QUANTUM CORRELATIONS IN EXCITON SYSTEMS

Transcription

1 INTERNATIONAL SCHOOL OF PHYSICS "ENRICO FERMI" SUMMER COURSES 2008 QUANTUM COHERENCE IN SOLID STATE PHYSICS Varenna (Italy) July 1-11, 2008 Course CLXXI QUANTUM CORRELATIONS IN EXCITON SYSTEMS Part 2 Raffaello Girlanda Università di Messina Dipartimento di Fisica della Materia e Ingegneria Elettronica

2 Outline Why QO with excitons and polaritons? Historical Howerview 2-photon Hyper parametric scattering Quantum optics with cavity polaritons Parametric emission of polaritons in bulk semiconductors Entangled photon pairs from the optical decay of biexcitons Some more recent and new results: Demonstration of spin-entangled polariton pairs Edamatsu et al. Quantum complementarity of microcavity polaritons Nonequilibrium Langevin approach to quantum optics in SMCs

3 Why quantum optics in SMCs? Excitonic polaritons propagate in a complex interacting environment and contain real electronic excitations subject to scattering events and noise: prototype systems where quantum-mechanical properties of many interacting particles can be studied Rapid development in the field of quantum information requires monolithic, compact sources of nonclassical photon states enabling efficient coupling into optical fibres and possibly electrical injection. Semiconductor-based sources of entangled photons would therefore be advantageous for practical quantum technologies. Possibility of ultrafast optical manipulation of quantum states very large resonant Giant amplification (3) χ macroscopic entanglement

4 WARNING! (1) ω ( ) (, t) (, t) 2 2 Er = Pr 2 c t c From QM Pr (,) t ω Pr (,) t = f Er (,) t +...NLterms 2 (1) 0 From QM Dynamics described by a Classical dipolar wave 2 ω ε ω = ( k ), k 2 c 2 Polaritons: Classical excitation waves strongly coupled with light waves (superposition principle already holds at a classical level) In contrast to matter waves from atoms whose classical description is that of massive pointlike objects

5 WARNING! (2)

6 Macroscopic Local Realism for Entangled Photons in a Cavity or what we mean by quantum correlations?

7 Collaboration: from Nanoscience theory lab at Torino Fausto Rossi Stefano Portolan from Semiconductor Quantum Optics group at Messina Salvatore Savasta Omar Di Stefano Raffaello Girlanda

8 Outline: Information as a new common principle Information and non-classical correlations Decoherence & macro local realism Entanglement Down-Converter and Semiconductor Microcavities Results Conclusions Information is physical

9 Historical overview: motivation and previous works Quantum entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. Macroscopic emergence of classical world by means of decoherence (Zurek) Macroscopic entangled state half dead or half alive? Decoherence, einselection and the quantum origins of the classical W. Zurek, RMP 75 (2003) We show the emergence of macro local realism in the presence of strong entanglement even in the abscence of decoherence

10 ENTANGLEMENT 2 subsystems a SEPARABLE bipartite pure state is a direct product of pure states in and : Real systems: decoherence and noise Separable, iff otherwise ENTANGLED N L T Entanglement cannot be created locally A Nanoscience Theory Lab interaction B

11 Group-theoretic approaches VS experimental viewpoint quantum phenomena treated by Peres: Quantum mechanics happens in labs not in Hilbert spaces Feasible measurements visibility (Mandel) with classical bounds, violated by quantum fields Bell Inequalities q comm complexity (Zeilinger) Entanglement: a prototypical non classical feature separability criteria (Simon, Bouwmeester)

12 2-particle correlation Down-converter (DC) (type II) Semiconductor Microcavity BBO crystal P.G. Kwiat et al., Phys. Rev. Lett., (1995) Quantum complementarity of Spontaneous microcavity polaritons Parametric Emission S. Savasta et al., Phys. Rev. Lett., 24 Ciuti et al., Phys. Rev. B, (R) (2001) (2005) R.M.Stevenson et al., Phys. Rev. Lett., (2000)

13 The physical system pairs of light pulses (a,b = signal,idler) entangled in polarization Stokes parameters per each mode Schwinger transform

14 The physical system (II) separability criterion: for a separable state C. Simon and D. Bouwmeester, Phys. Rev. Lett., (2003)

15 Results (I) In absence of noise is stricly Even when thermal noise largely exceeds vacuum flactuations, there is a value beyond which we are lower than 1/2. Moreover Macroscopic entanglement can in principle be reached even in the presence of strong fluctuations

16 Results (II)! With self stimulation in spontaneous parametric emission we can BEAT the noise!! Self stimulation effects are clearly visible in spontaneous parametric emission of polariton pairs So far presence of noise but no losses In real systems amplification, losses, noise disturbances happen on the same time scales Heisenberg-Langevin equations

17 Results (III) time resolved

18 Classical or Quantum? 1 self-stimulated true spontaneous emission (vacuum flactuations) 2 Classical-like thermal noise amplification Classical treatment would suffice!!

