I do theoretical and computational research at the interface between quantum optics and quantum information. Recent investigations include the following.


Quantum trajectory theory of quantum error correction

I have developed a quantum trajectory theory of quantum error correction in collaboration with Julio Gea-Banacloche which accounts for quantum error correction as a type of refrigeration to reduce the entropy of the data qubits via their coupling to ancillary qubits and then resetting the ancillary qubits by cooling them to a fiducial state.


Enhancing performance of atomic clocks with entanglement

It has been theoretically predicted that an atomic clock based on quantum interference of N atoms prepared in an entangled state (a many-atom Schrodinger cat state) will yield a precision scaling as 1/N rather than 1/sqrt(N) for traditional atomic clocks. This scaling assumes perfect preparation of the desired entangled state. Yet the difficulty of preparation must also increase with N. I have investigated the limits of this enhanced precision when the imperfect state preparation is accounted for using a quantum circuit model for state preparation which incorporates errors. Working with two undergraduates, Andrew Jacobs and Matthew Briel, I have found the number of atoms, as a function of the error rate, where the precision regresses to that of a traditional atomic clock. This work could be extended to include correlated noise models in the future.


Quantum teleportation based on collective emission

In conjunction with Richard Wagner, an undergraduate student, I investigated the performance of a quantum teleportation scheme which is based on the direct photodetection of the emission from a pair of atoms in order to implement the Bell state discrimination necessary for quantum teleportation. We have characterized the performance in terms of the success probability and fidelity of the teleported state and found them to be competitive with other conditional teleportation protocols. We have also extended our model to account for realistic photon collection and detection efficiencies. We found that the protocol will beat the performance of a classical teleportation protocol provided that the combined photon collection and detection efficiency exceeds 75%.


Multimode, multiatom entanglement in cavity QED

Cavity quantum electrodynamics (QED), consisting of one or more atoms coupled to electromagnetic field modes in an optical cavity, is one of several areas of experimental physics which show promise for implementing quantum information processing protocols. I am investigating the connection between entanglement and atom-field and field-field correlation functions in cavity QED. This is in collaboration with Perry Rice at Miami and Luis Orozco's group at the University of Maryland where they have the capability to measure these correlation functions experimentally. Currently I have calculated the correlation functions of interest in the steady state for three- and four-level atomic systems. Patrick Hemphill, a graduate student, has calculated the time dependent correlation functions numerically using quantum trajectories, making comparisons between the two-level and three-level models. We have also found that the four-level model shows qualitatively different results when extended from one to two atoms. The usual sqrt(N) enhancement of the atom-cavity coupling is not sufficient to account for the results.