Optically Driven Spins in Semiconductor Quantum Dots

DPG Physics School 2010 on "Nano-Spintronics"

Duncan Steel - Lecture 2

Semiconductor Quantum Coherence Engineering

|0>

|1>

|0> |1>

Optical Bloch Vector Qubit

Electronic Spin Qubit

Successful coherent optical manipulation of the optical Bloch vector necessary to manipulate the spin vector

The qubit for real systems is the electron or hole spin: The key to optically driven quantum computing in semiconductors is the

negatively charged exciton (trion) in a quantum dot

The electron spin vector

GaAs

AlGaAs

AlGaAs

|0>|1>

(GaAs)

(GaAs)

(InAs)

GaAs

AlGaAs

AlGaAs(GaAs)

(GaAs)

(InAs)

|0>|1>

l

The electron spin vector

GaAs

AlGaAs

AlGaAs(GaAs)

(GaAs)

(InAs)

|0>|1>

l

The electron spin vector

GaAs

AlGaAs

AlGaAs(GaAs)

(GaAs)

(InAs)

Long coherence time

|0>|1>

The electron spin vector

Optical Excitation of Spin Coherence:Two-photon stimulated Raman

• Circularly polarized pump pulse creates coherent superposition of spin up and down state.

• Raman coherence oscillates at frequency of the Zeeman splitting due to electron in-plane g-factor and decays with time.

CN

OS

(a.

u.)

Single Electron Spin Coherence:Raman Quantum Beats

X -

G G

G G

X

Charged Exciton System

Neutral Exciton System

0 500 1000 1500 2000 2500Delay (ps)

Single Charged Exciton

Ensemble Charged Excitons

Single Neutral Exciton

T2* >10 nsec at B=0

hgs (m

eV)

Phys. Rev. Lett. - 2005

Anomalous Variation of Beat Amplitude and Phase

(a) (b)

StandardTheory

• Plot of beat amplitude and phase as a function of the splitting.

(a)

StandardTheory

Anomalous Variation of Beat Amplitude and Phase

• Plot of beat amplitude and phase as a function of the splitting.

Spontaneously Generated Coherence (SGC)

Trion

GG

• Coupling to electromagnetic vacuum modes can create coherence* !!

• Modeled in density matrix equations by adding a relaxation term:

Normally forbidden in atomic systems or extremely weak.

Anomalous Variation of Beat Amplitude and Phase:The result of spontaneously generated Raman coherence

(a)

StandardTheory

• Plot of beat amplitude and phase as a function of the splitting.

Phys. Rev. Lett. - 2005

Two-Photon Spin Rabi

Trion Trion

Laser Pulse

Initialization

€

Rxπ

2( )ψ 0

€

ψ0

€

ˆ X and ˆ Y Rotations with ˆ Z Precession

y +

y − x −x +

€

Rz −π2( )Rx

π2( )ψ 0

€

R−y θ( ) = Rz −π2( )Rx θ( )Rz

π2( )

Phase Gate - Demonstration of Geometric Phase (Aharonov & Anandan)

€

Z +

€

Z −

€

Tz ±

Optical Control of Spin Bloch Vector

Optical Control of Trion Optical Bloch Vector

For   ψ 0 the state vector for the spin,

the trion 2π x rotation transforms ψ 0 to

ψ =U ψ 0 where U = −1 00 1

⎡

⎣⎢

⎤

⎦⎥ and U C− z− +C+ z+( ) = C− z− −C+ z+( )

Coherent Generation of a Geometrical Phase

Demonstration of the Phase Control

• Modulation effect clearly seen

• Frequency of the modulations depends on the strength of the CW field

• Phase change after modulation points consistent with theory for 0.2, 5 and 10 mW scans

• Action of CW field can be likened to a spin phase gate

The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion

Autler Townes Splitting

Mollow Spectrum: New physics in absorption

S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955) B. R. Mollow, Phys. Rev. 188, 1969 (1969). B. R. Mollow, Phys. Rev. A. 5, 2217 (1972)..

