Modulation of intersubband infrared absorption under intense terahertz irradiation A. Hernández-Cabrera* and P. Aceituno Dpto. Física Básica, Universidad de La Laguna, La Laguna, 38206-Tenerife, Spain F. T. Vasko Institute of Semiconductor Physics, NAS Ukraine, Prospekt Nauki 41, Kiev, 03028, Ukraine Received 5 April 2005; published 6 July 2005 We analyze the modification of the intersubband absorption of electrons in quantum wells under intense THz irradiation. An expression for the induced current is obtained, based on the adiabatic approach and the resonant approximation. We predict the occurrence of a significant fine structure as well as the broadening and shift of the absorption under THz pump in a MW cm -2 intensity range. DOI: 10.1103/PhysRevB.72.045307 PACS numbers: 73.63.Hs, 78.45.h, 78.47.p I. INTRODUCTION Strong transverse fields have long been known for modi- fying confined states in quantum wells QWs. The examina- tion of the interband optical transitions under transverse fields, both static and high-frequency, is a convenient method to study these modifications see references in Refs. 1–3 and Refs. 4 and 5, respectively. The excitonic effect and the modifications of both electron and hole states under trans- verse fields have to be taken into account for a quantitative description of the interband linear response. It is also inter- esting to study the intersubband response under infrared IR excitation of electrons between the ground and the excited conduction band states which are placed in a transverse field. Whereas the electro-optic modulation of the intersubband transitions is well investigated, 6 the influence of an intense THz irradiation on such transitions is not investigated to the best of our knowledge. In this paper we treat theoretically the effect of the THz pump on the infrared IR intersubband absorption. The confined electron states in a QW, of width d, sub- jected to a transverse electric field E  cos t, are described within the adiabatic approach, if   21 , where  21 /  is the frequency of the intersubband transitions. Since the levels oscillate with a frequency , the n +1-order intersubband transitions, with n THz photons and a single IR photon, take place resulting in a fine structure of the absorption. At the same time, the shape of the absorption peaks is modified under the THz irradiation. In addition, one may consider the THz irradiation as a perturbation if eE  d /2  21 . Other- wise, a numerical description of the electron states has to be applied. The calculations below are based on the one-particle den- sity matrix equation linearized with respect to the IR field E  exp-it, while the THz irradiation is taken into ac- count in the framework of the adiabatic approach. The broad- ening is described by the phenomenological approach which takes into account the LO-phonon emission in the spectral region   LO , where  LO is the optical phonon frequency. We have considered two cases: a symmetric rectangular QW and a nonsymmetric one. The last case may be realized by adding a transversal dc electric field E o to the symmetric case, as can be seen in Fig. 1a and 1b, respectively. The paper is organized as follows. In Sec. II we derive the relative intersubband absorption under THz pump starting on the density matrix equation. The case of the perturbative ap- proach is considered in Sec. III, while the results for the numerical description are discussed in Sec. IV. Concluding remarks and a list of assumptions made are given in the last section. II. INTERSUBBAND RESPONSE In this section, we obtain the averaged over the THz pump period relative absorption of the IR probe. The high- frequency addendum to the density matrix  t z , zexp -it is governed by the linearized equation written in the coordinate-momentum representation:  pt z, z t + i  h ˆ zt - h ˆ z  t -  pt z, z + i  h ˆ z - h ˆ z   pt z, z =0 1 with the transverse coordinate z and 2D momentum p. Here FIG. 1. The band diagrams for symmetric a and nonsymmetric b QWs under transverse THz irradiation. Dashed lines schemati- cally show variation of levels and potentials under maximal THz field. PHYSICAL REVIEW B 72, 045307 2005 1098-0121/2005/724/0453075/$23.00 ©2005 The American Physical Society 045307-1