Dynamical Condensation of ExcitonPolaritons
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1 ICSCE 2008 Dynamical Condensation of ExcitonPolaritons Y. Yamamoto, H. Deng, G. Weihs, C.W. Lai, G. Roumpos and S. Utsunomiya Stanford University and National Institute of Informatics Loeffler, S. Hoefling, and A. Forchel Technische Physik, Universität Wurzburg 4th International Conference on Spontaneous Coherence in Excitonic Systems 1 (Cambridge, UK, September 8 12, 2008)
2 Outline Exciton polariton condensation vs. photon laser Thermodynamics of the excitations: Quantum degeneracy at equilibrium condition Bogoliubov excitation spectrum Coherence properties of the condensate: First order and second order coherence Dynamical condensation at excited Bloch bands in one dimensional lattice Experimental tricks toward equilibrium BEC of polariton: Blue detuning, cooperative cooling (by spin mixture) and evaporative cooling (by weak lateral confinement) 2
3 Exciton Polariton Condensation vs. Photon Laser : Proposal Phys. Rev. A 53, 4250 (1996) Extended wave functions reinforced by photonic components of exciton polaritons suppress localization due to disorder and crystal defects, which are notorious enemies to exciton BEC. Light effective mass by dressing QW excitons with cavity fields mpolariton ~ 10 4 mexciton ~ 10 8 matom : 2D quasi BEC (Ketterle and van Druten, 1996) higher critical temperature lower particle density suppress Auger recombination and dissociation of excitons which are another enemies to exciton BEC. Main decay channel of exciton polaritons= Photon leakage from the cavity with k and E conservation direct experimental access to the energy momentum dispersion and population distribution of internal polaritons. 3
4 Exciton Polariton Condensation vs. Photon Laser (2) exciton polariton dispersion electron hole pair dispersion E E stimulated cooling spontaneous cooling external injection k = 0 LP via multiple phonon emission & polariton polariton scattering population inversion external pumping stimulated emission of photons final bosonic mode cavity photon leakage of photons via cavity mirror final bosonic mode crystal ground state Exciton Polariton Condensation k crystal ground state k Photon Laser 4
5 Exciton Polariton Condensation vs. Photon Laser (3) polariton condensation ELP= ev 103 photon laser ECAV= ev 102 photon laser polariton condensation Quantum degeneracy threshold 10 1 inversion no inversion Photons per Cavity Mode at k 0 Polaritons per Mode at k 0 Proc. Natl. Acad. Sci., 100, (2003) 1012 injected exciton density (cm 2) Polariton condensation threshold observed without electronic population inversion Polariton quantum degeneracy: GaAs, GaN, CdTe, ZnO,. 5
6 Exciton Polariton Condensation vs. Photon Laser (4) Proc. Natl. Acad. Sci. 100, (2003) P/Pth = 1.5 polariton photon below threshold broad Gaussian photon laser above threshold steep central peak polariton condensation suppressed expansion 6
7 Outline Exciton polariton condensation vs. photon laser Thermodynamics of the excitations: Quantum degeneracy at equilibrium condition Bogoliubov excitation spectrum Coherence properties of the condensate: First order and second order coherence Dynamical condensation at excited Bloch bands in one dimensional lattice Experimental tricks toward equilibrium BEC of polariton: Blue detuning, cooperative cooling (by spin mixture) and evaporative cooling (by weak lateral confinement) 7
