Optics and Quantum Optics with Semiconductor Nanostructures

Stephan W. Koch Department of Physics, Philipps University, Marburg/Germany and Optical Sciences Center, University of Arizona, Tucson/AZ Overview • background: optics with atoms • semiclassical semiconductor optics • semiconductor quantum optics: “which way” experiments and light – matter entanglement

Collaborators

theory: Kira, Hoyer et al., Marburg Hader, Moloney et al., Tucson

experiments: Gibbs/Khitrova et al., Tucson, Stolz et al., Rostock Marburg Marburg

You do not really understand something unless you can explain it to your grandmother (Albert Einstein) From Atoms to Solids …

atom

4 3 2 optical absorption/emission = transitions between atomic levels n=1 From Atoms to Solids …

(2 - 5) * 10-8cm

atom solid

unit cell

energy states

4 3 2 bands n=1 Bandstructure

E possible energy values of electrons in crystal

Eg k intrinsic semiconductor: full valence band(s), empty conduction band Realistic Bandstructure GaAs

6 4 effective mass approximation 2

)

V -2

(

y -4

r -6

n -8

E -10 -12

L Γ X

often: photon momentum typical carrier momentum Ω perpendicular transitions, Energy Gap in Semiconductors

conduction band

> > ω2 ω1

valence band

gap energy determines frequency and therefore color (wavelength) of absorbed and/or emitted light LEDs based on group-III nitride materials (Fraunhofer-Institut Freiburg) Bandgaps of III-V Alloys (300 K)

2.5 GaP 0.517 AlAs

2.0 0.620 ) ) n V

AlSb o r e

( 0.775 c

i 1.5 p m ( a

GaAs g

InP h y 1.00 t g g r n e

1.0 e l n e E v

GaSb 1.55 a 2.0 w 0.5

InAs 5.0 InSb 10.0 0.0 5.4 5.6 5.8 6.0 6.2 6.4 6.6 lattice constant (Angstrom) Quasi-Two Dimensional Structure

TEM picture: quantum well structure

band gap at Γ-point (direct semiconductor)

discrete states (z direction) and continuous bands (x-y plane) Semiconductors as Designer Materials

° quantum well = two-dimensional electronic mobility

° quantum wire = one-dimensional electronic mobility

° quantum dot = no (zero-dimensional) electronic mobility

self organized quantum dots Interband Light-Matter Interaction: Semiclassical Theory classical Maxwell’s wave equation macroscopic optical polarization

semiconductor: Bloch basis

Coulomb interaction of charge carriers → quantum mechanical many-body problem of interacting Fermions Semiconductor Bloch Equations (SBE)

field renormalization

energy renormalization

• nonlinearities: phase space fillinging, gap renormalization, Coulomb attraction • correlation effects: scattering, dephasing, screening, … Wannier Excitons

c • 2 parabolic bands electron-hole pair interband Coulomb

v attraction

• wavefunction

• relative motion (Wannier equation)

Coulomb potential

• hydrogen atom like solutions, Wannier excitons = quasi atoms (finite lifetime < nanoseconds) Wannier Excitons

• linear absorption Elliott formula

• linear optics: excitonic resonances • INTERACTION induced resonances, not just transitions between bands Exciton Saturation

F. Jahnke, M. Kira, and S.W. Koch, Z. Physik B 104, 559 (1997) Born-Markov approximation

Detuning saturation via excitation induced dephasing (EID) = Coulomb induced destructive interference between different Exciton Saturation

F. Jahnke, M. Kira, and S.W. Koch, Z. Physik B 104, 559 (1997)

Detuning n o i t p r o s b A

• experiment: InGaAs/GaAs QW • Khitrova, Gibbs, Jahnke, Kira, Koch, Rev. Mod. Phys. 71, 1591 (1999) • EID first observed in 4-wave mixing, Wang et al. PRL 71, 1261 (1993) Lineshape Problem

0.2 ] m

c 0.0 / 3

0 dephasing rate approximation 1 [

n -0.2 o i t p r full calculation o

s -0.4 b A

-0.6 -20 -10 0 10 Detuning

•

• gain of two-band bulk material

• nondiagonal scattering contributions → lineshape modification, no absorption below the gap absorption/gain absorption (x103/cm) O e C p x u p r : r t

e C i n c . t

E 0 a l - l 2 m 0 l e

m r G s A e … 8 t n

a a m D l D . e i

, I

n e n n t h t s G u e i

t n a o y i i A r

n n 0 y s g : . /

6 A A

- 3 l . S G

. G 0 a i x e A r 1 n s 0 d m 1 t 2 e c t m

i a - c l 2 .

M o a r n b u d r g u c t o r s :

absorption/gain [1/cm] T A C h 6 . o

. G u 8 e r r

t i n e n e o s m d x y p t

: r

o D F n f y 1 . .

B . 0 P J 4

o G n a h . s W a m h o s a N n e t

. 0 o r ( = k

n . t C 9 n 5 1 e e P . .

D h , t 6 2 E d

/ a , o a n e (

n l 2 w n A . m t , e .

