VOLUME 76, NUMBER 13 PHYSICAL REVIEW LETTERS 25 MARCH 1996 Undressing a Collective Intersubband Excitation in a Quantum Well K. Craig, 1 B. Galdrikian, 1 J. N. Heyman, 2 A. G. Markelz, 1 J. B. Williams, 1 M. S. Sherwin, 1 K. Campman, 3 P. F. Hopkins, 3 and A. C. Gossard 3 1 Department of Physics and Quantum Institute, University of California at Santa Barbara, Santa Barbara, California 93106 2 Department of Physics and Astronomy, Macalester College, St. Paul, Minnesota 55105 3 Materials Department, University of California at Santa Barbara, Santa Barbara, California 93106 (Received 7 September 1995) We have experimentally measured the 1– 2 intersubband absorption in a single 40 nm wide modulation-doped Al 0.3 Ga 0.7 AsGaAs square quantum well as a function of frequency, intensity, and charge density. The low-intensity depolarization-shifted absorption occurs near 80 cm 21 (10 meV or 2.4 THz), nearly 30% higher than the intersubband spacing. At higher intensities, the absorption peak shifts to lower frequencies. Our data are in good agreement with a theory proposed by Zalu˙ zny, which attributes the redshift to a reduction in the depolarization shift as the excited subband becomes populated. PACS numbers: 73.20.Mf, 42.65.Vh, 73.20.Dx, 73.50.Fq The properties of elementary excitations in solids are renormalized (“dressed”) by interactions with electrons, phonons, or other particles. An example is the absorption of light by a metal; electrons in a metal are nearly free, and the lowest excited state has an energy only infinitesimally greater than the ground state. However, interactions with other electrons dress the frequency at which light is absorbed, shifting it from zero frequency (dc) to the plasma frequency. A single electron in a semiconductor quantum well would have no electron-electron interactions. It would obey the single-particle, linear Schrödinger equation, and resonantly absorb light at a frequency equal to the difference between quantized subband energies. Many electrons are present in real quantum wells. Electron- electron interactions cause a static modification to the shape of the quantum well potential, but also allow electrons to dynamically screen oscillating fields inside the well. This screening blueshifts the frequency at which radiation is absorbed from the intersubband spacing to the dressed frequency at which collective oscillations of the entire electron gas occur [1]. This dressing of the intersubband absorption frequency by electron-electron interactions is called the depolarization shift. Intersubband dynamics have been well understood in narrow quantum wells which have intersubband transi- tions greater than the LO phonon energy of 36 meV [2– 4]. In such wells, the depolarization shift is insignificant at ordinary charge densities. In wider quantum wells, the intersubband separation is smaller, and the depolar- ization shift becomes a larger fraction of the absorption frequency. In this Letter, we report the first steady-state measurements of the intensity-dependent absorption line shape in a wide quantum well [5]. We find that the in- tersubband absorption is “undressed” by intense resonant excitation, as first predicted by Zalu˙ zny: As intensity is increased, the resonant frequency moves to the red from its depolarization-shifted value toward the intersubband spacing [6]. The 40.0 nm wide GaAs square well used in our measurements was grown by molecular beam epitaxy. The potential barriers on each side of the well are 675 nm of Al 0.3 Ga 0.7 As. The well is symmetrically modulation- doped by silicon layers of sheet density 1.3 3 10 12 cm 22 which are placed 125 nm from each side of the well. The relatively large distance between the donors and the well ensured that the charge transferred into the well was insufficient to begin occupying the second subband at low temperatures. The mobility at 4.2 K was 360 000 cm 2 V s, as measured by magnetotransport. All experiments reported here were performed on a sample 1.01 cm long, 0.7 cm wide, and 445 mm thick. An 80 nm thick aluminum gate was evaporated onto the front of the sample, with a similar layer evaporated on the back of the substrate. Ohmic contacts on the sample corners provide electrical connection to the electrons in the well. The charge density in the well was measured in situ by capacitance-voltage profiling. Far-infrared radiation (FIR) from the UCSB free- electron laser was used to excite the sample. The pulses were 2.5 ms long, with peak powers of 1 kW. The sample was mounted in a vacuum on the cold finger of a continuous-flow cryostat. All measurements were performed with the sample near 10 K. FIR was focused onto the edge of the sample, with the electric field parallel to the growth direction of the sample. A 3 mm thick plexiglass beam block prevented most of the FIR from leaking around the sample. The thick aluminum layers on the front and back serve to confine the FIR field within the sample. The transmitted FIR was measured using a 4.2 K bolometer. The entire experiment was performed in a dry nitrogen atmosphere to eliminate absorption of the FIR by water vapor. To avoid oscillations in transmittance due to standing waves within the sample, a broad-band 2382 0031-9007 96 76(13) 2382(4)$10.00 © 1996 The American Physical Society