Quantum transducers: Integrating transmission lines and nanomechanical resonators via charge qubits

We propose a mechanism to interface a transmission line resonator (TLR) with a nanomechanical resonator (NAMR) by commonly coupling them to a charge qubit, a Cooper-pair box with a controllable gate voltage. Integrated in this quantum transducer or simple quantum network, the charge qubit plays the role of a controllable quantum node coherently exchanging quantum information between the TLR and NAMR. With such an interface, a quasiclassical state of the NAMR can be created by controlling a single-mode classical current in the TLR. Alternatively, a “Cooper pair” coherent output through the transmission line can be driven by a single-mode classical oscillation of the NAMR.

Figure 1

(Color online) Schematic diagram of the coupled system of a nanomechanical resonator (NAMR) and transmission line resonator (TLR). The TLR is located right above the SQUID connected to the Cooper-pair box (CPB), so the TLR can produce a flux threading the loop in the SQUID. The Cooper pairs are schematically represented by two small overlapping circles inside the Cooper-pair box. The oscillating NAMR is shown right below the CPB. The CPB acts as a transducer mediating the interaction between the NAMR and the TLR.

Figure 2

(Color online) Parameter ${\mid K(-t)\mid }^2$ changes with time-dependent variable $\Delta =t\delta$ for different $\beta$ values.