Atomic squeezing under collective emission

Atomic squeezing is studied for the case of large systems of radiating atoms, when collective effects are well developed. All temporal stages are analyzed, starting with the quantum stage of spontaneous emission, passing through the coherent stage of superradiant emission, and going to the relaxation stage ending with stationary solutions. A method of governing the temporal behavior of the squeezing factor is suggested. The influence of a squeezed effective vacuum on the characteristics of collective emission is also investigated.

Figure 1

Temporal behavior of the coherence intensity $w$ (solid line) and population difference $s$ (dashed line) for ${\gamma }_1=0.1$, ${\gamma }_3=1$ (in units of ${\gamma }_2$), and $g=100$, without pumping, so that $\zeta =-1$. Both $w$ and $s$ are dimensionless. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 2

Evolution of the squeezing factor $Q$ for the parameters of Fig. 1. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 3

Squeezing factor $Q$ for the parameters ${\gamma }_1={\gamma }_3=1$, $g=100$, and $\zeta =-1$. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 4

Oscillations of the coherence intensity $w$ and population difference $s$ as functions of time (in units of ${\gamma }_2^{-1}$) in the presence of pumping, when $\zeta =1$, for the parameters ${\gamma }_1={\gamma }_3=1$, $g=10$.

Figure 5

Evolution of the squeezing factor $Q$ for the parameters of Fig. 4. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 6

Regulating the number of oscillations of $w$ and $s$, under $\zeta =1$, by varying the system parameters, which are ${\gamma }_1=1,{\gamma }_3=0.1$, and $g=100$. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 7

Evolution of the squeezing factor $Q$ for the parameters of Fig. 6. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 8

Governing the behavior of the squeezing factor $Q$ in the regime of punctuated atomic superradiance for the parameters ${\gamma }_1=0.1$, ${\gamma }_3=1$, $g=100$, and $\zeta =-1$, with equidistant inverting pulses at the moments of time $t_1=0.1$, $t_2=0.2$, $t_3=0.3$, $t_4=0.4$, and $t_5=0.5$. Time is measured in units of ${\gamma }_2^{-1}$.

Figure 9

Governing the evolution of the squeezing factor $Q$ in the regime of punctuated atomic superradiance for the same parameters as in Fig. 8, but with nonequidistant inverting pulses at the moments of time $t_1=0.1$, $t_2=0.2$, $t_3=0.3$, $t_4=0.4$, $t_5=0.5$, $t_6=1$, $t_7=1.1$, $t_8=1.2$, $t_9=2$, $t_{10}=2.4$, and $t_{11}=2.5$. Time is measured in units of ${\gamma }_2^{-1}$.