Control of excitons and exciton-polariton condensates in acoustic lattices

Transcription

1 Control of excitons and exciton-polariton condensates in acoustic lattices P. V. Santos Surface acoustic waves (SAWs) photons GaAs - + electrons, holes and spins excitons, polaritons polariton condensates PROCOPE Spice Workshop on Quantum Acoustics, Mainz, May 17, 2016

2 polaritons excitons Collaborations PDI A. Violante C. Hubert S. Lazic Hebrew Univ. of Jerusalem K. Cohen, R. Rapaport Univ. Autonoma Madrid S. Lazic Institut Néel, Grenoble C. Bauerle E. Cerda J. Buller Univ. of Sheffield (UK) D. Krizhanovskii, M. Sich, D. Sarkar, S.S. Gavrilov (Chernogolovka),M. Skolnick Univ. Autonoma San Luis Potosi, Mexico E. Cerda, R. Balderas Samples K. Biermann M. Höricke SAW technology W. Seidel, B. Drescher, S. Rauwerding S. Krauss, A. Tahraoui 2

3 Energy Outline Surface acoustic waves modulation of the semiconductor band structure tunable acoustic lattices SAW Acoustic exciton transport E SAW CB v indirect excitons (IXs) IX transport dynamics x VB photon Polariton modulation tunable polaritonic crystals cavity exciton control of polariton condensates k 3

4 SAWs in semiconductors V rf bulk wave SAW f SAW ~3-0.5 GHz l SAW ~ 1-5 mm GaAs quantum well (QW) M. Dühring, O. Sigmund, MEK.DTU, DK v SAW ~3km/s Dynamic acoustic fields in nanostructures spatial dependence: lateral pattering without interfaces penetration depth (mm) comparable to thickness of planar structures time dependence: dynamic control mobile character: transport with well-defined velocity v SAW 4

5 Modulation mechanisms strain field type I band gap mod. E g x v SAW CB hw PL tension: small gap compression: large gap hw L ~2 mev VB dimensions deformation pot. modulation band gap modulation refractive index modulation exciton confinement/transport IX trapping and transport m X de g /dx > v SAW 5

6 Modulation mechanisms piezoelectric materials strain field type II band gap mod. -ef SAW x v SAW CB tension: small gap compression: large gap ~100 mev VB deformation pot. modulation band gap modulation refractive index modulation photon manipulation piezoelectric potential F SAW electrical generation IX dissociation and e-h transport m E x = m df SAW /dx > v SAW 6

7 Semiconductor-related SAW activities Crespo et. al., Opt. Express, 2012 Photonic structures - membranes - waveguide mod. interdigital transducer (IDT) light control: WG, photonic systems SAWs: materials and technology Carrier and spin transport and manipulation SAWs on Si control-of-elementary-excitations-by-acoustic-fields/ main-research-projects/exciton-polariton-condensates/ High frequency SAWs on Si polariton Büyükköse et al. Nanotechnology modulation 23, (2012) lattice Quantum for polariton acousticscondensates - hf SAW >kt (Gustafsson et al., Science 346, 207 (14)) Exciton manipulation -exciton transport -polariton condensates surface-acoustic-waves-saws/sawqcp single carrier transport spin transport/manipulation single-photon sources/detectors

8 Energy Outline Surface acoustic waves modulation of the semiconductor band structure tunable acoustic lattices SAW Acoustic exciton transport E SAW CB v indirect excitons (IXs) IX transport dynamics x VB photon Polariton modulation tunable polaritonic crystals cavity exciton control of polariton condensates k 8

9 GaAs double quantum well Acoustic exciton transport excitation Surface acoustic wave SAWs emission excitons x Acoustically driven flying excitons: interface to photons!

10 Indirect (IX) Energy Direct (DX) Energy Quantum well (QW) excitons double QW (DQW) photons CB VB DX: t R <<T SAW z AlGaAs GaAs QW GaAs QW - p CB CB z IX z AlGaAs p GaAs V + VB VB z Quantum confined Stark effect (QCSE) Energy Recombination/spin lifetime Dipole moment: interactions 10

11 Indirect exciton electrically controlled coupling to photons coherent manipulation coherent spin control photon CB VB exciton p long lifetimes 1 control of spin-orbit (so) interaction 2,3 strong nonlinearities electric dipolar (p) interactions: devices confinement: single-excitons Schinner et al., PRL 110, (2013) bosonic character exciton condensates 4,5 1 Kowalik-Seidl et al., Appl. Phys. Lett. 97, (10) 2 Larionov and Golub, Phys. Rev. B78, (08) 3 Leonard et al., Nano Lett. 9, 4204 (09) 4 Blatt, Phys. Rev. 126, 1691 (61), Keldysh, JETP 27, 521 (68) 5 High et al., Nature 483, 584 (2012) 11

