13 research outputs found
Geometric Phases for Mixed States during Cyclic Evolutions
The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.Comment: 9 pages, 1 figur
Uhlmann's geometric phase in presence of isotropic decoherence
Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)]
is analyzed in the case of a qubit affected by isotropic decoherence treated in
the Markovian approximation. It is demonstrated that this phase decreases
rapidly with increasing decoherence rate and that it is most fragile to weak
decoherence for pure or nearly pure initial states. In the unitary case, we
compare Uhlmann's geometric phase for mixed states with that occurring in
standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]
and show that the latter is more robust to reduction in the length of the Bloch
vector. We also describe how Uhlmann's geometric phase in the present case
could in principle be realized experimentally.Comment: New ref added, refs updated, journal ref adde
Open system effects on slow light and electromagnetically induced transparency
The coherence properties of a three-level -system influenced by a
Markovian environment are analyzed. A coherence vector formalism is used and a
vector form of the Lindblad equation is derived. Together with decay channels
from the upper state, open system channels acting on the subspace of the two
lower states are investigated, i.e., depolarization, dephasing, and amplitude
damping channels. We derive an analytic expression for the coherence vector and
the concomitant optical susceptibility, and analyze how the different channels
influence the optical response. This response depends non-trivially on the type
of open system interaction present, and even gain can be obtained. We also
present a geometrical visualization of the coherence vector as an aid to
understand the system response.Comment: Several changes; journal reference adde