8 Trick one toward Equilibrium BEC: Blue detuning Polariton Cooling Time vs. Decay Time in Three Detuning Regimes 0.5 Pth Pth 2.5 Pth 102 rate equation model experiment, Emission Intensity = 6.9 mev Relaxation Time / Polariton Lifetime pump x red detuning ( = 6.6meV) x x 101 x on resonance ( =0) x x x x non equilibrium xx x x xx x x 100 xx blue detuning ( =8.5meV) equilibrium = 2.2 mev = 1.8 mev Time (ps) 80 Pump Power (mw) 102 Maximum excitonic component >80% at = 10meV = 7.7 mev Phys. Rev. Lett. 97, (2006) 8
9 Trick two toward Equilibrium BEC: Cooperative cooling Quantum Interference between Iso Spin and Hetero Spin Scattering amplitudes momentum space real space momentum space real space Linearly polarized pumping: Circularly polarized pump Linearly polarized pump Increasing pump power Injection of two spin components Repulsive interaction between iso spins and attractive interaction between hetero spins constructively interfere to accelerate a cooling process Output polarization is rotated by 90 Circularly polarized pumping: Relaxation bottleneck at threshold (polaritons condense into the excited state) 9
10 Trick three toward equilibrium BEC Evaporative cooling Position Uncertainty x and Momentum Uncertainty k in a weak trap 0 Photon field amplitude AlGaAs AlAs DBR GaAs Substrate DBR /2 AlAs cavity 3 stacks of 4 GaAs QWs Ti / Au x k=0.98 (the Heisenberg limit of 0.5) x, k and x k increase with P/Pth due to polariton polariton repulsive interaction k numerical results based on x Gross Pitaevskii equation Nature Physics, (online published on 10 August 1, 2008)
11 Outline Exciton polariton condensation vs. photon laser Thermodynamics of the excitations: Quantum degeneracy at equilibrium condition Bogoliubov excitation spectrum Coherence properties of the condensate: First order and second order coherence Dynamical condensation at excited Bloch bands in one dimensional lattice Experimental tricks toward equilibrium BEC of polariton: Blue detuning, cooperative cooling (by spin mixture) and evaporative cooling (by weak lateral confinement) 11
12 Quantum Degeneracy at Thermal Equilibrium Condition Phys. Rev. Lett., (2006) Theory: T.D.Doan et al., Solid State Commun. 145, 48 (2008) Temporal BE distribution observed at blue detuning regime ( =6.7 mev, t=40ps) TLP=4.4K, µ = 0.04 mev < BEC threshold ( 0.35 mev) NLP(E) ELP ELP0(meV) 1 12
13 Weakly interacting Bose gas : Bogoliubov transformation (1947) Diagonalization of the Hamiltonian of interacting bosonic particles p2 + 1 H = aˆ p aˆ p + 2 p 2m kinetic term p1+q g + aˆ p1 +q aˆ +p2 q aˆ p1 aˆ p2 (g > 0) p1, p2, q V interaction term p2-q p1 p2 Diagonalization using the linear transformation aˆ p = u p bˆp + v* p bˆ +p, aˆ +p = u *p bˆp+ + v p bˆ p, Diagonalized Hamiltonian Mean field energy Bogoliubov dispersion law for elementary excitations Energy of excitations ε ( p ) = cp N.N. Bogoliubov Mutual interaction of condensate linear at small k p2 ε ( p) = + gn 2m quadratic at large k 13 13
14 Observation of Bogoliubov Excitation Spectrum Nature Physics, (online published on August 1, 2008) Linear scale B D ev 8 mev E/ U 2 A C Bogoliubo v -15o 0 quadrat ic o kξ =1 Logarithmic scale ev kξ A: =1.41 (mev), P=4Pth B: =0.82 (mev), P=8Pth C: =4.2 (mev), P=4Pth D: =-0.23 (mev), P=24Pth -15o 15o Linear dispersion at low momentum regime c=de(p)/dp~108 kξ =1 cm/s (c~1cm/s for atomic BEC, c~104cm/s for superfluid 4He) 14
