Coherent inter-polariton scattering on moving gratings in microcavity with 25 nm GaAs/AlGaAs single quantum well

D. Birkedal†, V. G. Lyssenko‡ and J. M. Hvam†

Research Center COM, Technical University of Denmark,
DK-2800 Lyngby, Denmark
‡ Institute of Microelectronics Technology, RAS,
142432 Chernogolovka, Moscow District, Russia

Abstract. We report on a new coherent phenomenon in semiconductor microcavities at polariton selective resonance excitation by two femtosecond pulses, propagating along k₂ and k₁, associated with exciton gratings, travelling in lateral direction $\pm \left( k_{2}-k_{1}\right)$ . Diffracted polaritons experience a frequency shift as observed in nondegenerate spectrally resolved transient four-wave mixing experiments.

Introduction

Semiconductor microcavities offers opportunities to reach physical conditions not easily attained otherwise. This has led to a range of interesting effects, where in particular coherent scattering of polaritons have attracted considerably interest [1]. Coherent phenomena in semiconductor have most significantly been studied using transient four-wave mixing, where in the case of e.g. quantum wells a detailed understanding of the involved physics have resulted [2]. In contrast, relatively few reports have been published on transient four-wave mixing studies of semiconductor microcavities [3–6]. These studies have shown that the coherent nonlinear dynamics of semiconductor microcavities polaritons is modified from that of e.g. heavy-hole–light-hole excitons quantum beats in semiconductor quantum wells.

Travelling gratings

Here we report on a coherent nonlinear phenomenon in a semiconductor microcavities, which has no parallel for quantum well excitons. When two different polariton modes of the semiconductor microcavities are impulsively excited they will undergo normal mode oscillations with coherent energy exchange between the exciton and the cavity mode. In our experiment the two polaritons are excited with slightly different angles resulting in a travelling wave exciton grating. When a test polariton mode is excited it will scatter in the travelling grating producing amplitude modulation sidebands. This phenomenon produces a transient four-wave mixing signal, which is shifted in frequency from that of the test beam by the normal mode oscillation frequency. In our case, in the THz range corresponding to a grating velocity of $\approx 1\times 10^{7} \rm {m}/{s}$ , which is four order of magnitude larger than the sound velocity. The presence of such travelling exciton grating have been predicted [5] but so far not observed directly experimentally.

Results and discussion

The sample under investigation is a GaAs/AlGaAs $\lambda$ cavity with a single 25 nm GaAs quantum well at the center [7]. The sample is held at 5 K in He cryostat and is excited by two pulses from a self-modelocked Ti:Sapphire laser, propagating in the directions k₁ and k₂. The pulses are spectrally shaped to allow selective excitation of either of the polariton modes. The transient four-wave mixing signal is detected in the $2k_{2}^{\prime }-k_{1}^{\prime}$ reflection geometry spectrally resolved and recorded as a function of the time delay between the two pulses. The present experiments are performed for near resonant conditions.

First we excite and probe both polaritons with spectrally broad pulses k₁ and k₂. This results in transient four-wave mixing signal on the upper and lower polariton as shown in the spectrum in Fig. 1(a). In addition,

Fig 1. (a) Spectrally resolved transient four-wave mixing at zero delay. Solid line for probing only the upper polariton (UP) and dashed line for probing simultaneously the upper and lower polariton (LP). (b) Transient four-wave mixing as a function of delay. Upper figure shows the signals at the upper and lower polaritons when both polaritons are probed simultaneously. Lower figure for probing selectively the upper polariton.

strong beats in the transient four-wave mixing intensity is seen as a function of delay between the two pulses as shown in Fig. 1(b). This corresponds to our expectation from quantum well excitons and is in agreement with previous reports. In contrast, if we now probe selectively only one polariton, we observe a transient four-wave mixing signal resonant with the other polariton. This is shown here for selective probing of the upper polariton (Fig. 1(a): transient four-wave mixing spectrum; Fig. 1(b): delay dependence), where a strong signal resonant with the lower polariton is observed (Fig. 1(b)). We will demonstrate that these observations are in agreement with a theory based on the combined Maxwell and optical Bloch equations [5, 6, 8].

Thus, we discovered four-wave mixing signal at shifted frequency due to scattering on the polariton moving grating and developed theory, describing observed phenomena.

Acknowledgements

This work was financially supported by the Danish Ministry of Science and Technology, Russian Foundation for Basic Research and Program ''Physics and Technology of the Nanostructures''.

References

P. G. Savvidas et al, Phys. Rev. Lett. 84, 1547 (2000).
See e. g. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, (Springer, Berlin, 1997).
H. Wang et al, Phys. Rev. B 51, 14713 (1995).
M. Kuwata-Gonokami et al, Phys. Rev. Lett. 79, 1341 (1997).
H. Wang et al, Phys. Rev. Lett. 81, 3255 (1998).
M. Koch, J. Shah and T. Meier, Phys. Rev. B 57, 2049 (1998).
For details on the sample see e. g. J. R. Jensen, P. Borri, W. Langbein and J. M. Hvam, Appl. Phys. Lett. 76, 3262 (2000).
H. J. Kimble, H. J. Carmichael et al, in Cavity Quantum Electridinamics, 51, ed. by P. R. Berman (Academic, Boston, 1994).

URL: http://link.edu.ioffe.ru/nano2002/birkedal
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