Optimal Squeezing in Resonance Fluorescence via Atomic-State Purification

Squeezing of atomic resonance fluorescence is shown to be optimized by a properly designed environment, which can be realized by a quasiresonant cavity. Optimal squeezing is achieved if the atomic coherence is maximized, corresponding to a pure atomic quantum state. The atomic-state purification is achieved by the backaction of the cavity field on the atom, which increases the atomic coherence and decreases the atomic excitation. For realistic cavities, the coupling of the atom to the cavity field yields a purity of the atomic state of more than 99%. The fragility of squeezing against dephasing is substantially reduced in this scenario, which may be important for various applications.

Figure 1

Sketch of the coherently driven TLA inside a quasiresonant cavity with losses. The fluorescent light is detected (D) out the side of the cavity. Wavy lines indicate light fields driving the atom, emitted into the cavity, out of the cavity, or out the side of the cavity. Straight arrows indicate the frequencies of the atomic resonance and the quasiresonant cavity mode.

Figure 2

Dependence of the following quantities on ${\delta }_a$: atomic excitation $⟨{\widehat{A}}_{22}⟩$ (blue, dashed line), CPAE $|⟨{\widehat{A}}_{12}⟩{|}^2$ (green crosses), and maximum CPAE $⟨{\widehat{A}}_{11}⟩⟨{\widehat{A}}_{22}⟩$ (red circles), cavity excitation $⟨{\widehat{a}}^{†}\widehat{a}⟩$ (violet, dashed-dotted line), normally ordered field variance of the fluorescence of a TLA in the cavity (light blue, solid curve), and in free space (black, dotted curve). The straight line (black, solid) marks the free-space maximal squeezing of $-1/8$. The system parameters are ${\Omega }_{\mathrm{R}}/g=14$, $\kappa /g=1.58$, $\Gamma /g=0.04\overline{3}$, ${\delta }_c/g=-34$.

Figure 3

Normally ordered field variance over ${\delta }_a$ for different dephasings ${\Gamma }_{\mathrm{D}}$. From bottom to top: ${\Gamma }_{\mathrm{D}}/\Gamma =0$, 2, 4, 6, 8. The inset shows the dependence of the squeezing on ${\Gamma }_{\mathrm{D}}$ at the cavity resonance, ${\delta }_a=-19g$. All other parameters are as in Fig. 2.