Recent experiments have shown that the macroscopic quantum states of Josephson junctions have long enough coherence times for them to be used as qubits for quantum information processing. In collaboration with Andrew Cleland, we have proposed a scalable quantum computing architecture based on the integration of phase qubits with NEMS resonators [pdf] (for a more detailed discussion see [pdf]). The system is analogous that of cavity QED, but with tunable atomic level spacings and controllable electromagnetic interaction strength. Fast, high-fidelity quantum memory operations are achievable with this architecture [pdf], and the interesting superstrong coupling regime is beginning to be addressed theoretically [pdf]. Experiments on this and related systems are underway at UCSB, Yale, and Maryland. We are also working with John Martinis's group to design gates for their capacitively coupled phase qubits.

In collaboration with Andrew Sornborger, we are pursuing the use of control theory techniques for the design of fast gates for superconducting quantum computers, and eventially hope to design large-scale quantum circuits that can implement quantum algorithms.

We have been interested in the FQHE regime of the 2D electron gas, especially edge states. We are attempting to explain the tunneling experiments of Grayson and others by developing a new nonperturbative method to directly calculate the tunneling DOS in an interacting system, without using bosonization or Chern-Simons theory. We argue that the low-energy spectral anomolies in this and a variety of other low-dimensonal and strongly correlated electron systems are caused by the infrared catastrophe, a singular screening response of an electron gas to the sudden application of a localized potential, caused here by the addition of a new electron to the conductor during a tunneling event. In recent work [pdf pdf] we have developed a functional integral method that, in effect, maps the problem of calculating the interacting propagator to the x-ray edge problem, yielding qualitatively correct results in test cases. Our method also gives qualitatively correct results for the sharp FQHE edge, and we are curretly trying to obtain quantative agreement by including the leading corrections to the x-ray edge limit [pdf].

In collaboration with Lachezar Georgiev, we have also used conformal field theory methods to investigate edge state transport in nonabelian FQHE states, such as 5/2, which are candidates for topological quantum computation [pdf].

We are interested in two aspects of nanomechanics: quantum NEMS and thermal-conductance microscopy. The quantum limit of a nanomechanical resonator is in reach and several groups are attempting groundbreaking experiments. Our work is focused on exploring this new "quantum optics" limit of phonon dynamics. We are also working on the outstanding problem of what limits the Q factor in high-frequency NEMS resonators, building on our earlier investigations of energy dissipation in nanoparticles [pdf], and have developed a comprehensive theory of clamping loss and predict that this mechanism will become especially important in the microwave regime [pdf].

In a mesoscopic phonon wire, thermal energy is carried by coherent phonons and can be described with scattering theory. We have recently developed a theory of mesoscopic transport through curved wires, using techniques from differential geometry [pdf]. We have also shown that if there is strong reflection at the boundary between the reservoirs and wire, the energy transport is simply determined by the local vibrational DOS at the surface of the bodies acting as reservoirs, analogous to the tunneling limit of charge transport [pdf]. This result suggests the intriguing possibility of a new type of scanning probe, a scanning thermal-conductance microscope, which would be a phonon analog of the scanning tunneling microscope and which probes the local phonon DOS of a material, either conducting or insulating, with atomic-scale resolution. We are currently exploring this idea through a variety of theoretical and computational studies.