Relation between photoluminescence and photoluminescence-excitation spectra in the linear response regime measured on two- dimensional electron gas T. Ihara, Akiyama group, ISSP ’ 07 7/23 memo Outline - Target of this work - Optical setup and sample structure - Power/Energy dependence of PL and PLE spectra at 30K - Ratio of PL and PLE at Pex = 1.7  W (T = 30K) - PL/PLE at various temperatures (Pex = 16  W ) - PL with resonant/non-resonant excitation at 5K (Pex = 2  W) - Summary

Target of this work D. A. Sawicki and R. S. Knox, Phys. Rev. A 54, 4837 (1996). ’96’96 Kubo-Martin-Schwinger relation Kennerd-Stepanov relation Required condition : Linear Response, quasi- equilibrium PLE (photoluminescence-excitation) spectra : measurement of photoemission as a function of excitation photon energy -> lineshape of absorption spectra Using micro-PL technique, we can compare the lineshape of photo- absorption (PLE) with photoemission (PL) at the same microscopic region of 1  m order. Any general relation between PL and PLE spectra ? PL : emission PLE : absorption Weak excitation power !? S. Chatterjee, C. Ell, S. Mosor, G. Khitrova, and H. M. Gibbs, W. Hoyer, M. Kira, S. W. Koch, J. P. Prineas, and H. Stolz, Phys. Rev. Lett. 92, (2004). ’04’04

Optical setup and sample structure PL and PLE measurement in a backscattering geometry. Detect PL polarized with perpendicular to the polarization of excitation laser 2DEG density ( VDP measurement) : 6×10 10 cm -2

Power/Energy dependence of PL and PLE spectra at 30K Lineshape of PL are independent with excitation photon energy at P ex = 1.7  W. Lineshape of PL and PLE are independent with excitation power at P ex < 80  W. Our measurements at P ex < 80  W are in the Linear Response regime.

Ratio of PL and PLE at P ex = 1.7  W (T = 30K) Exponential decay against hv in the whole energy region. Estimated temperature (T * = 30±2 K) agrees with the thermometer (30.8±1K) -> Photo-excited quasi-equilibrium 2DEG at environmental temperature.

PL/PLE at various temperatures (P ex = 16  W ) T * agree with the thermometer at various temperature. -> verification of general relation between PL and PLE in the linear response regime for quasi-equilibrium system :

PL with resonant/non-resonant excitation at 5K (P ex = 2  W) In the case of resonant excitation, T * (= 6.2±0.3 K) agrees with the thermometer (5.6±1 K). In the case of non-resonant excitation (+ 6.3 meV), T * (= 7.2±0.5 K) is higher than the thermometer (5.6±1 K) and additional non-equilibrium component appears at higher energy side (ML fluctuation).

Summary Low-temperature photoluminescence and photoluminescence- excitation spectra of two-dimensional electron gas are measured at low-excitation power in the linear response regime. We found that the ratio between PL and PLE is proportional to exp(- hv/kT), where T agrees with environmental temperature. This should be the first verification of the general relation between photo-emission and absorption in the linear response regime, or Kubo- Martine-Schwinger relation, which is an exact solution under quasi- equilibrium condition.