12 IX motion-based functionalities neutral particles! light Electrostatic gates exciton transistor EXOT T: 10 to >100K A. A. High et al., Science 321, (2008) Transport by field gradients approx 50 mm Transport conveyers electrostatic 30 mm V 1 V 2 V 3 RF A. G. Winbow et al., PRL 106, (2011) Laser 1 Gärtner, APL 89, (06) acoustic moving strain fields 1000 mm z x V BIAS J. Rudolph et al., PRL99, (07) 12

13 Spin precession during transport s + optical excitation Energy (ev) Energy (ev) E+02 DX counts 2E+04 3x10 4 3E+04 s + x [110] (mm) s - IX P laser = 13 mw V BIAS = -2V Profile region Distance (mm) DX optical excitation s - IX 0 s + DX Profile region x [110] (mm) GaAs GaAs IX DQW z (%) x' (mm) P laser = mw I PL profiles extent >> excitation region exciton drift diffusion repulsive interactions I PL (counts/s) 13

14 Spin precession during transport s + Energy (ev) Energy (ev) optical excitation E+02 DX counts 2E+04 3x10 4 3E+04 s + s + x [110] (mm) s - IX P laser = 13 mw V BIAS = -2V Profile region Distance (mm) s - DX IX GaAs Profile region GaAs z (%) x' (mm) P laser = 13 mw Oscillating spin polarization z Precession in the spin orbit field B so I PL (counts/s) B so ~g (F z )(k) s k x [110] (mm) precession period l so 14

15 z (%) Electric precession control P laser = 6 mw x' (mm) F z = -8 kv/cm -13 kv/cm A. Violante, R. Hey, and P. V. Santos, Phys. Rev. B 91, (15) 1/lSO (mm-1 ) l -1 so D l -1 so R F z F z (kv/cm) Fits to model V BIAS l -1 so [110] [110] spin-splitting constants Dresselhaus: g =+/-17.9 eva 3 Rashba: r 41 = -/+8.5 ea 2 z IX s B SO Laser k electrical control of spin precession! s + s -PL DQW lso (mm) 15

16 Experimental setup SAW along x=[100] non-piezoelectric, l SAW =2.8mm piezo ZnO-layer for generation piezo ZnO IDT rf G semitransparent electrode (STE) PL semitransparent top gate: V g control of exciton lifetime SAW DQW [100] V g QW 1 QW2 direct (D) I electric field F z indirect (I) Detection: photoluminescence (PL) T: 2-4 K laser focused on spot G spatially resolved PL along SAW path 16

17 Acoustic transport of indirect excitons IX DX Spectrally resolved PL recombination at edge of STE transport distances ~ 500 mm limited by channel length transport efficiency ~ 50 % Lazic et al., Phys. Rev. B89, (14) 17

18 Transport dynamics l SAW =2.8 mm IX cloud v SAW RF Laser pulse d=50 mm z 130 mm 1.10 x V BIAS Dt Time (ns) 350 mm PL (arb.units) pulse delay Dt = d/v IX v IX : transport velocity pulsed shape: essentially maintained during transport conceptually different from drift! Violante et al., New J. Phys.16, (14) 18

19 transport distance Gaussian Packet g ( t ) A e g 2 ( t t c ) 2 2 t w Trapping model delayed excitons t ( t ) 1 t d e t t d Distance A B C Fits C D 350 mm t d : average trapping time t c : arrival time t w : width of the Gaussian packet PL (arb. units) mm B Fit to: h ( t, d ) ( g t )( t, d Pulse shape: gaussian packet + tail: delayed IXs due to trapping A. Violante, K. Cohen, S. Lazic, R. Hey, R. Rapaport, and P. V. Santos, New J. Phys.16, (14) ) Time (ns) 50 mm A 19

20 SAW SAW Acoustic exciton transistor Differential images: I PL (SAW)-I PL (no SAW) laser laser Gate: open gate (G) 50 µm drain (D) laser closed patterned electrodes EXOT source (S) electrostatic control of acoustic IX transport 20

21 Control of the flow direction: DQDs SAW 1 SAW1 SAW 6 simulation moving strain dots SAW 6 interference of two orthogonal SAW beams moving and tunable potential dots for IX storage and transport Blue regions: areas under compressive strain Red regions: areas under tensile strain reduced bandgap: IX confinement Lazic et al., Phys. Rev. B89, (14) A. Govorov et al., PRL 87, (2001) S. Lazić et al., Physica E 42, 2640 (2009) 21

