We investigate the field squeezing in a system composed of an initial coherent field interacting with two quantum dots coupled by electron tunneling. An approximate quantum-dot molecule Jaynes-Cummings model describing the system is given, and the effects of physical quantities, such as the temperature, phonon-electron interaction, mean photon number, field detuning, and tunneling-level detuning, are discussed in detail. 1. Introduction Thanks to the rapid progress of nanotechnologies, the exploration of the quantum-dot system, a mesoscopic synthetic material with a quantum confinement configuration, has provided a versatile tool for the simulation of many interesting phenomena in condensed matter physics [1, 2], among which, the quantum-dot molecule (QDM), formed from an asymmetric double quantum-dot system coupled by tunneling, has attracted much attention recently. New trends in nanotechnology even enable us to manipulate this kind of QDM using the external controlment, that is, electric field or optical field. The interaction between atoms and field, an intriguing topic in modern quantum optics, yields many novel properties of the optical system. Based on the study of Jaynes-Cummings model, a fully quantum mechanical model and one of the few exactly solvable models that describes an atom in an external field, many studies have been made including the generalization of the model, such as applying the initial conditions [3], considering the dissipation and damping [4], multilevel of atoms, and multimode field [5, 6]. Many nonclassical effects have been investigated within the framework of this model, like Rabi oscillations, collapse-revival phenomenon, sub-Poissonian photon statistics, and squeezed state of the radiation field [7, 8]. Specifically, the squeezed state of light, a pure quantum effect without classical parallelism, has attracted much attention in these decades [9]; it can be widely used in the exploration of gravitational wave [10, 11], nonlinear optics [12], quantum information [13], quantum communication [14], and even precision metrology [15]. For its artificial nature and properties similar to natural atoms and molecules, the QDM, an ideal candidate for the mimic of atoms interacting with external fields, has been studied extensively, because its levels could be controlled conveniently and tuned easily [16]. However, the QDM is often surrounded by the solid matrix which means that the electrons are inevitably coupled with phonons and it hints that the electron-phonon interaction cannot be neglected during the tunneling. Therefore the
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