2 d t , l r h ) n E

0 ,

e S . 2 i I 5 y n n o . . G . 5

M r g W G x ( y , e

a : 3 . a

V A 0 . p

S A 0 K . . ) 5 *

m s G ) 1 o e I / 0 i c o n A r 1 n h w 2 0 l d / r G . c 5 t t m o 1 i e a P n 2 m t A

a , 0 s

l . P . 4 , 9

. M e

B a r l n b o u o r d t g ,

Summary of Semiclassical Phenomena

• quantitative understanding of interaction phenomena • strong experiment – theory interactions • predictive capability of theory

CHALLENGES: • modified photonic environment (nano optics with nano structures) • optimized design for specific applications • nonequilibrium phenomena ….

Selected References: • Haug/Koch, “Quantum Theory of the Optical and Electronic Properties of Semiconductors” 4th ed., World Scientific Publ. (2004) • Khitrova et al., Rev. Mod. Phys. 71, 1591 (1999) Quantized Light-Matter Interaction

where is proportional to dipole matrix element and mode strength at the QW position

Kira et al., Prog. Quantum. Electron. 23, 189 (1999) Spontaneous Emission from Quantum Wells

-|qz| - +|qz|

recombination in electron-hole system no translational invariance perpendicular to QW no momentum conservation emission occurs simultaneously to left and right, i.e. with and Non Resonantly Excited Photoluminescence Experiments

non resonant excitation of QW ? (weak excitation) incoherent (random) emission at exciton resonance BS different emission directions collected in interferometer setup

Path1 Path2 measurement combines emission QW t to the left and right directions (less than one photon in interferometer) AP AP control of phase via delay Experiments (I)

QW perpendicular

Path1 Path2

QW t

AP AP Experiments (II)

QW tilted ?

Path1 Path2

t QW

AP AP Experiments (II)

QW tilted

Path1 Path2

t QW

AP AP Experiments (III)

Oct.2003 notilt 0.4 | clear interferences visible

0.2

Contrast if QW NOT tilted

withtilt 0.0 -2 0 2 t (ps) intensity(a.u.)

PL interferences vanish singlebeam if QW tilted intensities

0 20 40 60 80 100 CCDpixels Hoyer et al. PRL 93, 067401 (2004) Summary of Experimental Observations

interferences seen in incoherent (single photon) emission

, but intensity shows interferences

interference shows strong directional sensitivity Summary of Experimental Observations

interferences seen in incoherent (single photon) emission

, but intensity shows interferences

interference shows strong directional sensitivity

effects predicted in Prog. Quantum. El. 23, 189 (1999)

origin of effects: light-matter entanglement & which-way interferences Spontaneous Emission from Quantum Wells

q||

-|qz| - +|qz|

electron-hole recombination

simultaneous emission in and directions

photon emission with same

recoil momentum transferred to carrier system Explanation of Interferences (I)

CASE A: Emission with same

q|| q||

photon emission to the left many-body wavefunction with recoil emission to the right

paths not distinguishable with respect to carrier system (i.e. no entanglement) Explanation of Interferences (II)

q|| q|| variable phase

BL BR

interferometry:

emission intensity IL to the left IR to the right interference

INTERFERENCE can be seen Explanation of Entanglement (I)

CASE B: Emission with different

photons

q|| q'||

many-body wavefunction with recoil

emission to the left

emission to the right

paths identified by entanglement Explanation of Entanglement (II)

q|| q'||

emission to the left (BL) und to the right (BR) is combined in detector D = BL +BR

emissions intensity IL to the left IR to the right interference

NO interference pattern due to entanglement Theory of Entanglement-Interferences semiconductor luminescence equations PRL 97, 5170 (1997)

photon-assisted correlations

photon correlations

in the presence of Coulomb interaction

QUESTION: WHAT HAPPENS IF WE TAKE MANY QUANTUM WELLS ? Theory of Entanglement-Interferences

Predictions for n quantum wells with spacing d perfect interferences for Bragg no interferences for anti-Bragg (n-even)

Prog.Quantum.El. 23,189(1999)

/2 /4

1.0

0.5

0.0 0 1 2 3 4 5 6 7 8 9 Number of QWs Entanglement-Interference Experiment (IV)

interferences seen in multiple QW system with λ/2 spacing

interferences vanish in multiple QW system with λ/4 spacing

λ/4 spacing leads to complete randomizing of emission to the left and to the right

confirmation of theoretical predictions Summary of Entanglement-Interferences incoherent emission to the left and to the right are entangled with the many-body carrier system emission to the left and to the right with same q|| is not entangled emission to the left and to the right with same q|| is entangled description of entanglement via photon- carrier and photon-photon correlations of the type:

more in: Hoyer et al. PRL 93, 067401 (2004) Summary

• variety of novel quantum optical effects in semiconductors • strong experiment – theory interactions

MANY CHALLENGES:

• optimization and application of non-classical properties (quantum information science, …) • modified photonic environment (phot. x-tals, …) • role of incoherent excitons, biexcitons, ….