Interactions of a two-level atom and a field with a time-varying frequency

The interactions between a two-level atom and a coherent field with a time-varying frequency have been investigated. The two typical cases—the frequency of the field varying with time in the forms of sine and rectangle—have been considered. It is found that the collapse-revival phenomena of the atomic population inversion are deformed as the frequency changing with time in sine form and the rectangular frequency modulation can lead to some new collapses and new revivals in the evolution of the atomic population inversion.

Figure 1

Population inversion as a function of time in the standard JCM (numerical results) for $⟨n⟩=25$, $\mathrm{\Delta }=0$, $f\left(t\right)=0$.

Figure 2

Population inversion as a function of time as the field frequency varies with time in the form of sine for $\beta =0.1g_0$ and $\alpha =g_0$. The dotted line represents the field-frequency modulation.

Figure 3

Population inversion as a function of time as the field frequency varies with time in the form of sine for $\beta =0.1g_0$ and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 4

Population inversion as a function of time as the field frequency varies with time in the form of sine for $\beta =g_0$ and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 5

Rabi oscillation related to the photon number $\mid n⟩$ with $n=25$ as a function of time as the field frequency varies with time in the form of sine for $\beta =0.1g_0$ and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 6

Population inversion as a function of time as the field frequency varies with time in the form of pulse for $g_{0}T=32$, $g_0\tau =2$, $g_0{t}_0=15$, and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 7

Population inversion as a function of time as the field frequency varies with time in the form of pulse for $g_{0}T=32$, $g_0\tau =2$, $g_0{t}_0=0$, and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 8

Population inversion as a function of time as the field frequency varies with time in the form of pulse for $g_{0}T=16$, $g_0\tau =2$, $g_0{t}_0=15$, and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.

Figure 9

Population inversion as a function of time as the field frequency varies with time in the form of pulse for $g_{0}T=10$, $g_0\tau =2$, $g_0{t}_0=0$, and $\alpha =20g_0$. The dotted line represents the field-frequency modulation.