| The term "quantum electromechanics" describes a system consisting of a nanofabricated mechanical resonator coupled to a superconducting device called a charge qubit (quantum bit) or Cooper-pair box. Modeled as a quantum harmonic oscillator coupled to a two-level system, the electromechanical system parallels that of an atom interacting with the electromagnetic field in a cavity. Current experiments indicate that this system should be capable of reaching the quantum regime in the near future. Such experiments offer a chance to study the quantum behavior of a manmade mechanical device. In addition, because of the strength of the capacitive coupling, the electromechanical system has the potential to demonstrate coherent quantum behavior in limits very different from those considered in quantum optics.; After the model and the analogy to quantum optics are established, three different limits are studied. The first limit, in which the coupling strength is small, is treated with perturbation theory. Energy shifts due to the interaction enable two complementary measurement schemes. The shift of the resonator frequency distinguishes the two levels of the qubit. On the other hand, measurement of the qubit energy allows the creation and detection of energy eigenstates of the resonator.; Second, the frequency of the oscillator is taken to be larger than the frequency of the qubit. In this limit an adiabatic approximation gives excellent results for all coupling strengths. The dynamical behavior of the qubit under various initial conditions is explored. For some oscillator states, the coherent oscillations of the qubit collapse and revive. This behavior is similar to, although more complicated than, the corresponding atomic behavior in quantum optics.; Finally, the limit in which the oscillator frequency is small compared to the qubit frequency is considered. Despite the lack of an accurate approximation, three primary physical effects are distinguished. The small coupling regime results in frequency shifts consistent with the perturbative approach. In the large coupling regime, interaction with the qubit creates an effective double-well potential for the oscillator. Between these regimes the oscillator state becomes "squeezed" with respect to its uncoupled state. A deeper understanding of this limit is important for future experiments. |
