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Indirect excitons in coupled quantum wells Exciton pattern formation and exciton transport Exciton transport in potential landscapes Lattices Traps Circuit.

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Presentation on theme: "Indirect excitons in coupled quantum wells Exciton pattern formation and exciton transport Exciton transport in potential landscapes Lattices Traps Circuit."— Presentation transcript:

1 Indirect excitons in coupled quantum wells Exciton pattern formation and exciton transport Exciton transport in potential landscapes Lattices Traps Circuit devices Random potentials Spin transport of excitons Conveyers Vortices In collaboration with: Michael Fogler, Joe Graves, Martin Griswold, Aaron Hammack, Alex High, Jason Leonard, Andrew Meyertholen, Katya Novitskaya, Mikas Remeika, Averi Thomas, Alex Winbow, Sen Yang, Yuliya Kuznetsova (UCSD) Tomas Ostatnick´y, Alexey Kavokin (Southampton), Yura Rubo (Cuernavaca) Leonid Levitov (MIT), Ben Simons (Cambridge) Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff) Micah Hanson, Arthur Gossard (UCSB) Transport and spin transport of excitons Leonid V. Butov, UCSD

2 What temperature is “cold” for exciton gas? 3D:2D: m exciton ~ m atom Kelvin for excitons is like microKelvin for atoms transition from classical to quantum gas takes place when thermal de Broglie wavelength is comparable to interparticle separation 3D gas of Rb atoms: n = cm -3, m atom = 10 5 m e → T dB ~ 5×10 -6 K 2D gas of excitons in GaAs QW n = cm -2, m exciton = 0.2 m e → T dB ~ 3 K n < n Mott ~ 1/a B 2 ~ 2×10 11 cm -2

3 How to realize cold exciton gases ? T lattice << 1 K in He refrigerators finite lifetime of excitons could result to high exciton temperature: T exciton > T lattice find excitons with lifetime >> cooling time T exciton ~ T lattice Challenges for realization of exciton condensates To solve: Find or design semiconductor structures where short lifetimeexcitons have long lifetimes >> cooling times competing ground states, e.g. EHLexcitons form the lowest energy state exciton destruction, e.g. due to Mott transition excitons have large binding energy disorderdisorder is weak solving these challenges has led to studies of various experimental systems and various types of exciton condensate Indirect excitons in coupled quantum wells Electron-electron bilayers in magnetic fields at =1 Electron-hole bilayers with gate-induced carriers Electron-hole bilayers with photoexcited carriers ee

4 T X ~ 100 mK has been realized experimentally 30 times below T dB Why indirect excitons in CQW ? high quality CQW samples with small in-plane disorder are required to overcome exciton localization times longer exciton lifetime due to separation between electron and hole layers 10 3 times shorter exciton cooling time than that in bulk semiconductors TXTX Time (ns) A.L. Ivanov et al in PRL 86, 5608 (2001) ~ 10 ns to cool to 300 mK ~ 100 ns to cool to 100 mK realization of cold exciton gas in separated layers was proposed by Yu.E. Lozovik & V.I. Yudson (1975); S. I. Shevchenko (1976); T. Fukuzawa, S.S. Kano, T.K. Gustafson, T. Ogawa (1990)

5 Repulsive interaction between indirect excitons indirect excitons are oriented dipoles Repulsive dipole-dipole interaction ● stabilizes exciton state against formation of metallic EHL ● results in effective screening of in-plane disorder A.L. Ivanov, EPL 59, 586 (2002) R. Zimmermann D. Yoshioka, A.H. MacDonald, J. Phys. Soc. Jpn. 59, 4211 (1990) X. Zhu, P.B. Littlewood, M. Hybertsen, T. Rice, PRL 74, 1633 (1995) the ground state is excitonic energy shift:  E ~ n/C  estimate for exciton density approximation for short-range 1/r 3 interaction C =  /4  e 2 d Repulsive interaction in experiment exciton energy increases with density L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993) C. Schindler, R. Zimmermann, PRB 78, (2008)  C and n in experiments are higher also high quality CQW samples with small initial disorder are required to overcome exciton localization d

