Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir

We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by adiabatically manipulating the environment with which it interacts. As a specific scheme, we analyze a multilevel atom interacting with a broadband squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We also propose a scheme to measure such a geometric phase by means of a suitable polarization detection.

Figure 1

(a) Schematic representation of the four systems considered. The energy gap between states $|-1⟩$ and $|0⟩$ and between $|0⟩$ and $|1⟩$ is $\Omega$. The transitions between these levels are coupled to the modes $\widehat{a}(\omega )$ of the reservoir. The reference state $|a⟩$ is decoupled from the reservoir. (b) Five-level system, transitions $1\leftrightarrow 0$ and $0\leftrightarrow -1$ are coupled to modes ${\widehat{a}}_1(\omega )$ and $1^{\prime }\leftrightarrow 0$ and $0\leftrightarrow -1^{\prime }$ are coupled to modes ${\widehat{a}}_2(\omega )$ of the reservoir.