Quadrature Squeezing Of Mechanical Resonator In Two Coupled Quantum Dots

Mechanical resonator (MR) have been actively explored not only platform to test the quantum mechanics, but also can coupled with other systems and have important prespect applications. Due to the decelopments in nanofabrication and nonequilibrium cooling, the exploration of the interaction of quantum nanomechanical resonators has become realistic, How to effectively use this carrier to study quantum mechanics are still an interesting subject.In this paper, we present a solution for the generation the quadrature squeezing by using the coupling between mechanical resonator and quantum dots. The two coupled quantum dots is coupled by electron-phonon interaction, where the quantum dot which is capacitively coupled with the mechanical resonator is driven by a strong light field and two weak light fields. In the dressed state basis, under the condition of Born-Markov approximation and rotating wave approximation, we take the trace of the quantum dots and electrode reservoirs operator by using the second perturbation theory. By caloulating the reduced density matrix element, we can get the quadrature squeezing. We adjusting the gate voltagefind when the population of the dressed state|-＞is far larger than|+＞, then forming the four wave mixing between the dressed state|-,n＞and|+,n+1＞.So we can get the correlated mechanical resonator mode biphonons, therefore, causing the squeezing of the MR.Our organization is as follows. In Sec.I we present some basic knowledge of this article. In Sec.2, we reprsent the master equation for the reduced density operator for a mechanical resonator-quantum dot system, including the phonon-mediated processes. In Sec.3, we devoted to the investigationss of phonon-mediated squeezing of the MR and investigated the condition for the appearance of squeezing. Finally, we summarize our results in Sec.4.