Quantum decoherence modulated by special relativity

By investigating the evolution of a moving spin-$\frac{1}{2}$ Dirac electron coupled with a background magnetic noise, we demonstrate that the effects of special relativity will significantly modify the decoherence properties of the spin state. The dephasing could be much suppressed, and for a sufficiently long time the decoherence even seems to halt. This interesting phenomenon stems from the dressed environment induced by special relativity.

Figure 1

(Color online) A spin-$\frac{1}{2}$ Dirac electron, at rest in the moving inertial frame $R_S$ with the velocity $\mathbf{v}$, is coupled with the background magnetic noise in the $\hat{\mathbf{z}}$ direction of the rest frame $R_E$.

Figure 2

(Color online) Decoherence modulation factor as a function of the moving rapidity and angle, $\eta$ vs $\xi$ and $\theta$.

Figure 3

(Color online) (a) Maximum value of decoherence modulation factor as a function of rapidity, ${\eta }_{\text{max}}$ vs $\xi$; (b) off-diagonal element as a function of time, ${\rho }_{\uparrow \downarrow }\left(t\right)$ vs $\gamma t^2$, and the rapidity $\xi =2.5$ (solid line), $\xi =0$ (dashed line). The initial spin state is $|\psi ⟩=\frac{1}{\sqrt{2}}\left(|\uparrow ⟩+|\downarrow ⟩\right)$.