QM1D.1.pdf
CLEO:2013 Technical Digest © OSA 2013
Time-resolved Terahertz Mapping of a Cold Exciton-Polariton Gas J.-M. Ménard1, C. Poellmann1, M. Porer1, E. Galopin², A. Lemaître², A. Amo², J. Bloch², R. Huber1 1. Department of Physics, University of Regensburg, 93040 Regensburg, Germany 2. CNRS-Laboratoire de Photonique et Nanostructures, Route de Nozay, 91460 Marcoussis, France
[email protected]
Abstract: Time-resolved terahertz absorption by intra-excitonic 1s-2p transitions traces the matter part of cavity polaritons while they cool into a condensed phase. The population dynamics close to the zero-momentum state is correlated with simultaneous angle-resolved photoluminescence. OCIS codes: (240.5420) Polaritons; (320.7130) Ultrafast processes in condensed matter, including semiconductors
Semiconductor microcavities constitute an ideal playground to tackle one of the most interesting, yet evasive macroscopic states in physics: Bose-Einstein condensation. Strong coupling between excitons and a cavity photon field leads to the formation of so-called cavity polaritons. The dual light-matter nature confers unique properties to these custom-designed quasiparticles, such as a small effective mass, that allow them to condense into a macroscopic quantum state at standard cryogenic temperatures [1-3]. This phenomenon has been extensively studied via photoluminescence (PL) measurements, monitoring the collapse of polaritons into their photonic part [1-4]. On the other hand, there remains no direct experimental probe of the material part of the polariton, the excitonic component that ensures thermalization within the bosonic distribution and establishes coherence leading to a condensate. Here we employ few-cycle terahertz (THz) pulses to project out the matter part of cold polariton gases and correlate this information with simultaneously recorded angle-resolved PL data. A Ti-Sapphire amplifier (repetition rate of 400 kHz) focused within a (110)-oriented ZnTe crystal generates THz radiation between 6 and 15 meV. This energy range constitutes an ideal probe to investigate the transition between the 1s and the 2p states of excitons in GaAs quantum wells [5,6]. When embedded into a high-quality semiconductor microcavity, strong light-matter coupling modifies the band structure of the 1s state, especially at small in-plane momenta k||. In contrast, the dispersion of the optically dark 2p excitons remains set by the center-of-mass motion of the bare exciton (Fig. 1a). Therefore, the energy difference between the 1s and 2p states depends on k|| and THz spectroscopy may be used to map out the polariton distribution in momentum space. This idea allows us to investigate the time dynamics of the LP population as it relaxes towards a condensed state. Our GaAs/AlGaAs microcavity contains 12 quantum wells located at the anti-nodes of the optical mode [1]. Polaritons are injected by 100-fs non-resonant optical pulses (photon energy: 1.65 eV). PL measurements taken at low pump fluence show the LP dispersion around k|| = 0 (Fig. 1b). However, when exceeds a threshold th, the angular distribution of the PL undergoes a dramatic narrowing indicative of Bose quasi-condensation [1-3]. (a)
(b)
= 0.5 th
= 1.3 th
Fig. 1 (a) Schematic idea of our novel experiment indicating the dispersion of the lower-polariton (LP) branch in a planar GaAs/AlGaAs microcavity together with THz transitions from 1s to 2p states. The non-parabolic LP dispersion induced by strong light-matter coupling allows us to map out the polariton population over the complete k||-space via the momentum dependent 1s-2p resonance. While this transition is mediated by the excitonic part of the polariton, the recorded photoluminescence (PL) occurring at low k|| allows us to gain insight on the photonic component. (b) Angle-resolved PL of a GaAs/AlGaAs microcavity, recorded for different fluences of the femtosecond optical pump (photon energy ћ = 1.65 eV) below (upper panel) and above (lower panel) the threshold th = 0.04 mJ/cm2 for condensation.
QM1D.1.pdf
CLEO:2013 Technical Digest © OSA 2013
We extract the optically induced THz conductivity 1 from the transmitted THz wave forms. Excitonic transitions are displayed by a sharp maximum in 1 [5,7]. At early delay times tD < 40 ps after carrier injection, 1 is dominated by two main features: a free-carrier Drude response and a dominant maximum at ћ = 9 meV that originates from the transition between the initially warm LP reservoir and the 2p exciton (Fig. 2a). At tD = 200 ps, the peak associated to the reservoir reaches its maximum amplitude while the free-carrier contribution becomes negligible. Interestingly, a 2 meV blueshift of the peak is observed during the first 1000 ps. This dynamics quantitatively maps out the cool-down of the polariton distribution in the non-parabolic dispersion curve which can be associated to a thermalization of the Bose-Einstein distribution. For = 1.3 th (Fig. 2b), the intra-excitonic resonance at ћ = 10.5 meV remains the dominant feature in 1. For tD < 100 ps an additional peak of weaker amplitude occurs at ћ = 13.4 meV. This value coincides with the expected THz absorption of polaritons at k|| = 0, suggesting a first direct experimental evidence of the excitonic wavefunction involved in the polariton condensate. An ongoing quantitative analysis of the THz response is expected to yield a precise momentum-dependent distribution function of the polariton population in the vicinity of the degenerate ground state. (a)
(b)
tD = 15 ps
?
Fig. 2 (a) Induced THz conductivity 1 after non-resonant free-carrier injection at = 0.5 th. The dashed line is a theoretical fit of the data at a delay time of tD = 1 ps based on a Drude model . The peak at ћ ≈ 10 meV is associated to the exciton reservoir at large k||. This peak shifts by 2 meV over a time window of 1000 ps, due to the cooling of polaritons. (b) Same as (a), but = 1.3 th, tD = 15 ps. The maximum at ћ = 13.4 meV suggests a transition within the polariton gas at k|| = 0.
Our novel approach may become instrumental in deciphering the role of excitons, photons and free carriers in the regime of Bose-Einstein condensation in solid state systems. Important new insight into the nature of the microscopic interaction establishing a macroscopic quantum phase and the origin of multiple thresholds leading to polaritonic and photon lasing is anticipated [1,3]. References [1] H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto. "Condensation of semiconductor microcavity exciton polaritons," Science 298, 199 (2002). [2] J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, "Bose-Einstein condensation of exciton polaritons ," Nature (London) 443, 409 (2006). [3] E. Kammann, H. Ohadi, M. Maragkou, A.V. Kavokin, and P. G. Lagoudakis "Crossover from photon to exciton-polariton lasing," New Journal of Physics 14, 105003 (2012) [4] E. Wertz, A. Amo, D. Solnyshkov, L. Ferrier, T.C.H. Liew, D. Sanvitto, P. Senellart, I. Sagnes, A. Lemaitre, A. V. Kavokin, G. Malpuech, and J. Bloch, "Propagation and amplification dynamics of 1D polariton condensates," Phys. Rev. Lett. 109, 216404 (2012) [5] R. A. Kaindl, M. A. Carnahan, D. Hägele, R. Lövenich, and D. S. Chemla. "Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas," Nature 423, 734 (2003) [6] S. Chatterjee, C. Ell, S. Mosor, G. Khitrova, H. M. Gibbs, W. Hoyer, M. Kira, S. W. Koch, J. P. Prineas, and H. Stolz, "Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons," Phys. Rev. Lett. 92, 067402 (2004) [7] S. Leinß, T. Kampfrath, K. v.Volkmann, M. Wolf, J. T. Steiner, M. Kira, S. W. Koch, A. Leitenstorfer, and R. Huber, "Terahertz coherent control of optically dark paraexcitons in Cu2O, " Phys. Rev. Lett. 101, 246401 (2008)
