Deterministic generation of tailored-optical-coherent-state superpositions

Pulsed coherent excitation of a two-level atom strongly coupled to a resonant cavity mode will create a superposition of two coherent states of opposite amplitudes in the field. By choosing proper parameters of interaction time and pulse shape the field after the pulse will be almost disentangled from the atom and can be efficiently outcoupled through cavity decay. The fidelity of the generation approaches unity if the atom-field coupling strength is much larger than the atomic and cavity decay rates. This implies a strong difference between even and odd output photon number counts. Alternatively, the coherence of the two generated field components can be proven by phase-dependent annihilation of the generated nonclassical superposition state by a second pulse.

Figure 1

Scheme of the system.

Figure 2

(Color online) Wigner function of the intracavity field for a rectangular pulse with Rabi frequency $\eta =\sqrt{8}g$ and strong coupling $\kappa =\gamma =g∕100$ at time $gt=2\pi$.

Figure 3

(Color online) Evolution of upper-state population (solid line), photon number (divided by 10, dashed line), and the trace of the squared atomic density matrix (dot-dashed line) for parameters as in Fig. 2.

Figure 4

(Color online) Atomic population (solid line), photon number divided by 10 (dashed line), and trace of the squared atomic density matrix for a Gaussian pulse (dot-dashed line) of duration $\tau =g∕5$ with peak Rabi frequency $\eta =9_g$ and strong coupling $\kappa =\gamma =g∕100$.

Figure 5

(Color online) Wigner function of the intracavity field for the parameters of Fig. 4 after the pulse.

Figure 6

(Color online) (a) Maximum negative value of the Wigner function of the intracavity field and photon number as a function of atomic decay rate $\gamma$. (b) Probability distribution for $x$ (dashed) and $y$ solid quadratures of the intracavity field for the parameters of Fig. 4.

Figure 7

(Color online) Simulated accumulated photocurrent (300 traces) for the two field quadratures ($x$, left; $y$, right) during the time of the decay of the intracavity field after the pulse.

Figure 8

(Color online) (a) Probabilities of counting an even (solid line) and odd (dashed line) number of photons as functions of a field shift along the $x$ quadrature. (b) Probability of vacuum state after the second pulse as a function of the atomic phase shift between pulses for three different delay times ${\delta }_t\kappa =1∕100,{\delta }_t\kappa =1∕8,{\delta }_t\kappa =1∕4$.

Figure 9

(Color online) $Q$ function of the field after the second pulse for different atomic phase shifts $\varphi =(0,\pi )$ between the pulses.