6 potential energy of indirect excitons can be controlled by voltage the ability to control electron fluxes by an applied gate voltage electronic circuit devicesmesoscopics the field which concerns electron transport in a potential landscapes in-plane potential landscapes can be created for excitons by voltage pattern e.g. traps, lattices, circuit devices the ability to control exciton fluxes by an applied gate voltage excitonic circuit devices mesoscopics of bosons in semiconductors e h

7 condensation pattern formation potential profiles can be created and in situ controlled indirect excitons energy can be controlled by gate voltage can cool down to 0.1 K well below T dB ~ 3K can travel over large distances have built-in dipole moment ed cold Bose gases in solid-state materialsexcitonic devices transport spin transport have long lifetimes optical methods → local probe of excitons d

8 Exciton pattern formation and exciton transport

9 external ring ring fragmentation localized bright spots 2D-fire Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State same spatial order on macroscopic lengths PL intensity position on the ring (  m) inner ring 410  m T=1.8 KT=4.7 K appears abruptly at low T L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)

10 DiscussionDiscussion flow of excitons out of excitation spot due to exciton drift, diffusion, phonon wind, etc. r (  m) Energy (eV) PL pattern spatial distribution of optically active low energy excitons excitons can travel in a dark state after having been excited until slowed down to a velocity below photon emission threshold, where they can decay radiatively PL Intensity repulsive interaction → drift excitation spot high T X exciton drift lower occupation of radiative zone inner ring lower T X excitons relax to radiative zone higher occupation of radiative zone exciton transport over tens of microns kk E E Inner ring L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002) A.L. Ivanov, L. Smallwood, A. Hammack, Sen Yang, L.V. Butov, A.C. Gossard, EPL 73, 920 (2006) inner ring forms due to exciton transport and cooling

11 Localization-delocalization transition for exciton transport in random potential exp. theory exp. theory low densities: emission profile follows excitation spot excitons are localized in random potential high densities: emission extends well beyond excitation spot excitons screen random potential, travel away from excitation spot and form inner ring

12 Kinetics of inner ring formation time of inner ring ~ 30 ns kinetics of inner ring estimate of exciton transport characteristics D X reaches ~ 20 cm 2 /s PL jump vs r → excitons outside laser spot including inner ring region are cooled to T lattice even during laser excitation exp. theory A.T. Hammack, L.V. Butov, J. Wilkes, L. Mouchliadis, E.A. Muljarov, A.L. Ivanov, A.C. Gossard, PRB 80, (2009)

13 external ring External ring above barrier laser excitation creates additional number of holes in CQW heavier holes have higher collection efficiency to CQW holes created at the excitation spot diffuse out this depletes electrons in the vicinity of the laser spot creating electron-free and hole rich region electrons excitons holes excess holes are photogenerated in the laser excitation spot electron source is spread out over the entire plane due to current through the CQW from n-doped GaAs layers same for e ↔ h x y z E L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, PRL 92, (2004) R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, PRL 92, (2004) external ring forms at interface between electron-rich and hole-rich regions

14 Radius (  m) c 40 cm 2 /s D h = 16 cm 2 /s 26 cm 2 /s 100  m  s  s  s 0.2  s 1.5  s 2.5  s 3  s 4  s -10  s 0 5s5s laser pulse e h external ring LBS ring h e expansion of external ring collapse of external ring abcdefgh i j cm 2 /s D e = 200 cm 2 /s 30 cm 2 /s 0 collapse of external ring expansion of LBS rings kinetics of external and LBS rings estimation of e and h transport characteristics D e ~ 80 cm 2 /s, D h ~ 20 cm 2 /s Kinetics of external ring and LBS rings time Sen Yang, L.V. Butov, L.S. Levitov, B.D. Simons, A.C. Gossard, PRB 81, (2010)

15 rings are far from hot spots due to long lifetimes of indirect excitons T X ≈ T lattice rings form is region where cold and dense exciton gas is created macroscopically ordered exciton state (MOES) localized bright spots have hot cores no hot spots in external ring and LBS rings indirect exciton PLdirect exciton PL – pattern of hot spots

