev. Phys" et al. Y. Benny,
0X( )↑⇓+↓⇑
21
( )↑⇓−↓⇑2i|V>
|H>
|V>
|H>
Writing the spin of the dark exciton by one ps optical pulse
Bright Exciton
Dark Exciton
BE-DE mixing induced by the QD assymmetry
M. Zielinski et al. Phys Rev B 91 085403 (2015).
Unpolarized DE quasi resonance
Coherent Writing the Dark Exciton spin State by a Single Picosecond-long Optical Pulse
( , )P θ φ
Pola
rizat
ion
degr
ee
Summary
The dark exciton is a neutral, long-lived, physical two-level system:
– Lifetime: longer than 1 µs – Coherence time ( ): longer than 100 ns – No magnetic field, without spin echo!
We demonstrate:
• Deterministic photogeneration of the DE. • Control of the DE state by a picosecond pulse - 6 and 5 orders
of magnitude faster than its lifetime and coherence time, respectively.
• Coherent writing by a single polarized picosecond pulse
Consequently, the dark exciton is an excellent solid state spin qubit.
*2T