We study the optical amplification and absorption properties in a double-Λ four level system of GaAs/AlGaAs multiple quantum wells (MQWs) under realistic experimental conditions. The amplification and absorption responses of two weak fields can be achieved by adjusting the relative phase, the probe detuning, and the two pump Rabi frequencies appropriately. The investigation is much more practical than its atomic counterpart because of its flexible design and the wide adjustable parameters. It may provide a new possibility in technological applications for the light amplifier working on quantum coherence effects in MQWs solid-state system. In recent years, semiconductor quantum wells has drawn significant attention for the reasons that it can be viewed as the two dimensional electron gas, having properties similar to atomic vapors such as the discrete levels. Due to the small effective electron mass, it has advantages of high nonlinear optical coefficients and large electric dipole moments. Several typical interesting phenomena such as electromagnetically induced transparency (EIT) [1][2][3][4][5], lasing without inversion [6], highly efficient four-wave mixing [7], all-optical switching [8], and slow light [1] have been demonstrated. As a method to study quantum coherent control and interference, the relative phase of the applied laser fields has been widely used, which is usually termed as phase control, in several important processes in atomic, molecular, and solid-state systems [9][10][11][12][13][14], but the study of amplification and absorption properties in double-Λ system of GaAs/AlGaAs MQWs has not been reported. In this paper, we study controllable optical amplification and absorption responses of the probe and the signal laser fields in a double-Λ four-level system on GaAs/AlGaAs MQWs under realistic experimental conditions [1,3,15]. The main advantages of applying our considered MQWs scheme over other approaches are as follows. The MQWs medium studied here is a solid, which is much more practical than that in gaseous medium due to its flexible design and the wide adjustable parameters. The MQWs medium here provides a highly tunable quantum system. The quantum properties of these nanostructures such as the transition energies and dipole moments can be well-manipulated by accurately tailoring their shapes and sizes while they can hardly be found in the models for cold atom media.