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

Transcript of Deterministic Coherent Writing and Control of the Dark ... · Deterministic Coherent Writing and...

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

Presenter
Presentation Notes
We work with self assembled semiconductor quantum dots. These dots are grown in the following manner: On a substrate of one type of semiconductor, GaAs in our case, a thin layer of another, similar semiconductor is grown, InAs in this case. The lattice spacing in InAs is similar to that of GaAs, but a little bit different This mismatch between the two layers results in strain, and the strain results in the formation of little islands of InGaAs. These are the quantum dots. Their size, as you can see, is a few tens of nanometers in the lateral directions, and with a height of anywhere between about 3 to 7nm. lThese quantum dots form a three diemensional potential well trapping charge carriers with discrete energy levels, therefore they are also termined artifical atoms.

• 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

Presenter
Presentation Notes
Unlike atoms in cavities, quantum dots live forever. Since they are based on semiconductors, they’re compatible with semiconductor fabrication techniques and can be easily incorporated into semiconductor microcavities, photonic crystal structures (like Prof. Waks spoke about), or diode structures. The level separation in these artificial atoms is compatible with fast optics, like picosecond pulsed lasers, and if electrical contacts are attached to the sample, the quantum dots can be easily charged and discharged.

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

Presenter
Presentation Notes
In the highest electron levels of the valence bands of strain induced QDs the electron spin is parallel to the orbital angular momentum thus total spin 3/2. In the conduction band the orbital momentum is 0 thus the circular polarization of the resonantly tuned light selects the spin of the electron which is promoted. In the hole picture, RHCP light generate e-h pair with spin 1 and LHCP light generate e-h pair with spin -1. These are also called BE. Strongly coupled to light and radiatively recombine within 1 nsec. Under non resonant excitation the spin is randomized and in half of the cases DE with total spin 2 maybe generated. These are optically almost forbiden and therefore live much longer 9more than a microsecond as I will show you, due to residual lh-hh mixing.

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).

Presenter
Presentation Notes
Can this system be a qubit? For that, among other criteria, it needs to be initializable in a defined eigenstate, we need to be able to manipulate it and read it out and it needs to have a long lifetime and a long coherence time so that several control operations can be performed. Our group has been working on the DE as a qubit candidate for a few years now, and today I will demonstrate deterministic initialization and state manipulation. Due to the exchange interaction between the electrons and holes the degeneracy between the four possible exciton states Is fully removed: Forming two (symmetric linearly H polarized and anti-symmetric linearly V polarized) BE states ~1/3 meV above the DE states. The BE states are separated by about 30 ueV resulting in Larmor precession of coherent superpositions of the two eigenstates of about 100 psec. The same happens for the DE, but here the separation is only 1.4 ueV resulting in Larmor precession of ~3 nsecs. (Poem’s Nature Physics). Due to mixing with lh the symmetric state (constructive interference) becomes slightly optically allowed and the anti symmetric (destructive interference) remains forbidden (see below).

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

Presenter
Presentation Notes
J_z =2

Low intensity

Spectroscopy of the DE

M. Zielinski et al. Phys Rev B 91 085403 (2015).

Presenter
Presentation Notes
At high energy high intensity above bandgap excitation (e-h pairs populate the QD faster than the radiative rate) bright excitons and biexcitons are easily formed we identify the optical transitions discussed previously: the exciton, the biexciton of the BE the biexcitons of the DE. Note that the SP transition of the DE biexciton is a factor of 30 smaller than its SS transition (overlap integral). At 3 orders of magnitude lower excitation rate BE recombines immediately but DE stays until a next pair arrive. Thus, if the DE also recombines radiatively at some excitation level the DE and BE emission equilibrates. This is shown here. (very low emission rate one night acquisition) Also, note that the DE emits only in one polarization Michal Zielinski) .

|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−

DE Rabi Oscillations

Deterministic writing of the DE!

Pulse width 50ns Rep rate 1 MhZ

Direct Measurement of the DE Lifetime

Pump (H)

Probe Probe Probe

τDE ≈1.1 μs

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

Presenter
Presentation Notes
P0 + decaying exponent - animation

*2 100nsecT ≈

Coherence of the Dark Exciton

Detector Start

Detector

Stop

polarizer

polarizer

Timer Rep rate 76MHz

Presenter
Presentation Notes
Laser rep rate 76 MHz (arrow 13 ns). Pulsed excitation. Tuned to the biexciton. Here, we have a Hanbury Brown Twiss apperatus to measure correlations. One detector is connected to start, one to stop, and we measure time differences between detections. Since QD is single photon source, we see that there are no two simultaneous detections. All of the other detections are spaced by the pulse spacing of 13 ns. The colors represent co-circular polarization (Red) and cross-circular polarization (blue) of the two photons in the pair. Emission of the first photon from the biexciton leaves the DE in a coherent superposition of eigenstates. As long as the DE remains in this coherent superposition of eigenstates, we will see time-dependent differences in the amount of co-circularly polarized events vs cross-circularly polarized events. Here, we look at the circular polarization degree of these detections as a function of time. We see that the polarization degree decays with a characteristic time of 100 ns, providing a lower bound for the DE coherence time.

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 +=

Presenter
Presentation Notes
To add period

Technion – Israel Institute of Technology Physics Department and Solid State Institute

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

Presenter
Presentation Notes
The writing pulse is energetically tuned to the excited dark exciton resonance. We found out that due to quantum dot shape deviation from C2v symmetry the bright and dark exciton eigenstates are mixed. This small mixture of bright exciton in the dark-exciton state allows the dark exciton to couple with light. The first pulse writes the dark-exciton state in a coherent spin state, determined by the lasers polarization. The second pulse, tuned to the biexciton transition, probes the dark exciton spin state. The polarization degree of the photons emitted from the biexciton state is detected and displayed in a two-dimensional map of the Writing pulse polarization and the duration from the writing pulse. The polarization of the writing pulse is described on the Poincaré sphere by longitudinal and azimuthal angles. In map d and e the longitudinal angle theta is changed while in f the azimuthal angle psi is changed. The change in color is actually the precession of the spin state. The green line represents a dark exciton photogenerated on the equator of the Bloch sphere. The light blue line also represents a dark exciton generated on the equator but with pi half phase shift to the green line. The dark blue line represents a dark exciton generated in one of his eigenstates, so the spin state doesn’t precess in time. This data proves that like for the bright exciton we can photogenerate the dark exciton with one to one correspondence between the dark exciton spin state and the pulse polarization.

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

Thank you for your attention!

Dan Cogan

Ido Schwartz Liron Gantz

Emma Schmidgall

Prof. David Gershoni