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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?
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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
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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
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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
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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
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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
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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
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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)
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Hamiltonian
initial final
(Helmes et al. ’04)
Anderson model (AM)
(symmetric Anderson model)
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Proposed Parameters
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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:
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Anderson Model
(Kondo)
(Nozières)
chargefluctuations
spinfluctuations
eε +U
eε Γ
TK
screenedsinglet
FO
LM
SC
T
(Anderson)
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Numerical Renormalization Group (NRG)(Wilson ’75)
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Transient Relaxation
FO LM SC
t = 0+ t = ∞
nonzero final magnetizaton is finite-size effect
magnetization
total charget-NRG: Anders, Schiller ‘05
[1/D]
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Absorption Lineshape (SAM)
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Absorption Lineshape: T = 0 (SAM)
Helmes et al, ‘04
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Fixed-Point Perturbation Theory (FO, LM)
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Scaling Collaps (asymmetric AM)
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Scaling Collaps (asymmetric AM)
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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)
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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)
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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)
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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
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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
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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
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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!
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Absorption Line Shape: T-Dependence (SAM)
Korringa relaxation rate:(Garst et al., ’05)
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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
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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