1. Hui Deng Stephan Gotzinger David Press Yoshihisa Yamamoto Robin Huang Hui Cao Francesco Tassone Gregor Weihs Stanley Pau (Former members) Quantum Entanglement Project, SORST, JST E.L. Ginzton Laboratory, Stanford University and National Institute of Informatics BaCa Tec-Summer School, Würzburg, June 26 – July 01, 2005

2. 2 Outline Microcavity exciton polaritons Polariton BEC vs. exciton BEC Non-equilibrium, quasi-equilibrium and thermal equilibrium BEC Final state stimulation in exciton-exciton scattering processes Amplification of exciton polaritons Dynamic condensation (lasing) of exciton polaritons in CdTe and GaAs MQW-microcavities  Polariton population per state N(k // )  Effective mass  Relaxation time  polariton vs. lifetime  0  Momentum and real space distributions  Chemical potential and polariton temperature  Second order coherence function Transverse confinement of exciton polaritons

3. Microcavity Exciton Polaritons

4. 4 Wannier-Mott Excitons in Quantum Wells Momentum eigenstate – A valence electron with and  is excited to a conduction electron with and Exciton state mode indexenvelope function in k-space plane wavehole electron momentum eigenstate

5. 5 Exciton creation operator Composite boson in the 1 st order approximation Exciton Hamiltonian Diagonalize with polariton operator: Hamiltonian of Coupled Cavity Photon-QW Exciton Rabi-splitting:when cavity photon on resonance with bare exciton QW Excitons and Microcavity Polaritons

6. 6 1 or 2? r’ A rBrB rArA r’ B e 1 r’ A h 1 r A e 2 r’ B h 2 r B  ~ + e 1 r’ A h 2 r A e 2 r’ B h 1 r B e 2 r’ A h 1 r A e 1 r’ B h 2 r B e 2 r’ A h 2 r A e 1 r’ B h 1 r B ex 2 r A ex 1 r B ex 1 r A ex 2 r B + 1 2  = Two-Exciton State: Spatial Correlation induced by Coulomb Interaction. A composite particle (exciton) behaves as a “massive boson”. Exciton as a Composite Boson

7. 7 Polariton dispersion curves  osc ~ 1 TH z C. Weisbuch, et al. Phys. Rev. Lett. 69, 3314 (1992) S. Jiang et al., Appl. Phys. Lett. 73, 3031 (1998) Exciton Polariton Dispersion, Normal Mode Splitting and Oscillation UPLP ～

8. 8 Atom Cavity QED vs. Semiconductor Cavity QED single-atom cavity QEDmany-atom cavity QEDexciton cavity QED single atom ensemble of atoms QWs d: atomic dipole moment V: optical mode volume eigenstate of collective angular momentum (J =N/2, N: # of atoms) effective # of atomic oscillators: S: cavity mode area, ~2  m  : Bohr radius, ~100 

9. Non-equilibrium Polariton Laser vs. Equilibrium Polariton BEC

10. 10 Dynamic vs. Equilibrium Condensation Polariton decay vs. Two relaxation processes exciton-phonon scattering k // equilibrium is established with a lattice at  lattice exciton-exciton scattering k // equilibrium is established within polaritons at  polariton Non-equilibrium (multi-mode polariton laser) Quasi-equilibrium (single-mode polariton laser) Thermal equilibrium (polariton BEC)  0 <  polariton  lattice  polariton not defined  polariton  0 <  lattice  polariton > T lattice  polariton <  lattice  0  polariton = T lattice Fragmentation of the condensate Fock exchange term Dynamic single-state condensation Steady state single- state condensation polariton decay k // polariton decay by leakage of photonic component at  0 leakage photon