Dressed State Picture

Power Spectrum of the Rabi Oscillations:Gain without inversion

The Mollow Spectrum of a Single QD

|2>

|3>

Strong pumpWeak probe

X. Xu, B. Sun, P. R. Berman, D.G. Steel, A. Bracker, D. Gammon, L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science, 317 p 929 (2007).

Autler-Townes Splitting in a Single Quantum Dot

Abs

orpt

ion

(a.u

.)

|2>

|1> |3>

|a(N-1)>

|b(N-1)>

|a(N)>

|b(N)>

} WR

} WR

Dressed state Picture

Rab

i Spl

itti

ng (

GH

z)0

1

Pump Field Strength( )1/ oI0 4 8

Probe Frequency (GHz)321591 321594

0 Io

10 Io

20 Io

30 Io

40 Io

50 Io

5 Io

Probe Abosorption as a Function of the Pump Intensity (on resonance)Pump intensity(Io=0.03w/cm )2

Probe Absorption as a Function of Pump Frequency Detuning

Experimental Data Theoretical Plot

Probe Frequency (GHz)

321591 321594

Probe Detuning ( G units)

0-2.5-5.0 2.5 5.0

-1.7

-0.6

-0.30.00.3

1.70.6

Pump Detuning (GHz)

Pump Intensity30Io

Abs

orpt

ion

(a.u

.)

Thy Physical Model of the Dark State Experiment

V1 V2H1 H2

Laser Detuning (GHz)0-8 8

|X+>|X->

Bx

|T+>

|T->

V1 V2

H1 H2

DT

/T (

10-4)

0

1

|T->

|X+>

|X->

H1 V2Wp

Wd

2 2

p d

p d

X XDarkstate

Ω −+Ω +=

Ω +Ω

Laser Detuning (G units)0-3 -3

Theoretical plot of the CPT including electron spin dephasingB=1.32 T

The Quartet Transition Pattern

The Observation of the Coherent Population Trapping of an Electron Spin

|T->

|X+>

|X->

H1 V2Ωp Ωd

The probe absorption spectrum scanning across transition H1

Solide lines are the fits, which yield electron spin T2

* of 4 ns.

5

DT

/T (

10-4)

Wd/2p(GHz)

0

0.56

0.78

0.83

1.26

1.38

Probe Detuning (GHz)0-5

0

0

1

0

1

0

1

0

1

0

1

Nature - Physics, 2008

0

1

2

3

Rel

ativ

eA

bsor

ptio

n x

10-4

319074 319077

Probe Frequency (GHz)

Black: forward

Probing Dynamic Nuclear Spin Polarization by Dark State Spectroscopy

ee

hee

ΩprobeΩpump

|T->

|X->|X+>

0

1

2

3

Rel

ativ

eA

bsor

ptio

n x

10-4

319074 319077

Probe Frequency (GHz)

Black: forwardRed: backward

Broadened & rounded trion peak Large trion excitation (absorption) is favored

Scan direction dependence: hysteresis & dark state shift (Dark state position reflect Zeeman Splitting)

Dynamic control of nuclear field

Probe absorption spectra by varying the laser scan rate

B=2.6 T

Time Dependent Probe Absorption Spectrum

e e

hee

ΩprobeΩpump

|T->

|X->|X+>

Laser frequency parked herePartial backward scan

Stable configuration: maximum trion excitation (absorption)

Time Dependent Probe Absorption Spectrum

e e

hee

ΩprobeΩpump

|T->

|X->|X+>

Time Dependent Probe Absorption Spectrum

Probe Frequency (GHz)

Rel

ativ

eA

bs. x

10

-4

0

1.5

319083 319089

(e)

L

D

R

e e

hee

ΩprobeΩpump

|T->

|X->|X+>

Time (S)0 300 600

(f)L

D

R

Dark State is a meta-stable state for nuclear field

anisotropic hyperfine from hole

Zh kS I

2

, ,Z

f h k i t i t f t tS Iψ ψ

2

, ,Z

f h k i t i t f t tS Iψ ψ

Flip up rate:

