Towards Quantum Entanglement in Nanoelectromechanical Devices

We study arrays of mechanical oscillators in the quantum domain and demonstrate how the motions of distant oscillators can be entangled without the need for control of individual oscillators and without a direct interaction between them. These oscillators are thought of as being members of an array of nanoelectromechanical resonators with a voltage being applicable between neighboring resonators. Sudden nonadiabatic switching of the interaction results in a squeezing of the states of the mechanical oscillators, leading to an entanglement transport in chains of mechanical oscillators. We discuss spatial dimensions, $Q$ factors, temperatures and decoherence sources in some detail, and find a distinct robustness of the entanglement in the canonical coordinates in such a scheme. We also briefly discuss the challenging aspect of detection of the generated entanglement.

Figure 1

The degree of entanglement as a function of time in a chain of length 8 with open boundary conditions. Depicted in light, medium, and dark grey are the curves for the values $c=0.3$, $c=0.2$, and $c=0.1$ in the above units. The figures in the lower row depict the entanglement between the first and the last oscillator in an open chain, for the upper row the two diametrically opposed oscillators in a ring are considered. The figures on the left corresponds to the noiseless case. The figures on the right show the degree of entanglement under the decoherence and for nonzero temperature. Values are chosen that correspond to the $Q$ factor $Q={10}^3$, fundamental frequency 5 GHz, and temperature of 10 mK.

Figure 2

Maximum degree of entanglement between the end points as a function of the switching time $t^{\prime }$ in the above units for a chain of length eight and $c=0.1$. The dotted line represents the unit frequency of a free oscillator.