19 weaker NON locality concept Adherence on the physical system Herzog et al. Phys. Rev. Lett., (1994) Herzog et al. Phys. Rev. Lett., (1994) Zou, Wang, Mandel, Phys. Rev. Lett., (1991)

20 Results (IV)

21 Macroscopic limit Large class of quantum correlation functions that cannot differ from the corresponding classical ones in the macro limit Theorem: It is impossible to observe violations of macro local realism (Bell s even not yet known) by means of any set of expectation values that can be expanded as finite sums of these functions

22 Our interpretation States with more than two-photons NEGLIGIBLE measurements of and of can probe at a microscopic level as increase the two both become macroscopic observable unable to probe the system fluctuation at a few quanta level information recovered coarse grained quantity missing the underlying quantum structure This lack of information seems able to introduce elements of local realism

23 Conclusions (Gaussian) our findings does not imply that macroscopic entangled systems cannot display quantum nonlocality effects! Z. Cheng et al.,phys. Rev. Lett., (2002) N. D. Mermin, Phys. Rev. Lett, (1990) Observation of quantum as well as classical phenomena is resource dependent the lack of information gathered by coarse-grained observations may lead to the introduction of elements of local realism (strong entanglement and no decoherence) Coarse-graining

24 L (longitudinal polariton) The starting point!

25 DCTS + EM Field-Q Anomalous correlators Anomalous correlators

26 Engineering quantum optical correlations in semiconductor microcavities quantum noise reduction % γ x = 0.8 mev γ x = 1.5 mev V = 5.6 mev photon escape rate γ c (mev) γ x = γ c = 1.5 mev exciton-photon coupling V (mev)

27 10 UP 5 Cavity 0 Exciton -5 V LP Pump Idler Signal 10-1x x10 7 Wave-vector (m -1 )

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32 Bulk: microscopic quantum theory

33 Q X Energy (ev) Energy (ev) 0 <n1 > <n2 > (arb.) dephasing rate (mev) Bulk

34 Bulk 1 Ψ = iφ ( e ) A B A B

35 A r B 1 ψ = r + r r 2 ( fa( ) passage through slit a fb( ) passage through slit b ) No which way information which way information ( r) = ( r) + ( r) 2 P f f a ( r) = ( r) + ( r) P f f a b 2 2 b

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37 Quantum complemetarity in presence of Quantum correlations (the q-eraser) X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991) L. Mandel, Review of Modern Physics

38 i i 1 2 i + i i p1 p2 = pe φ 1 s = s 1 2 s 2 φ i1 i 2 i + i i p1 p2 = pe φ 1 s 1 s 2 s + s φ

39 Two-pump parametric emission p k = p e k 2 1 iφ χ Ψ = iφ e 0 1 s i i i i χ = gp k 2 1 χ ( i Ψ pp Ψ = 2+ e φ ) = s s χ = 0 No interference! ( )( ) ( ) 2 pˆ ˆ ˆ ˆ ˆ ˆ i pi pi pi2 2 χ pi pi cc.. Ψ + + Ψ = + Ψ Ψ Ψpˆ pˆ Ψ = χ e Interference! 2 2iφ i i 1 2

40 K-matching K y K x

41 x k y (nm -1 ) k x (nm -1 ) x 10-3

42 x k y (nm -1 ) k x (nm -1 ) x 10-3

43 x k y (nm -1 ) k x (nm -1 ) x 10-3

44 Two-pump extension of:

45 excitation wavevectors Experimental setup K p1 (k px, k py ) K p2 (-k px, k py ) detection wavevectors K (k x, k y ) K (-k x, k y ) t-resolved under pulsed excitation ( k ) ( ) ( ) imaging = kx, k y + kx, k y I E E S = I t dt t-integrated 0 () 2

46 Experimental results Time-integrated visibility x k y (nm -1 ) V S = S S Max Max S + S min min k (nm -1 ) x x 10-3 S k i ( φ) k y (μm -1 ) 3 2 a) 2 3 k x (μm -1 ) b) pum p phase φ (2π) 1 intensity (norm.) S k s ( φ)

