Geometric phases in open systems: A model to study how they are corrected by decoherence

We calculate the geometric phase for an open system (spin-boson model) which interacts with an environment (ohmic or nonohmic) at arbitrary temperature. However there have been many assumptions about the time scale at which the geometric phase can be measured, there has been no reported observation of geometric phases for mixed states under nonunitary evolution yet. We study not only how they are corrected by the presence of the different type of environments but estimate the corresponding times at which decoherence becomes effective as well. These estimations should be taken into account when planning experimental setups to study the geometric phase in the nonunitary regime, particularly important for the application of fault-tolerant quantum computation.

Figure 1

(Color online) Comparison between the $\Gamma \left(t\right)$ coefficients for the ohmic case $(n=1)$ and the supraohmic case $(n=3)$ for different environments for high $(T=1000)$, low $(T=1.55)$, and zero temperature $(\hslash =1=k_B)$. $\Lambda =100\Omega$ and ${\gamma }_0=0.3$ (top) and ${\gamma }_0=0.03$ (bottom). Time is measured in units of $\Omega$. It is easy to note that the low temperature limit is not zero temperature.