Two remarkable features of quantum mechanics are superposition states and entangled states. In the context of a nanomechanical resonator, these states allow the possibility of preparing a mechanical system which is in two spatial locations at the same time. It occurred to Miles Blencowe (Dartmouth), Andrew Armour (Nottingham), and myself that superconducting qubits could provide a way to drive a mechanical system into these unusual states. As we investigated this theoretically, we were surprised to discover that this indeed appears technically possible (PRL 2002); the coupling between the qubit and the mechanical system should be strong enough to produce two orthogonal mechanical states, and the coherence time of the mechanical resonator should be sufficiently long to perform an interference experiment. This work formed the basis of schemes by others to use mechanical structures in quantum computation.
As we investigated a mechanical system coupled to a qubit, we quickly realized that our Hamiltonian is very similar to that of an atom interacting with a single mode of the electromagnetic field: cavity QED. We found that the qubit energy splitting should be dependent on the mechanical number state, and that the mechanical frequency should depend on the qubit state. (Irish and Schwab, PRB 2003). These frequency shifts form the basis for quantum non-demolition measurements and measurements of the mechanical system number state (Fock state.)
We have taken the first experimental steps to couple a superconducting qubit to a nanomechanical resonator. We have formed a collaboration with Matt LaHaye (Caltech), Michael Roukes (Caltech) and Pierre Echternach (JPL). We have been able to show that the interaction between the qubit and the resonator is as we predicted in 2003. We have observed that the mechanical frequency is pulled by the state of the qubit as expected, and that the mechanical frequency can be used to detect the qubit excited state which is driven by a resonant microwave field (LaHaye et al., Nature 2009.)
We will continue in this direction and have begun preparations to form and detect entangled states. This will be one of our major thrusts in the new lab at Caltech.
The SEM micrograph above shows a sample fabricated by Pierre Echternach (JPL) and Matt LaHaye (Caltech). The nanomechanical resonator is formed by surface micromachining using RIE, and resonates at ~60MHz with a Q~50,000 at milli-kelvin temperatures. The mechanical motion is driven and detected capacitively using the electrode shown in the center-bottom. The superconducting qubit (Cooper-pair box) is capacitively coupled to the mechanical structure and is located in the upper-left of the micrograph. The Coulomb and Josephson energy are ~13GHz.
Prof. Michael Roukes, Caltech
Dr. Matt LaHaye, Caltech
Dr. Pierre Echternach, Jet Propulsion Laboratory
Prof. Miles Blencowe, Dartmouth College
Prof. Andrew Armour, University of Nottingham
Prof. Aashish Clerk, McGill University
Prof. Gerard Milburn, University of Queensland
Dr. Salman Habib, Los Alamos National Laboratory
Prof. Kurt Jacobs, University of Massechusets, Boston
Prof. Ari Mizel, Pennsylvainia State University
Dr. Rusko Ruskov, Pennsylvainia State University