15 Quantum Depletion (intrinsic) vs. Thermal Depletion (extrinsic) n p = v p 2 + u p 2 bˆp+ bˆp + u p 2 bˆ +p bˆ p Quantum depletion Thermal depletion Quantum depletion nk Thermal depletion nk mu 2 k mk BT ( k )2 ˆ+ ˆ 1 b p b p = exp[ β ε ( p )] 1 (proportional to 1/k) (proportional to 1/k2) aˆ k+ aˆ +k aˆ0 aˆ0 Quantum depletion aˆ k+ aˆ 0 bˆph Thermal depletion phonon 15
16 Outline Exciton polariton condensation vs. photon laser Thermodynamics of the excitations: Quantum degeneracy at equilibrium condition Bogoliubov excitation spectrum Coherence properties of the condensate: First order and second order coherence Dynamical condensation at excited Bloch bands in one dimensional lattice Experimental tricks toward equilibrium BEC of polariton: Blue detuning, cooperative cooling (by spin mixture) and evaporative cooling (by weak lateral confinement) 16
17 Off Diagonal Long Range Order (Spatial Coherence) Phys. Rev. Lett. 99, (2007) Interference Pattern through Young s Double Slit Interferometer Experimental Solid lines: Fourier transform of the experimental momentum distribution Theoretical 17 T. Doan, H. Cao, D.T. Thoai and H. Hang, Phys. Rev. B (in press, 2008) D. Sarchi and V. Savona, Phys. Rev. B75, (2008)
18 Off diagonal long range order (spatial coherence (2)) d=2µ m ~Threshold Increasing pump rate d=4µ m d=8µ m e V d = 16 µ m1 Intensity E =1 me V θ º = sin(θ ) = v/fobj
19 Hanbury Brown and Twiss Correlation Bunching Effect Science 298, 199 (2002) g (2 ) (τ) = ˆ ( ) (t ) E ˆ ( ) (t +τ) E ˆ ( +) (t +τ) E ˆ ( +) (t ) E ˆ ( ) (t ) E ˆ ( +) (t ) E 2 = n1 (i ) n2 (i + j ) n1 i intensity correlation n2 P/Pth << 1 single mode thermal state Threshold delay τ measurement window intensity correlation P/Pth 1 measurement window delay τ single mode coherent state Photon bunching effect due to bosonic final state stimulation observed at threshold. g(2)(0) > 1 at well above threshold suggests the excess intensity noise in the condensate. Theory: P. Schwendimann and A. Quattropani, Phys. Rev. B 77, (2008) (Co existence of thermal and quantum depletions) 19
20 Hanbury Brown & Twiss correlation (2) Near field filtering dependence 1.8 (a) pinholes aperture k1 r space 2 BS pinhole diameter g ( τ=0, k1=0, k2= k ) k2 k space (c) (b) k ( µm 1) (d) ky g ( τ=0, k1=0, k2= k ) pinhole diameter pinhole kx k1 or k2 plane k ( µm 1)
21 Exciton Polariton Condensate Array in One Dimensional Lattice below threshold bright = gap region above threshold on top of metal gate bright = metal region well above threshold bright = gap region 21
22 Competition between Anti Bonded p wave and Bonded s wave in One Dimensional Exciton Polariton Condensate Array Nature 450, 529 (2007) Atomic BEC: T.Mueller et al., PRL 99, (2007) Below threshold Periodic potential Above threshold 0 state (s wave) stable π state (s wave) unstable π state (p wave) meta stable 22
23 Future Prospects Physics of Polariton BEC Quantum states of the ground state (phase locking between condensate and excitations) Superfluidity (second sound wave, quantized vortices) Exotic excitation spectrum (maxon, roton, negative energy branch) BEC BKT cross over, BEC BCS cross over Quantum emulation of many body systems Orbital physics (p wave, d wave and f wave ordered states) Bose Hubbard model Generation of single photons (repulsive interaction) and entangled photon pairs (attractive interaction) by SF MI phase transition Novel quantum computational scheme Stimulated cooling machine to find the ground state of model Hamiltonians New coherent light source Polariton BEC at room temperature Electrically driven polariton BEC 23
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