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.