11. 11 Polariton BEC vs. Exciton BEC Enemies of exciton BEC: Dissociation of excitons (screening, phase space filling) Disorder, localization and inhomogeneous broadening Advantage of Polariton BEC Extended phase coherence reinforced by a cavity field suppressed localization, disorder and inhomogeneous broadening Light effective mass by dressing a cavity field m polariton ~ 10 -4 m exciton ~ 10 -7 m H-atom Enhanced binding energy/decreased Bohr radius in the very-strong-coupling regime [J. B. Khurgin et. al., Solid State Commun. 117, 307 (2002)] suppressed dissociation of excitons Photonic component out-coupling from the cavity with k conservation in contrast to spontaneous decay of an un-dressed exciton direct experimental access to internal polariton population higher critical temperature lower particle density

12. Bosonic Final State Stimulation

13. 13 Exciton-polariton Nonlinear Interaction same spinsopposite spins U1U1 T 1 /2 Exciton LPUP smaller spitting Blue shift M. Kuwata-Gonokami et al., Phys. Rev. Lett. 79, 1341 (1997) S. Schmitt-Rink, et al., Phys. Rev. B 32, 6601 (1985) J. Fernandez-Rossier et al., Phys. Rev. B 54, 11582 (1996) J. Inoue, et al., Phys. Rev. B 61, 2863 (2000)

14. 14 Measurement of Exciton Interaction – Pump-probe experiments with optical heterodyne detection Experimental results Probe Energy Experimental setup Excitons with same spins (theory) (experiment) (Fermionic exchange + phase space filling) (theory) (experiment) (Fermionic exchange)

15. 15 Idea:UP=background free measurement window leakage from cavityphonon scatteringexciton-exciton scattering Stimulated scattering exc. beam Spontaneous scattering

16. 16 Observation of Bosonic Final State Stimulation in exciton-exciton scattering in a GaAs SQW-Microcavity n exc = 1.5  10 9 cm -2 1.2 0.54 R. Huang et al., Phys. Rev. B 61, R7854 (2000) Upper-polariton emission decay time ~ 95 ps bottle-neck polariton decay time ~ 190 ps

17. Amplification of Exciton Polaritons —Probing Quantum Degeneracy

18. 18 Strong Coupling to Weak Coupling Transition Normal mode splitting at resonance (  c =  exc ) (weak coupling) polariton cavity photon Exciton densities: A: 1.1  10 8 cm -2, B: 1.1  10 9 cm -2, C: 5.5  10 9 cm - 2, D: 1.1  10 10 cm -2, E: 2.0  10 10 cm -2, F: 2.7  10 10 cm -2 G: 4.4  10 10 cm -2, H: 6.6  10 10 cm -2, I: 1.1  10 10 cm -2 S. Jiang et al., Appl. Phys. Lett. 73, 3031 (1998)

19. 19 1. Exciton localization and inhomogeneous broadening Dressing QW excitons with a microcavity vacuum field Strong coupling to weak coupling transition when an exciton decoherence rate exceeds a normal mode splitting. Use of multiple QWs Use of excitons with small Bohr radius 2. Exciton saturation QW excitons are easily trapped by a local minimum of a QW potential fluctuation. Comparison of Exciton Properties 2510Binding Energy (meV) 2890Bohr Radius in QW(A) 504 Saturation Density (10 10 cm -2 ) CdTe GaAs Obstacles and Tricks for Polariton Lasing extended phase coherence

20. 20 Gain =15 Bare Exciton k // = 0:LP Bottleneck effect Bottleneck Exciton decay rate = 120 ps Gain decay rate = 60 ps A CdTe QW exciton survives at higher densities due to small Bohr radius. R. Huang et al., Phys. Rev. B 65, 165314 (2002) Observation of Stimulated Scattering Gain in a CdTe DQW-Microcavity A gain is provided by two-body exciton-exciton scattering.

