Engineering superpositions of coherent states in coherent optical pulses through cavity-assisted interaction

We propose a scheme to engineer quantum superpositions of coherent states (“Schrödinger-cat states”) of propagating optical pulses. Multidimensional and multipartite cat states can be generated simply by reflecting coherent optical pulses successively from a single-atom cavity. The influences of various sources of noise, including atomic spontaneous emission and pulse-shape distortion, are characterized through detailed numerical simulation, which demonstrates the practicality of this scheme within the reach of current experimental technology.

Figure 1

(Color online) (a) Schematic setup for generation of cat states by reflecting a coherent optical pulse from a single-atom cavity. (b) The relevant level structure of the atom trapped in the cavity.

Figure 2

(Color online) Pulse-shape functions for the input and output pulses. The solid curve shows the shape of the input pulse. The dashed-dotted, dashed, and dotted curves correspond to the output pulses with $g=0$ (for the atom in the level ∣0⟩), $g∕\kappa =3$, and $g∕\kappa =6$, respectively. In the calculation, we assumed ${\gamma }_s=\kappa$.

Figure 3

(Color online) The cat-state fidelity shown as a function of the average input photon number ${\mid \alpha \mid }^2$ when the spontaneous-emission rate is set to zero $({\gamma }_s=0)$. Other parameters are $g∕\kappa =3$ and $\kappa T=210$ for the solid curve; $g∕\kappa =6$ and $\kappa T=210$ for the dotted curve (exactly overlapped with the solid curve); $g∕\kappa =6$ and $\kappa T=100$ for the dash-dotted curve; and $g∕\kappa =6$ and $\kappa T=400$ for the dashed curve.

Figure 4

(Color online) (a) The cat-state fidelity shown as a function of the average photon number ${\mid \alpha \mid }^2$ of the input pulse. The dash-dotted, dashed, and solid curves correspond to $g∕\kappa =3$, $g∕\kappa =6$, and $g∕\kappa =10$, respectively. (b) The fidelity shown as a function of the coupling rate $g$. The solid and dashed curves correspond to the average input photon number ${\mid \alpha \mid }^2=1$ and ${\mid \alpha \mid }^2=3$, respectively. In both calculations for (a) and (b), we have taken ${\gamma }_s=\kappa$ and $\kappa T=210$.

Figure 5

(Color online) The cat state fidelity shown as a function of the mode-matching efficiency $ϵ$. The solid, dashed, and dash-dotted curves correspond to ${\mid \alpha \mid }^2=1$, ${\mid \alpha \mid }^2=2$, and ${\mid \alpha \mid }^2=3$, respectively. Other parameters are ${\gamma }_s=\kappa$, $g=6\kappa$, and $\kappa T=210$.