Detection of Qubit-Oscillator Entanglement in Nanoelectromechanical Systems

Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg uncertainty limit. Therefore, it is just a question of time before we will routinely see true quantum effects in nanomechanical systems. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a realistic scenario making it possible to detect entanglement of a mechanical resonator and a qubit in a nanoelectromechanical setup. The detection scheme involves only standard current and noise measurements of an atomic point contact coupled to an oscillator and a qubit. This setup could allow for the first observation of entanglement between a continuous and a discrete quantum system in the solid state.

Figure 1

Possible experimental setup consisting of a qubit and an oscillator coupled to an atomic point contact (APC). Electrons tunnel at the APC ($t_a$) and a fixed tunnel junction ($t_b$), which are both biased with a voltage $V$. The area enclosed by the junctions (red dashed line) is threaded with a magnetic flux to create an Aharonov-Bohm phase. The qubit is realized as a Cooper pair box (CPB, yellow). Its state can be tuned using the gate voltage $V_g$ and it couples capacitively to both junctions. The oscillation of the nanomechanical resonator (NR, green) modulates the tunneling amplitude $t_a$. As discussed in more detail in 24, this setup can be used to realize the tunneling amplitude (3).

Figure 2

Schematic density plot of the prefactors $S_X(\omega )$ ($X=x{\sigma }_x,x{\sigma }_y,\dots$) of the frequency-dependent noise $S(\omega )=\sum _X{S}_X(\omega )⟨X⟩$ as a function of ${\delta }_1$ and $\omega$.