1. 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?

2. 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 ω th

3. VgVg self-organised quantum dots back contact top gate InAs/GaAs laser z 0 Experimental Setup ωLωL EFEF conduction band V’ g z 0 VgVg back contact valence band 2DEG InAs dots

4. Warburton, Karrai et al., Nature 405, 926 (2000): Optical Emission of Single (!) Quantum Dot Discrete charge states tunable by back gate voltage

5. 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

6. 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

7. initialfinal (Helmes et al. ’04) Optical absorption induces a quantum quench: H initial ≠ H final What is subsequent transient dynamics of dot + Fermi-sea ? Transient dynamics after Kondo interaction is suddenly switched on ? Proposed Experimental Setup: Absorption

8. 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)

9. Hamiltonian initialfinal (Helmes et al. ’04) Anderson model (AM) (symmetric Anderson model)

10. Proposed Parameters

11. 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 fridgemicroscope xyz-positioners objective single-mode fiber sample mixing chamber (~10 mK) gas handling system and dewar 0100200 0.000 0.001 0.002  T/T laser detuning (μeV) Relative Transmission:

12. Anderson Model (Kondo) (Nozières) charge fluctuations spin fluctuations Γ TKTK screened singlet FO LM SC T (Anderson)

13. Numerical Renormalization Group (NRG) (Wilson ’75)

14. Transient Relaxation FOLMSC t = 0 + t = ∞ nonzero final magnetizaton is finite-size effect magnetization total charge t-NRG: Anders, Schiller ‘05 [1/D]

15. Absorption Lineshape (SAM)

16. Absorption Lineshape: T = 0 (SAM) Helmes et al, ‘04

17. Fixed-Point Perturbation Theory (FO, LM)

18. Scaling Collaps (asymmetric AM)

20. Strong-Coupling Regime (T << << T K ) 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)

21. X-Ray-Edge & Anderson-Orthogonality (without spin) initial state t < 0 perturbation t = 0 + final state t = ∞ Fermi sea 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)

22. X-Ray-Edge & Anderson-Orthogonality (with spin) initial state t < 0 perturbation t = 0 + final state t = ∞ Fermi sea lattice atoms (ii) orthogonality: (Anderson ’67) Mahan vs. Anderson:Mahan wins, if Deep hole causes: (i) enhanced density of final states: (Mahan ‘67)

23. Kondo-Exciton 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 >> T K : Mahan wins Anderson wins (!) SAM Affleck, Ludwig, ‘94

24. Kondo-Exciton (B >> T k ) 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 >> T K : Mahan wins Anderson wins (!) SAM

25. Kondo-Exciton (B >> T k ) 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 >> T K : Mahan wins Anderson wins (!) SAM

26. Absorption Line Shape: B-Dependence (SAM) A lower : divergence is strengthened A upper : divergence disappears, peak at = B Magnetization is universal function of B/T K, hence so are the exponents!

27. Absorption Line Shape: T-Dependence (SAM) Korringa relaxation rate: (Garst et al., ’05)

28. 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

29. Absorption spectrum contains information about all energy regimes of the Anderson-Model Characteristic T- und B-dependence (scaling with T K ) 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