16 Spontaneous coherence experimental method: Mach-Zehnder interferometry with spatial and spectral resolution probing coherence far from laser both in space and energy: coherence is spontaneous Coherence Length (  m) Temperature (K) PL Contrast along the Ring left arm right arm the increase of the coherence length  is correlated with the macroscopic spatial ordering of excitons  ~ 2  m >> the classical value ~ dB ~ 0.1  m spontaneous coherence = = condensation in k-space Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, PRL 97, (2006) MOES is a state with: ● macroscopic spatial ordering and ● large coherence length → a condensate in k-space model: L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, (2005)

17 Exciton transport in potential landscapes Lattices Traps Circuit devices Random potentials

18 potential energy of indirect excitons can be controlled by voltage in-plane potential landscapes for excitons can be created by voltage pattern e h A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, JAP 99, (2006) obstacle: in-plane electric field can lead to exciton dissociation proposed design in which in-plane electric field is suppressed allows creating virtually arbitrary in-plane potential landscape for excitons by voltage pattern can be controlled in-situ by voltages on timescale much shorter than exciton lifetime

19 source drain gate ONOFF 5  m Exciton Optoelectronic Transistor (EXOT) photon input photon output electronic control prototype EXOT performs switching at speeds > 1 GHz prototype excitonic IC performs directional switching and merging Time (ns) x exciton flow is on exciton flow is off Gate QWs n i photonic source photonic drain optical input gate optical output gate Exciton energy energy bump controlled by the Gate similar in geometry and operation to electronic FET 0 1 Distance (  m) Intensity ON OFF A.A. High, A.T. Hammack, L.V. Butov, M. Hanson, A.C. Gossard, Opt. Lett. 32, 2466 (2007) A.A. High, E.E. Novitskaya, L.V. Butov, M. Hanson, A.C. Gossard, Science 321, 229 (2008) demonstrated operation up to ~ 100 K G. Grosso, J. Graves, A.T. Hammack, A.A. High, L.V. Butov, M. Hanson, A.C. Gossard, Nat. Photonics 3, 577 (2009) delay between signal processing and optical communication is effectively eliminated in excitonic devices → advantage in applications where interconnection speed is important

20 A.A. High, A.K. Thomas, G. Grosso, M. Remeika, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 103, (2009)

21 5 meV 5  m Width Collection of exciton cloud to trap center with increasing density density → ▲ exp ▬ theory excitation power (  W) repulsive interaction screening of disorder collection to trap bottom cold exciton gas in trap can be controlled in situ like traps for cold atoms width of exciton cloud in trap

22 E lattice = 0 E lattice = 3.7 meV M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, I. Bloch, Nature 415, 39, (2002) J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, W. Ketterle, Nature 443, 961 (2006) Excitons in lattices Atoms in lattices atoms in lattices – system with controllable parameters use atoms in lattices to emulate solid state materials controllable: exciton density, interaction, mass lattice amplitude, structure, constant a tool with a number of control knobs for studying the physics of excitons M. Remeika, J. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 102, (2009)

23 Localization - delocalization transition (LDT) estimate for the strength of disorder: E rand ~ 0.8 meV E lattice >> E rand interaction energy at LDT ≈ amplitude of unscreened lattice model attributes LDT to interaction-induced percolation of exciton gas through external potential E total = E lattice + E rand E lattice << E rand interaction energy at LDT ≈ amplitude of unscreened random potential loc: emission profile follows excitation spot deloc: emission extends well beyond excitation spot

24 Conveyers

25 A.G. Winbow, J.R. Leonard, M. Remeika, A.A. High, E. Green, A.T. Hammack L.V. Butov, M. Hanson, A.C. Gossard, unpublished conveyer off conveyer on Electrostatic conveyers for excitons study dynamic LDT with varying conveyer amplitude conveyer speed exciton density conveyers are created by applying AC voltages to lattice electrodes → traveling lattice wavelength  electrodes amplitude  voltage speed  frequency Transport of electrons, holes, excitons, and polaritons via SAW C. Rocke, S. Zimmermann, A. Wixforth, J.P. Kotthaus, G. Böhm, G. Weimann, PRL 78, 4099 (1997) P.V. Santos, M. Ramsteiner, R. Hey, PSS B 215, 253 (1999) J. Rudolph, R. Hey, P.V. Santos, PRL 99, (2007) this conference phonon wind in the conveyer frame crossing phonon velocity