22 Dz (arb. units) Dz (arb. units) Interferometric mapping 1 SAW SAW 2 x (µm) SAW 1 2 SAWs rf Mirror IDT Laser Detector SAW Lazic et al., Phys. Rev. B89, (14) y (µm)

23 IX multiplexer Exciton (EXAM) acoustic multiplexer switching (EXAM) direction SAW 1 SAW 1 V SOURCE,1 = V GATE,1 = V DRAIN = -1.4 V 80 µm I/O 1 in EXOT 1 ON 780 nm, 80 MHz laser SAW 6 drain EXAM out SAW 6 I/O 3 PL simulation EXOT 3 OFF 4.5 K experiment P RF = 10 dbm SAW 1 PL image of transport channel PL IX transport with SAW 1 and SAW 6 : SAW 6 IXs transport from I/O 1 to I/O 3 IXs switching efficiency > 90% I/O 3 Lazic et al., Phys. Rev. B89, (14) 23

24 EXAM electrostatic switching (EXAT) V SOURCE,1 = V GATE,1 = V DRAIN = -1.4 V I/O 6 EXOT 6 ON V GATE,6 = out V SOURCE,6 = -1.4 V OFF ON drain 80 µm EXAM SAW 1 I/O 1 in EXOT 1 ON 780 nm, 80 MHz laser SAW 3 Electrostatic switching: EXOT 6 : isolation of I/O ports EXAM time-averaged channel width: 50 mm defined by SAW beam width long transport IX distances ~1 mm: lifetime > 330 ns SAW clock: synchronization! scalable! dimensions~ #ports planar 4.5 K PL image of transport channel P experiment RF = 10 dbm P RF = 10 dbm I/O 6 EXOT 6 ON Lazic et al., Phys. Rev. B89, (14) 24

25 Distance (mm) x [110] DOTs Acoustic spin transport circularly polarized light v DQD x [110] B so B ext SAW ON Energy (ev) G P RF = dbm z oscillations 10 no SAW laser 5 dbm 8 13 dbm IX spin precession in the spin orbit field B SO spin lifetime: 6 ns (Hanle effect, B ext ) Low spin transport efficiency z (%) z I I s s I I s s SAW changes in amplitude/precession frequency weak IX confinement 0-2 B ext =10 mt no SAW x' (mm) 25

26 Few/single IX transport Few/single IX manipulation small traps for IX confinement small SAW wavelengths lateral IX-IX interactions short IX interaction range light light V control channel Cohen, Rapaport, Santos, PRL106, (11) collaboration: Neel Institute

27 Energy Outline Surface acoustic waves modulation of the semiconductor band structure tunable acoustic lattices SAW Acoustic exciton transport E SAW CB v indirect excitons (IXs) IX transport dynamics x VB photon Polariton modulation tunable polaritonic crystals cavity exciton control of polariton condensates k 27

28 Direct (DX) Energy Exciton-polaritons in microcavities mirror 16 x l/4 layers l/2 (AlAs) 20 x l/4 layers T=5 K Laser DQW k - q + CB [001] VB DX z photons z - AlGaAs + + GaAs QW - Microcavity (MC) mirror Excitons (Al,Ga)As in DBR, QWs 6x15 nm GaAs QWs Mediate light-matter interation ns lifetimes DBR: Distributed Bragg Reflector Weisbuch, C.; Nishioka, M.; Ishikawa, A. & Arakawa, Y. Phys. Rev. Lett., 1992, 69, 3314 Excitons in a microcavity strong coupling to photons exciton polaritons: matter-wave particles short (sub-ns) lifetimes: photon loss 28

29 Exciton polaritons properties Microcavity (MC) polaritons QW excitons + MC photons Properties very small mass mirror photon mirror exciton m p ~ m e long de Broglie wavelength (mm) spatial coherence: l B > l SAW UP upper polariton k bosonic character: condensation non-equilibrium densities n Cond > l B -2 temporal coherence Energy W R k Photon Exciton LP lower polariton macroscopic quantum phases! Angle resolved PL5K Kasprzak, J. et al., Nature 443, 409 (06). Pump intensity 29

30 Tunable modulation Macroscopic quantum phase - MQP + tunable modulation preparation tunable lattice (r,t) + = tunneling control Realizations: Cold atom condensates + lasers Exciton-polariton condensates + SAWs optical lattices acoustic lattices 30

