Quantum Quench of a Kondo-Exciton

SFB/TR-12

Hakan Tureci, Martin Claassen, Atac Imamoglu (ETH),

Markus Hanl, Andreas Weichselbaum, Theresa Hecht, Jan von Delft (LMU)

Bernd Braunecker (Basel), Sasha Govorov (Ohio), Leonid Glazman (Yale)

What happens when an optical excitation is used to “switch on” Kondo correlations?

Outline

• Experimental background

• Proposed experiment

• Transient dynamics of charge and spin

• Absorption spectrum at T=0

• Finite magnetic field B

• Finite temperature T

• Absorption threshold ωth

Vg

self-organised quantum dots

back contact

top gate

InAs/GaAs

laserz

0

Experimental Setup

ωL

EF

conduction band

V’gz

0

Vgback contact

valence band

2DEG

InAs dots

Warburton, Karrai et al., Nature 405, 926 (2000):

final initialE E

Optical Emission of Single (!) Quantum Dot

Discrete charge states tunable by back gate voltage

Optical Absorption for Single (!) Quantum Dot

Högele et al., PRL, 2004

Transition energies tunable by magnetic field; optical polarization selects spin state

T = 4.2 K

Hybridization of Dot with Fermi Sea (2DEG)Smith et al, PRL’05

dark exciton

bright exciton

Further signatures for hybridization: Karrai et al, Nature ’04 ; Dalgorno et al., PRL’08

Hybridization with 2DEG can be strong, causing spin-flip dynamics for electron-levels

initial final

(Helmes et al. ’04)

Optical absorption induces a quantum quench: Hinitial ≠ Hfinal

What is subsequent transient dynamics of dot + Fermi-sea ?

Transient dynamics after Kondo interaction is suddenly switched on ?

Proposed Experimental Setup: Absorption

Transient Dynamics after Quantum Quench

Quantum dynamics after sudden

change in Hamiltonian?

Modern Example: “Collapse & Revival” of coherent matter waves of cold atoms. (Greiner et al, Nature ‘02)

Old, well-known example:X-Ray-Edge Singularity(Mahan, PR ‘67)

Exciton + Fermi-See: Analogous to X-ray-edge problem (Helmes, Sindel, Borda, von Delft, PRB ‘04)

Hamiltonian

initial final

(Helmes et al. ’04)

Anderson model (AM)

(symmetric Anderson model)

Proposed Parameters

Experimental Parameters (Imamoglu, ETH Zürich)

Absorption spectrum

Base temperature: 50 mK

Spectral resultion 100 mK

Dot-Fermi-sea coupling: 10 – 100 K

Charging energy: 150 – 250 K

Magnetic field: 6 Tesla

fridge microscope

xyz-positionersobjective

single-mode fiber

sample

mixing chamber (~10 mK)

gas handling system and dewar

0 100 200

0.000

0.001

0.002

T

/T

laser detuning (μeV) Rel

ativ

e T

ran

smis

sio

n:

Anderson Model

(Kondo)

(Nozières)

chargefluctuations

spinfluctuations

eε +U

eε Γ

TK

screenedsinglet

FO

LM

SC

T

(Anderson)

Numerical Renormalization Group (NRG)(Wilson ’75)

Transient Relaxation

FO LM SC

t = 0+ t = ∞

nonzero final magnetizaton is finite-size effect

magnetization

total charget-NRG: Anders, Schiller ‘05

[1/D]

Absorption Lineshape (SAM)

Absorption Lineshape: T = 0 (SAM)

Helmes et al, ‘04

Fixed-Point Perturbation Theory (FO, LM)

Scaling Collaps (asymmetric AM)

Scaling Collaps (asymmetric AM)

Strong-Coupling Regime (T << << TK)

X-ray-edge (Mahan ’67, d’Ambrumenil, Muzykantskii, ‘05)

Problem: fixed-point perturbation theory is not possible:

change in local charge(enters via Friedel sum rule)

(Hopfield ’69)

X-Ray-Edge & Anderson-Orthogonality (without spin)

initial statet < 0

perturbation

t = 0+

final state

t = ∞

Fermisea

lattice atoms

(too naïve)

Deep hole causes:

(ii) orthogonality: (Anderson ’67)

(Mahan ‘67)

Mahan vs. Anderson: Mahan always wins!

(i) enhanced density of final states: (Mahan ‘67)

X-Ray-Edge & Anderson-Orthogonality (with spin)initial state

t < 0perturbation

t = 0+

final state

t = ∞

Fermisea

lattice atoms

(ii) orthogonality: (Anderson ’67)

Mahan vs. Anderson: Mahan wins, if

Deep hole causes:

(i) enhanced density of final states: (Mahan ‘67)

Kondo-Exciton initial state

t < 0perturbation

t = 0+

final state

t = ∞

exponents are tunable (e.g. as function of B or gate voltage)

B = 0:

Universal exponents for SAM with:

Mahan wins

B >> TK:

Mahan wins

Anderson wins (!)

SAM

Affleck, Ludwig, ‘94

Kondo-Exciton (B >> Tk)

initial state t < 0

perturbation

t = 0+

final state

t = ∞

+

exponents are tunable (e.g. as function of B or gate voltage)

B = 0:

Universal exponents for SAM with:

Mahan wins

B >> TK:

Mahan wins

Anderson wins (!)

SAM

Kondo-Exciton (B >> Tk)

initial state t < 0

perturbation

t = 0+

final state

t = ∞

-

exponents are tunable (e.g. as function of B or gate voltage)

B = 0:

Universal exponents for SAM with:

Mahan wins

B >> TK:

Mahan wins

Anderson wins (!)

SAM

Absorption Line Shape: B-Dependence (SAM)

Alower : divergence is strengthened

Aupper : divergence disappears, peak at = B

Magnetization is universal function of B/TK , hence so are the exponents!

Absorption Line Shape: T-Dependence (SAM)

Korringa relaxation rate:(Garst et al., ’05)

B-Dependence of Threshold Frequency (T=0)

Threshold:

GS energy difference of e-level + Fermi sea

Shift with B:

In Kondo limit

(neglecting Zeeman- shift for leads)

hole

(Tk defined via linear static susceptibility: )

Ground state energy shifts directly accessible via absorption

NRG

Absorption spectrum contains information about all energy regimes of the Anderson-Model

Characteristic T- und B-dependence (scaling with TK)

Mahan-exponents are - tunable;- have universal values for SAM in the limit of small or large magnetic fields

(threshold frequency contains information about magnetization)

Open Questions

Exchange interaction between electron and hole

Role of nuclear spins

Time-dependent measurements (pump-probe)

Raman transitions with virtual Kondo intermediate states

Summary