Non-Markovian transient Casimir-Polder force and population dynamics on excited- and ground-state atoms: Weak- and strong-coupling regimes in generally nonreciprocal environments

The transient Casimir-Polder force on a two-level atom introduced into a three-dimensional, inhomogeneous, generally nonreciprocal environment is evaluated using non-Markovian Weisskopf-Wigner theory in the strong- and weak-coupling regimes. Ground-state and excited atoms are shown to decouple into two separate initial-value problems, and both the short-time and long-time atomic population and force are evaluated. The results are compared with various Markov approximations of the Weisskopf-Wigner theory and with previous Markov results from the Heisenberg picture.

Figure 1

A two-level system near the surface of a nonreciprocal material, experiencing the Casimir-Polder force, and, for an excited atom, a spontaneous-emission optical force. The main decay channel is the SPPs on the interface.

Figure 2

Non-Markovian population dynamics in the weak-coupling regime, obtained from the numerical solution of (10) and compared with the usual Markov population decay using (C6). The insert shows the behavior near $t=0$. The atom is located $z_0=0.7c/{\omega }_p$ above the interface, such that $g=0.0455$.

Figure 3

Non-Markovian population dynamics in the strong-coupling regime, obtained from the numerical solution of (10) and compared with the usual Markov population decay using (C6). The atom is located $z_0=0.1c/{\omega }_p$ above the interface, such that $g=0.8427$.

Figure 4

Normalized non-Markovian vertical force (15) in the weak-coupling regime compared with the Markov approximation (D1) and the HEM result [8]. ${\mathcal{F}}_0=3{\left|\gamma \right|}^2/\left(16\pi z_0^4{\varepsilon }_0\right)$ (N). The atom is located $z_0=0.7c/{\omega }_p$ above the interface, $g=0.0455$.

Figure 5

Normalized non-Markovian vertical force (15) in the strong-coupling regime compared with the Markovian HEM result [8]. ${\mathcal{F}}_0=3{\left|\gamma \right|}^2/\left(16\pi z_0^4{\varepsilon }_0\right)$ (N). The atom is located $z_0=0.1c/{\omega }_p$ above the interface, $g=0.8427$.

Figure 6

Non-Markovian ground-state atom population dynamics in the strong-coupling regime, obtained from the numerical solution of (17). The atom is located $z_0=0.1c/{\omega }_p$ above the interface such that $g=0.8427$.

Figure 7

Vertical force dynamics (transient Casimir-Polder force) on a ground-state atom in the weak-coupling regime. The atom is located $z_0=0.7c/{\omega }_p$ above the interface such that $g=0.0455$.

Figure 8

Vertical force dynamics (transient Casimir-Polder force) on a ground-state atom in the strong-coupling regime ($z_0=0.1c/{\omega }_p$, $g=0.8427$).

Figure 9

Depiction of the $s$ plane showing the pole, branch cut, and integration contour.

Figure 10

Casimir force ($t\to \infty$) comparing the Markov and non-Markovian results for the weak-coupling situation, $z_0=0.7c/{\omega }_p$, $g=0.0455$.