26 Spin transport of excitons

27 exciton spin transport over substantial distances requires exciton transport over substantial distances long spin relaxation time long  r high D

28 Spin-Flip Pathways  ex hh ee ee rr rr optically active states dark states polarization relaxation time GaAs SQW direct exciton GaAs CQW indirect exciton with small e-h overlap fast depolarization within tens of ps makes possible exciton spin transport over substantial distances  ex is determined by exchange interaction between e and h control  p by changing e-h overlap J.R. Leonard, Y.Y. Kuznetsova, Sen Yang, L.V. Butov, T. Ostatnick´y, A. Kavokin, A.C. Gossard, Nano Lett. 9, 4204 (2009) M.Z. Maialle, E.A. de Andrada e Silva, L.J. Sham, PRB 47, (1993). orders of magnitude enhancement of exciton spin relaxation time Polarization of emission decays when both e and h flip their spins. This can occur in two-step process due to separate e and h spin flips and single step process due to exciton spin flip. exciton spin transport over substantial distances is problematic

29 mo Density dependence  P of indirect excitons reaches several ns >>  P of direct excitons P and  P drop with increasing density decrease of  P is correlated with the increase D →  P drops when excitons become delocalized loc deloc complies with DP spin relaxation mechanism

30 experiment theory experiment and theory Spin transport of excitons extension of polarization profiles beyond excitation spot shows exciton spin transport spin transport of indirect excitons originates from long spin relaxation time and long lifetime

31 Decrease of P and  P with increasing density complies with D’yakonov-Perel’ spin relaxation mechanism experiment: theoretical estimate: spin splitting constant

32 Vortices

33 quantized atom vortices S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, PRL 87, (2001) F. Chevy, K.W. Madison, V. Bretin, J. Dalibard, PRA 64, (R) (2001) Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006) quantized optical vortices J. Scheuer, M. Orenstein, Science 285, 230 (1999) and references therein quantized polariton vortices K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, Le Si Dang, B. Deveaud-Plédran, Nature Physics 4, 706 (2008) K.G. Lagoudakis, T. Ostatnický, A.V. Kavokin, Y.G. Rubo, R. André, B. Deveaud-Plédran, Science 326, 974 (2009) quantized vortex is characterized by point (or line) around which phase of wave function varies by 2  n fork-like dislocation in phase pattern is signature of quantized vortex Vortices polariton half-vortices

34 P ex Fork-like topological defects in interference pattern of indirect excitons indicating the presence of quantized vortices hor vert 11 22 topological defects in multicomponent spin systems Y.G. Rubo, PRL 99, (2007) for different polarizations A.A. High, A.T. Hammack, J.R. Leonard, L.V. Butov, T. Ostatnicky´, A. Kavokin, Y.G. Rubo, A.C. Gossard, unpublished

35 LBS ring region external ring region excitation and inner ring region number of forks in LBS ring region number of forks in external ring region no forks in excitation and inner ring region Number of forks in various regions of exciton pattern formation

36 Acknowledgements supported by ARO, NSF, DOE UCSD: Aaron Hammack Alex High Alex Winbow Anton Mintsev Averi Thomas James Lohner Jason Leonard Joe Graves Gabriele Grosso Katya Novitskaya Martin Griswold Mikas Remeika Sen Yang Yuliya Kuznetsova Collaborators in studies of indirect excitons: Gerhard Abstreiter, WSI Daniel Chemla, UCB&LBNL Valerii Dolgopolov, ISSP RAS Alexander Dzyubenko, CSB Michael Fogler, UCSD Nikolai Gippius, Blaise Pascal Arthur Gossard, UCSB Atac Imamoglu, UCSB Alexei Ivanov, Cardiff Alexey Kavokin, Southampton Leonid Levitov, MIT Peter Littlewood, Cambridge Yuri Lozovik, IS RAS Yuri Rubo, Cuernavaca Ben Simons, Cambridge Arthur Zrenner, WSI In collaboration with: Tomas Ostatnick´y, Alexey Kavokin (Southampton) Yuri Rubo (Cuernavaca) Andrew Meyertholen, Michael Fogler (UCSD) Leonid Levitov (MIT) Ben Simons (Cambridge) Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff) Micah Hanson, Arthur Gossard (UCSB)


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