Non-local exciton-polariton spin switches

PLMCN 10, Cuernavaca, Mexique, avril 2010 Non-local exciton-polariton spin switches Laboratoire Kastler Brossel, Paris (experimental part) : C. Adrados R. Hivet J. Lefrère • Amo E. Giacobino and A. Bramati University of Southampton : A.V. Kavokin (theoretical part) EPFL, Lausanne : T.C.H. Liew (theoretical part) R. Houdré (fabrication of the sample)

Why the use of SC microcavities for all-optical spin switches ? Semiconductor Microcavities in strong coupling regime : POLARITONS, mixture of excitons and photons. Excitons : High non-linearities at low thresholds due to the Coulomb interaction Photons : Propagate fast (~ 1% speed of light) Short lifetime (a few ps) High repetition rate Exciton switch with electrical control : G. Grosso et al. Nature Photonics 3, 577–580 (2009) All optical control : … power of the incident beam : density of polaritons … transverse direction of the incident beam : polaritons velocity … polarization of the incident beam : polaritons spin state + reduced size of the system : integrability

All-optical switch A off A kp (μm-1) Non linear transmission (theory) : Power dependence of the pump Excitation power P1< Pthreshold Pthreshold

All-optical switch on B B kp (μm-1) Non linear transmission (theory) : Power dependence of the pump Excitation power P2> Pthreshold Pthreshold Renormalization of the dispersion curve Polariton switch configuration : the amount of power P2-P1 necessary to switch is added thanks to a small probe.

Experimental set up Cw pump (red) : big spot 60 μm (diameter) Cw probe (blue) : small spot 6 μm (diameter) with incident in plane angle = 3.8° Near field CCD (d) kz k Y  k║ X Pump + probe superposed, with same k Microcavity sample Laser wavelength = 836.95 nm, blue detuned by 0.16 meV from the LPB

Non local switch B Polariton density of the σ+pump vs excitation power on A off Very localized cw probe laser Sub threshold cw pump laser, large Pump (σ+) Probe (σ+) Pump+Probe B on A off Detection σ+ Polariton flow Polariton flow 20 µm Transmitted power : 3 mW Transmitted power : 54 mW Transmitted power : 9 mW Pump + probe : switch (renormalization) of the whole pump spot, induced by the probe.

Non local switch Model : Blueshift propagation t=0 t=60 ps PROBE ELaser B Energy x A ELPB Polaritons Energy PUMP x Non-local action : The small probe switches on the pump polaritons of the arrival probe area. vpolariton = hk///mpolariton= 0.94 μm/ps : propagation all over the pump beam.

Non local switch Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right. Polariton flow (pump and probe)

Exciton-Polariton Spin Strong EXCHANGE INTERACTION (exchange of holes and electrons) between 2 excitons (Sz=±1)dressed with light |g↑↑|>> |g↑↓| With Interaction constant between polaritons with parallel spins g↑↑ Interaction constant between polaritons with antiparallel spins g↑↓ Ref : P.Renucci et al, PRB 72, 075317 (2005); C.Ciuti et al, PRB 58 p7926-7933 (1998); M.Wouters, PRB 76, 045319 (2007); M.Vladimirova et al, PRB 79, 115325 (2009); M.Combescot, PRB 74, 125316 (2006).

pump σ ++ probeσ + pump σ ++probeσ - 1 THEORY 0 Spin selectivity on Pump σ+ B Polariton density of the σ+pump vs excitation power >> A off pump σ +(no probe) probe σ +(no pump) FLOW 25 μm Solution of the Gross-Pitaevskii equation EXPERIMENT pump σ ++ probeσ + pump σ ++probeσ - 1 0

pump σ ++ probeσ + pump σ ++probeσ - 1 0 Spin selectivity Pump σ+ Ellipticity of the probe Threshold in the ellipticity of the probe : minimum amount of σ+ required to switch on the σ+pump. Only on the pump (zone without probe) σ+ σ- Pump σ+ and probe σ+ * Gain x6 * Propagation and spin dependence σ+

Polarization control on Spin dependent interaction B Linearly polarized pump σ+ >> A Final polarization:that of the probe off σ++σ- pump TE+ probeσ+ pump TE+ probeσ+ 1 det det det det FLOW 25 μm 0 THEORY EXPERIMENT

Polarization control on Spin dependent interaction B Linearly polarized pump σ- >> A Final polarization:that of the probe off σ++σ- pump TE+probeσ - pump TE+probeσ - 1 det det det det FLOW 25 μm 0 THEORY EXPERIMENT

Polarization control Pump TE (linear) Detected Ellipticity

CONCLUSION spin switch at k≠0 ● Interaction between parallel spins >> interaction between opposed spins Pump purely circular + probe : EXCLUSIVE SWITCH Pump linearly polarized + probe : polarization CONTROL ● Non local action ● Low threshold : strong non-linearities and 5 ps polariton lifetime we need low energy densities to induce the switch : 1-2 fJ/μm2 , 2 orders of magnitude less than the state-of-the-art all optical spin switch. ● High potential repetition rate (for a 60 μm spot and a 3.8° incident angle) : about 10 GHz Amo et al., Nature Photonics (DOI : 10.1038/NPHOTON.2010.79 )

Bistability at k// = 0 At normal incidence, we can observe a hysteresis cycle (ref : A.Baas, PRB 70, 161307(R), 2004)

Spin switch at k// = 0 with bistability Switch off the probe pump + probe : ON Pump only : ON + COPOLARIZED probe pump 10800 736

Spin switch at k// = 0 with bistability ● Exclusive switch : when the pump and the probe are crosspolarized, no switch. ● Propagation mecanism : diffusion of the polaritons (probe and pump) thanks to theirΔk (around k=0). To check in real time.

Spin switch at k// = 0 with bistability ● How to switch off the pump thanks to the probe only ? By dephasing the probe with respect to the pump. Probe and Pump must have the SAME SIZE. Switch off the probe Pump only : ON state Pump + probe : ON Constructive interferences Destructive interferences Add a probe (same size as pump) in phase with pump Excitation power Pump + probe out of phase Pump OFF state Ref : I.A.Shelykh et al, PRL 100, 116401 (2008)

CONCLUSION spin switch at k=0 ● We have one bit : we can go from 1 state to the other by tuning an external probe (perturbation), and the bit keeps the memory of the perturbation. ● Also here, we have a high speed of switch : when pump and probe with the same size, it is given by the polariton lifetime (ps range), repetition rate of about 1 THz. ● Very low thresholds (strong non-linearities thanks to the excitonic part of the polaritons)

Non-local exciton-polariton spin switches