Quantum dynamics of a two-level emitter with a modulated transition frequency

The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects, and consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.

Figure 1

Schematic diagram of a two-level emitter with modulated transition frequency (a) without and (b) with showing the involved quantum coherences among specific transition pathways. Due to modulation, multiple induced decaying channels $n=0,\pm 1,\pm 2,...$, interfere such that spontaneous emission is slowed down. ${\gamma }_0$ is the single-qubit spontaneous decay rate in the absence of modulation.

Figure 2

The time dependence of the mean value of the inversion operator $\langle S_z\left(t\right)\rangle$ as a function of $\kappa t$. Here the solid line corresponds to $\chi =50$ and $\varphi =0$, the long-dashed one to $\chi =50$ and $\varphi =\pi /2$ while the dotted curve to $\chi =50$ without taking into account quantum coherences. The short-dashed line depicts the usual spontaneous decay, i.e., when $\chi =0$. Other parameters are $g=0.3\kappa$, $\omega =0.12\kappa$, ${\delta }_c=0$, and $\kappa =1$.

Figure 3

The time dependence of the decay rate $\gamma \left(t\right)$ given in Eq. (10) versus $\kappa t$. Here the solid line corresponds to $\chi =50$ and $\varphi =0$ whereas the long-dashed line one to $\chi =50$ and $\varphi =\pi /2$. Other parameters are the same as in Fig. 2.

Figure 4

The mean value of the inversion operator $\langle S_z\left(t\right)\rangle$ versus the modulation depth $\chi$ when $\kappa t=30$. Here the solid line corresponds to $\varphi =0$, while the long-dashed line one to $\varphi =\pi /2$. Other parameters are the same as in Fig. 2.

Figure 5

The frequency shift $\Omega$ (in units of $\kappa$) as a function of modulation depth $\chi$ when $\kappa t=10$. Here the solid line corresponds to $\varphi =0$, while the long-dashed line to $\varphi =\pi /2$. Other parameters are the same as in Fig. 2.

Figure 6

The free-space mean-value of the inversion operator $\langle S_z\left(t\right)\rangle$ versus $\gamma t$. Here, $\rho =0.2$, $\omega /\gamma =1$, $\varphi =0$ while ${\omega }_0/\omega =2\times {10}^4$ and, hence, $\chi =100$. (a) $n_0=1$; (b) $n_0=50$. The dashed line shows the usual free-space spontaneous decay law in the absence of frequency modulation.