We show that an asymmetric semiconductor quantum well that forms a three-level cascade configuration can be controlled by the relative phase of a laser field and its second harmonic. The electron population in the three subbands and the probe absorption/dispersion spectra are crucially phase dependent. As an example, electron inversion between the upper and lower subbands and change of the spectrum from absorption to gain is found by solely varying the relative phase of the two fields.In the past decade several quantum optical coherence and interference effects 1,2 have been studied theoretically and experimentally in intersubband transitions ͑ISBTs͒ in the conduction band of semiconductor quantum wells ͑QWs͒. Some of these phenomena are tunneling induced transparency, 3,4 electromagnetically induced transparency, 5-7 pulsed-induced quantum interference, 8 Autler-Townes splitting, 9 gain without inversion, 10-13 enhanced second harmonic generation, 14,15 enhanced index of refraction without absorption, 16 coherently induced one-dimensional photonic band gaps, 17 and coherent population trapping. 18 In addition, extremely useful devices such as ultrafast optical switches, 19-21 quantum switches, 22 and sensitive infrared detectors 23 are based on quantum optical coherence and interference effects in ISBTs in QWs.Furthermore, the relative phase of applied laser fields has been widely used for the coherent control of several important processes in atomic, molecular, and solid-state systems. 24 This method is usually termed as phase control. Phase control has already been applied for the coherent manipulation of coherent population trapping, 25 coherent population transfer, 26 and electromagnetically induced transparency 27,28 in a closed-loop four-level atomic system. Also, the simultaneous excitation of a two-level atom by a fundamental laser field and its third harmonic can also lead to the phase control of light propagation in this medium. 29 In the area of semiconductors intensive interest has been given to the control of photocurrent directionality by simultaneous excitation of the semiconductors by a fundamental laser field and its second harmonic. [30][31][32][33][34] In the present brief report, we study phase control of an asymmetric semiconductor quantum well by simultaneous application of a laser field and its second harmonic. We consider an asymmetric quantum well structure with three energy levels that forms the well-known "cascade" configuration, where all possible transitions are dipole allowed, see Fig. 1. The energy differences of the ͉1͘Ϫ͉2͘ and ͉2͘Ϫ͉3͘ transitions are taken to be equal. Such structures have been already studied for quantum interference and gain, 12 for controlled coherent population trapping, 18 and for efficient second harmonic generation. 35,36 Actually, this system can be realized experimentally with only one laser frequency such as that derived from a CO 2 laser. The fundamental CO 2 laser frequency drives both the ͉1͘Ϫ͉2͘ and ͉2͘Ϫ͉3͘ transitions simultaneously and the ͉1͘Ϫ͉3͘...