21. 21 N exc =3.4x10 6 Gain =23 N exc =1.6x10 6 Gain =5.4 N exc = 0.41x10 6 Gain = 0.34 Probe (mW/cm 2 ) Circles: 2  10 4 Squares: 900 Rate equation solutions Low Gain Regime High Gain Regime R. Huang et al., Phys. Rev. B 65, 165314 (2002) exciton-phonon scattering exciton-exciton scattering A. Imamoglu et al. Phys. Rev. A 53, 4250 (1996) F. Tassone et al., Phys. Rev. B 59, 10830 (1999) Amplification of Polaritons in a CdTe DQW-Microcavity

22. 22 Spontaneous build-up of ground state population Polariton effective mass Spontaneous spin polarization Second order coherence Real space distribution (spontaneous localization) Momentum space distribution (BE) (chemical potential and temperature) Experimental evidence: Dynamic Condensation (Lasing) of Exciton Polaritons

23. 23 Polariton Lasing vs. Photon Lasing lasing threshold observed without electronic population inversion H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003) polariton laser standard photon laser

24. 24 Effective Mass Measurement: Polariton and Photon Dispersions -202 1.612 1.614 1.616 1.618 1.62 k || (10 4 cm ) Energy (eV) P/P th =7.6 -202 1.646 1.648 1.65 1.652 1.654 k || (10 4 cm ) Energy (eV) photon laser P/P' th =3 -202 1.612 1.614 1.616 1.618 1.62 k || (10 4 cm ) Energy (eV) P/P th =0.5 photon polariton Polariton Laser Photon Laser polariton mass measured to be ~ twice the photon mass strong-coupling preserved above threshold H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003)

25. 25 Spontaneous Spin Polarization

26. 26 Second Order Coherence (Hanbury Brown-Twiss experiment) single-mode coherent state Poissonian light single-mode thermal state H. Deng et al., Science 298, 199 (2002) The on-set of bosonic final state stimulation manifests itself by increased g (2) (0). A gradual decrease in g (2) (0) suggests non-standard macroscopic coherence.

27. 27 Real Space Distribution photon laser fitted spot size: 26  m polariton laser suppressed ‘expansion’ P/P th = 1.5 polariton photon below threshold broad Gaussian above threshold steep central peak

28. 28 Momentum Space Distribution Exp. Data BE Fit MB Fit P/P th =1.5P/P th =0.6 resolution H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003) J ． Keeling et al., Phys. Rev. Lett. 93, 226403 (2004) The k-distribution is in agreement with BE distribution, except for the population at k 11 =0.

29. 29 Chemical Potential and Effective Temperature chemical potential  ~ -k B T at threshold chemical potential   zero above threshold fitted polariton temperature fitted (normalized) chemical potential T polariton >> T lattice BEC threshold H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003)

30. From Non-equilibrium Polariton Laser To Equilibrium Polariton BEC

31. 31 Relaxation Rate vs. Decay Rate of Polaritons Non- equilibrium Equilibrium

32. 32 Future Prospects Room temperature polariton laser (GaN （ＮＴＴ）, ZnSe （Ｐａｄｅｒｂｏｒｎ）, ·····) Practical issues: Very low-threshold and very fast (~psec) coherent light source Theoretical issues: Bogoliubov theory predicting a squeezed ground state F. Tassone et al., Phys.Rev.B59,10830(1999) F.P. Laussy et al., Phys. Rev. Lett. 93, 016402 (2004) phase-locked Transverse confinement and long polariton lifetime by a 2D photonic crystal or microdisk cavity BEC  BCS phase transition Impurity bound exciton in homogeneous bulk (F. M. Marchetti, et al., arXiv:cond-mat/0405295) Acknowledgement Atac Imamoglu, David Snoke, Jacqueline Bloch, Regis Andres, Hiromi Ezaki Transverse confinement by a cavity trap (V~10meV for 12 GaAs MQW)

33. 33 Optical Trapping of Microcavity Polaritons A. Forchel (Würzburg)

34. 34 UP LP condensate  normal state  thick lines: quasi-particle excitations in the condensed phase  upper line: creating a quasi-particle  lower line: absorbing a quasi-particle gap 4g|  Coherent light BEC-BCS Phase Transition M.H. Szymanska et al., Solid State Comm. 124, 103 (2002)