Frozen Condition of Quantum Coherence for Atoms on a Stationary Trajectory

The quantum coherence (QC) of two comoving atoms on a stationary trajectory is investigated. We develop a formalism to characterize the properties of atoms on a stationary trajectory. We give a criterion under which QC is frozen to a nonzero value. The frozen condition that vanishing super- or subradiant decay rate is not so sensitive to the initial condition of state. We show that enhanced QC and a subradiant state can be gained from the initial state.

Figure 1

Schematic illustration for two identical two-level atoms comoving on an arbitrary stationary trajectory (AST). The observer (O) located in the local inertial frame (LIF) of AST is instantaneous static with respect to the atoms. The coordinate of atoms $(t,{\overrightarrow{x}}_j)$ is characterized by proper time $\tau$ as $x_j(\tau )=(t(\tau ),{\overrightarrow{x}}_j(\tau ))$. The observer can also be in a laboratory reference frame, and the difference is that the total Hamiltonian we have used should be multiplied by $d\tau /dt$.

Figure 2

Measure of coherence for static atoms with an initial separable state in free space as a function of ${\mathrm{\Gamma }}_{\downarrow }^{11}t$ and $\ln ({\mathrm{\Gamma }}_{\downarrow }^{11}t)$, respectively. In such a case, the modulation ${\mathrm{\Gamma }}_{\downarrow }^{12}=3{\mathrm{\Gamma }}_{\downarrow }^{11}(\sin R-R\cos R)/R^3$ and the interaction potential $V=-3{\mathrm{\Gamma }}_{\downarrow }^{11}(\cos R+R\sin R)/2R^3$ with $R=r{\omega }_0/c$ and $r$ being atomic separation. The blue dotted line is the $R=0.14$ case. For comparison, the red solid line with $R=1$ and yellow dashed line with $R=0.014$ are plotted.