47 A true nonclassical effect? Time resolved visibility Vt () = IMax () t Imin () t I () t + I () t Max min Heisenberg-Langevin (quantum versus classical model) with constant noise The classical model understimates the measured visibility! The starting low value of the visibility V(t) id due to noise from PL

48 Spin-entangled cavity-polaritons Excitation with circular polarization : light emitted same circular polarization Excitation with linear polarization : light emitted totally unpolarized Neglect of TE-TM splitting: negligible with a 2-pump scheme Sufficient negative detuning in order to avoid excitation of states + and EID (Savasta et al. PRL 2003) s i 1 Ψ = ( ) s i s i

49 Evaluation of the entanglemetn degree including the influence of pump PL Solving the H-L equations under excitation with linear polarization, ones obtains: Stokes parameters s s s s s s = = = First indirect evidence of spin-entanglement direct evidence by means of coincidence detection as in

50 A problem: The signal is much brighter than the idler s i

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52 Rayleigh scattering more symmetric signal-idler emission negligible TE-TM splitting for pump and emitted polaritons Biexcitons sufficiently out of resonance (better with some mev of negative detuning) Strong suppression of PL noise (bottelneck+ γ ph <<γ c )

53 Advantages (respect to bulk): High efficiency symmetric emission (γ ph <<γ c ) Suppression of EID and Spin-flip events (unavoidable with biexcitons) Suppression of + - events due to biexitons (++ or - events cannot be easily eliminated in bulk) Possible direct implementation of hyperentanglement useful for quantum cryptography Better control of parameters as detuning, Rabi splitting

54 PL versus Parametric emission It is worth noting that in a realistic environment phase-coherent nonlinear optical processes involving real excitations compete with incoherent scattering as evidenced by experimental results. In experiments dealing with parametric emission, what really dominates emission at low pump intensities is the photoluminescence (PL) due to the incoherent dynamics of the single scattering events driven by the pump itself and the Rayleigh scattering of the pump due to the unavoidable presence of structural disorder. Only once the pumping become sufficient the parametric processes start to reveal themselves and to take over pump-induced PL as well. Indeed, usually, parametric emission and standard pump-induced PL cohabit as shown by experiments at low and intermediate excitation density. In order to address quantum coherence properties and entanglement the preferred experimental situations are those of few-particle regimes, namely coincidence detection in photon counting. In this regime, the presence of incoherent noise due to pump-induced PL tends to spoil the system of its coherence properties lowering the degree of nonclassical correlations.

55 DCTS-Langevin approach for PL+PaE Heisenberg-Langevin eqs. for signal/idler polariton operators (lower polariton branch) S. Portolan et. al., PRB 2008

56 DCTS-Langevin approach (II) 1-time 2-body = intensity after 2-times 2-body = spectrum VFs S. Portolan et. al., cond-mat/

57 Numerical Results centered at no fitting parameters needed, nor exploited see W. Langbein, Phys. Rev. B. 70, (2004)

58 positive part of the ky=0 section Numerical Results realistic competition between pump PL and parametric scattering threshold around Parametric process removes ph bottleneck at PL t-integrated intensity / pump (arb. units) PL pol. occ. (arb. units) 0 1x10 6 2x10 6 3x10 6 4x10 6 k x (m -1 ) 0 1x10 6 2x10 6 3x10 6 4x10 6 k x (m -1 ) time integrated photon emission

59 centered at I = 40I 0 0 () S = I t dt

60 Vt () IMax () t Imin () t N1() t N2() t = = I () t + I () t N () t + N () t Max min 1 2 quantum 0,8 0,6 classical 0,4 visibility 0, ,0 tim e (ps)

61 Conclusions&Outlook While for many years proposals for experimental quantum optics with polaritons were believed unfeasible, now there is evidence both in Bulk (ultraviolet entanglement in CuCl) and in SMCs (QC)! Two pump schemes in SMCs are revealing a powerful means to probe coherence and correlation in SMCs (see e.g. Phys. Rev. Lett. 98, , Four Wave Mixing Oscillation in a Semiconductor Microcavity: Generation of Two Correlated Polariton Populations M. Romanelli et al.) Spin entangled (singlet and triplet) polaritons in SMCs (S. Savasta and O. Di Stefano, Phys. Stat. Solidi b, 243, 2322 (2006)), to be realized experimentally. many-polariton entangled states thanks to self-stimulation or by coherent stimulation from a polariton condensate. We presented realistic quantitative calculations of PaE emerging in presence of PL-noise. Full microscopic characterization of q-correlations among cavity-polaritons is under development by V. Savona, S. Portolan, and S. Savasta.