Generation of a superposition of multiple mesoscopic states of radiation in a resonant cavity

Using resonant interaction between atoms and the field in a high-quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasiprobability distributions and demonstrate the nonclassicality of the superposition in terms of the zeros of the $Q$ function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by [Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.

Figure 1

(Color online) The Wigner distribution $W\left(\gamma \right)$ for (a) the generated state (8) and (b) the approximated state (10), using parameters $\alpha =4$, $g{t}_1=3.7\pi$, and $g{t}_2=1.9\pi$.

Figure 2

(Color online) The $Q$-distribution function $Q\left(\gamma \right)$ for (a) the generated state (8) and (b) the approximated state (10), using the same parameters as in Fig. 1.

Figure 3

(Color online) The $Q$-distribution function $Q\left(\gamma \right)$ for the generated state after passing three atoms through the cavity, for $\alpha =8$. The interaction times for the first atom, second atom, and the third atom are chosen such that $g{t}_1=8\pi$, $g{t}_2=4\pi$, and $g{t}_3=2\pi$.

Figure 4

The probability of detecting a probe atom in its ground state as a function of $\varphi$ for the generated superposition (7). The parameters used are the same as in Fig. 1 and the interaction time for the probe atom is selected such that $g{t}_p=1.5\pi$.

Figure 5

The decoherence of the approximated state (12) in terms of the Wigner function at different times, (a) for $\kappa t=0$, (b) for $\kappa t=1∕2{\mid \alpha \mid }^2$, (c) for $\kappa t=1∕{\mid \alpha \mid }^2$, and (d) for $\kappa t=2∕{\mid \alpha \mid }^2$, for $\mid \alpha \mid =4$.