Cooling Mechanism Of A Double Quantum Dot Mechanical Resonator

In recent years, the studies on the field of laser cooling of an atom, a trapped ion ornanomesoscopic systems have attracted wide attention of a large number of physicists andrapidly developed in many disciplines of physics, such as quantum information science, quan-tum optics and laser physics. Cooling the nanomechanical oscillator down to the quantumground state has become a hot research spot, due to it not only has important applications inthe high-precision measurement(such as displacement detection, quality detection and spindetection) and the quantum information processing, but also can make the basic principlesof quantum mechanics well verified, and provide a solid theoretical foundation and an idealplatform for the research on the properties of quantum dynamics in nanomesoscopic system-s. In addition, semiconductor quantum dots are easy to integrate and expand, and its levelgap, as well as the tunneling coupling among the quantum dots can be well adjusted andcontrolled, so semiconductor quantum dots become an experimental platform to build andassemble quantum engineering device in the application of quantum information science.Therefore, by using the electro-acoustic interaction between the electron and the mechani-cal resonator and the tunneling effect during electrons transport in the quantum dots, it hasbecome one of interesting topics that how to rapidly and efficiently cool the mechanical res-onator down to the quantum ground state in the system made of the quantum dots and themechanical resonator.In this paper, we propose a new cooling scheme of mechanical oscillator, trying to usethe electro-acoustic interaction between the tunneling of electrons in double quantum dotand the mechanical resonator to cool the mechanical resonator down to the quantum groundstate. Firstly, we design a smart model like that. A double quantum are connected to theleft and right electrodes with the tunneling barrier, and the left dot fixed on the left electrodecan not move, but the right dot fixed on a metal cantilever which is connected to the rightelectrode can vibrate side-to-side like a’pendulum’. Secondly, under the condition of Markovapproximation, we derive the master equations of reduced density operator of the mechanicalresonator by making use of the second-order perturbation approximation theory, from which the rate equations of the mechanical resonator are derived, then we obtain two expressionsof the cooling rate and the steady-state average phonon of the resonator. Thirdly, the coolingconditions of the mechanical resonator we proposed here are discussed, and the effects ofvarious parameters in the system on the cooling efficiency of the mechanical resonator areanalysed numerically, in addition the conditions the system should have are given to realizethe the maximum cooling efficiency of the mechanical resonator. Finally, we get an importantconclusion that the mechanical resonator also can be cooled under the suitable conditionseven though the electrons jump from the high energy level to the lower energy level in thequantum dot system.