Flip down rate:

Whichever increases rt dominates!

nuclear Zeeman << trion linewidth

DNP rate tt

Trion Induced Dynamic Nuclear Spin Polarization

|T>

tN t

d

dt

Nuclear field dynamics:

Probe laser frequency

Nuc

lear

fie

ldAb

sorp

tion

Probe detuning ( = 2-ph detuning - nuclear field )

Two photon detuning

Dynamic Nuclear Spin Polarization Induced Spectral Servo

Experiment

Theory

11.5 sN 32.4 (MHz) ~ 3hA eV

Parameters:

Nuclear T1 ~ sec

tN t

d

dt

Nuclear field dynamics:

Numerical Simulation Results : Slow Scan

Experiment

Theory

10.4 sN 350 (MHz) ~ 20hA eV

Parameters:

Nuclear T1 ~ sec

Numerical Simulation Results : fast Scan

Microscopic theory: Weng Yang et al., Q14.00002; http://arxiv.org/abs/1003.3072

Stable configurations for DNP

DNP rate: tt

Two-photon detuning pump prob

t

Metastable configurations

( )2pump

pump probe Ω

Nuclear field locked to stable value

Nuclear Field Locking Effect

Dynamic Nuclear Spin Feedback Suppresses Fluctuations

Stable-confignuclear field

locked to frequencies

Nuclear field

unstable against DNP

CW laser excitation

Nuclear field self-focus to stable value

Nuclear spin fluctuation

2-photon resonance

shifts

Single QD arbitrary

nuclear spin config

Medium trion excitation

Maximum trion excitation

DNP by trion

C. Latta et al., Nature Phys. 5, 758 (2009)Ivo T. Vink et al, Nature Phys. 5, 764 (2009)

Probe detuning

Abso

rptio

n

– More enhancement on spin T2* with larger pump strengthlarger pump larger slope in tighter locking t

t

Pump intensity2040607090

spin T2*

peak-to-dip ratio

Pump Rabi (GHz)0 0.5 1.0 1.5

Slo

pe (

a.u.

)

0

-0.5

(b)

Suppression of Nuclear Field Inhomogeneous Broadening

– Spin decoherence rate extracted from dip-to-peak ratio

– Deficiency: locking position changes with probe scan

– T2* extended well above thermal value

Thermal value

e e

hee

ΩprobeΩpump

|T->

|X->|X+>

Suppression of Nuclear Field Inhomogeneous Broadening

Coherent Spin Manipulations without Hyperfine Induced Dephasing

– Pump 1 + pump 2 locks nuclear field to a constant value

– Pump 1 + probe measures spin T2*

Pump 1 >> Pump 2 >> Probe(fixed freq) (fixed freq)

(freq scan)

Spin decoherence rate ~ 1 MHz, reduced by a factor of 400

Three Beam Measurement

Clean line shape

Xu, X. et al., Nature 59, 1105 (2009)

Where’s the Frontier?

• Engineering coupled dot system with one electron in each dot with nearly degenerate excited states.

• Demonstration of optically induced entanglement.

• Integration into 2D photonic bandgap circuits.

• Understanding of decoherence.

• Possible exploitation of nuclear coupling.

Semiconductor Nano-Optics:An Interdisciplinary Collaboration

Dan GammonNaval Research Lab

Lu ShamUC-San Diego

Paul BermanLuming DuanRoberto MerlinU. Mich.

Outstanding Graduate Students**• Nicolas Bonadeo (graduated)• Jeff Guest (graduated)• Gang Chen (graduated)• Todd Stievater (graduated)• Anthony Lenihan (graduated)• Elizabeth Tabak (graduated)• Elaine Li (graduated)• Gurudev Dutt (graduated)• Jun Cheng (graduated)• Yanwen Wu (graduated)• Qiong Huang (graduated)• Xiaodong Xu• Erik Kim• Katherine Smirl• Bo Sun• John Schaible• Vasudev Lai

**Alberto Amo - Autonoma University of Madrid