31 Tunable strain modulation rf mirror SAW IDT MC C QW AlGaAs QW Bragg mirror Bragg mirror x photon SL exciton mirror Photonic modulation: Microcavity Excitonic modulation: type I bandgap due to SAW strain refractive index (nc) Deformation potential E SAW strain ( zz) thickness (dc) In phase! mechanic > elasto-optic z SAW d1 1 d2 2 CB VB x dc M. M. de Lima et al. Phys. Rev. Lett. 97, (2006); M. M. de Lima, Jr. and P. V. Santos, Rep. Prog. Phys. 68, 1639 (2005). QWs x 31

32 rf-reflection rf-transmission SAW propagation: simulations SAW wavelength l SAW =8 mm SAW frequency f SAW =0.37 GHz SAW fingers rf ZnO l SAW BM C BM f SAW 0 u (pm) 50 SAW Absorber Sender IDT SAW Receiver IDT BM C BM 0 u (pm) 50 GetDP/gmsh,

33 ħ(w-w c ) (mev) Periodic SAW modulation MC k L Photoluminescence-PL k S k x tunable polaritonic crystal reflection k SAW =2p/l SAW x l SAW w0 c k SAW laser Dispersion 1 st MBZ no SAW ħ(w L -w c ) k x k x (k SAW ) Dħw 2 Dħw 1 lower polariton branch SAW effects: - dispersion folding - gaps M. M. Lima Jr., et al., Phys. Rev. Lett. 97, (06) 33

34 Polariton dispersion Collected PL k Non-piezoelectric SAW Increasing PRF + Laser power) 010 (low 1 Ex=0 - Non-piezo Sample y Energy (ev) SAW Piezoelectric SAW ZnO Piezo GaAs ky/ksaw + Piezoelectric SAW - -1 E0x x4 x2 1 k /ksaw E. Cerda et al., Superlattices and Microstruct.49, 233 (11) -1 0 k /ksaw k /ksaw 34

35 Energy (ev) Energy (ev) Polariton Exciton-polaritons in a square in lattices square lattices T=8 K 16 x l/4 layers l/2 (AlAs), 6x15nm GaAs QWs Laser k q real space [001] G X M k-space 20 x l/4 layers (Al,Ga)As Angle (k) resolved PL spectra SAWs off low density SAWs on 1 st MBZ Low density laser Energy pump k (mm -1 ) E. Cerda et al., Phys. Rev. Lett.105, (10) k (mm -1 ) DE g ~P rf 1/2 k signal low particle density - long spatial coherence >> l SAW!!! - short time coherence 35

36 Energy (ev) Polariton Exciton-polaritons condensate in in square a square lattices T=8 K 16 x l/4 layers l/2 (AlAs), 6x15nm GaAs QWs Laser k q real space [001] G X M k-space 20 x l/4 layers (Al,Ga)As Angle (k) resolved PL spectra High density Optical parametric oscillator Energy laser stimulated scattering k signal pump idler E. Cerda et al., Phys. Rev. Lett.105, (10) low density SAWs on 1 st MBZ k (mm -1 ) DE g ~P rf 1/2 Energy ev high density SAWs on Full confinement k SAW 0 k SAW k k(k x SAW ) Polariton condensation - long temporal coherence (100 s ps) - tunable spatial coherence E k 36

37 Imaging dot condensates Square lattice: 8 mm Time-resolved PL SAW 1 v dots homogeneity gaussian laser profile no transport of coherence! condensate coherence time (~150 ps) << SAW period (3 ns) SAW 2 37

38 interferometry v SAW Tunable spatial coherence o + o v SAW o = o no SAW image reversed Increasing P RF contrast y x 10 mm 10 mm 10 mm 10 mm extended coupled wires isolated wires Acoustic tunability: controlled interaction between neighboring sites! 38

39 Coherence control y x 10 mm Coherence length (mm) Ly Lx Contrast mm P RF (mw) P RF (mw) E. Cerda et al., NJP (12) 39

40 Summary and outlook RF Laser Acoustic manipulation of excitonic structures storage and long-range transport of excitons as well-defined packets optical control of microcavity polaritons tunable photonic/polaritonic crystal control coherence length z x V BIAS l SAW / 2 Future perspectives single IX transport polariton condensates explore analogy with atomic optical lattices Josephson oscillations, polariton blockade IX-polariton interconversion position atomic lattice Treutlein et al., Fortschr. der Physik 54, 701 (06) 40

41 electric field SAW-modulated excitons BM BM Polaritons strong coupling to photons controllable coherence in acoustic lattices Indirect excitons long lifetimes long-range transport by SAWs Shahnazaryan, PRB91, (15) Szymanska, Science 336, 679 (12) Interconversion: polariton IX 41