Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2013 Apr 26;110(17):170401. doi: 10.1103/PhysRevLett.110.170401. Epub 2013 Apr 22.
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
我们将多粒子薛定谔-牛顿方程应用于宏观力学物体，该方程描述了多粒子量子波函数和经典时空几何的共同演化。通过对物体内部自由度运动的平均化，我们得到了质心的有效薛定谔-牛顿方程，该方程可以通过最先进的光机械实验在量子水平上进行监测和操纵。对于在调和势阱中量子力学运动的单个宏观物体，其量子不确定性的演化频率与其经典本征频率不同——这种差异取决于物体的内部结构——并且可以使用当前技术进行观测。对于几个物体，薛定谔-牛顿方程预测的半经典运动与牛顿物理学一样，但量子不确定性不能从一个物体转移到另一个物体。
