Quantum correlations of an atomic ensemble via an incoherent bath

A rich variety of quantum features can be found in a collection of atoms driven only by an incoherent bath. To demonstrate this, we discuss a sample of three-level atoms in ladder configuration interacting via the surrounding bath, and show that the fluorescence light emitted by this system exhibits nonclassical properties. Realizations could be thermal baths for microwave transitions, or incoherent broadband fields for optical transitions. In a small sample of atoms, the emitted light can be switched from sub- to super-Poissonian and from antibunching to superbunching controlled by the mean number of atoms in the sample. Larger samples allow us to generate superbunched light over a wide range of bath parameters and thus fluorescence light intensities. We also identify parameter ranges where the fields emitted on the two transitions are strongly correlated or anticorrelated, such that the Cauchy-Schwarz inequality is violated. As in a moderately strong bath this violation occurs also for larger numbers of atoms, such samples exhibit macroscopic quantum effects.

Figure 1

The system setup. A sample of $N$ atoms, each with three atomic states in ladder configuration, is confined to a region small as compared to the emission wavelengths $\lambda$. The whole setup is placed in an incoherent bath. The excited states decay spontaneously with rates $2{\gamma }_{1\left(2\right)}$, giving rise to fluorescence lights with nonclassical features.

Figure 2

(Color online) Plot of the second-order correlation function $g_{11}^{\left(2\right)}\left(0\right)$ against bath parameters ${\eta }_1$, ${\eta }_2$. The number of atoms in the sample is $N=150$.

Figure 3

(a) The second-order correlation function $g_{11}^{\left(2\right)}\left(0\right)$ for small numbers of atoms $N$ in the sample. Solid, long dashed, and short dashed curves are for ${\eta }_1={\eta }_2=1$, $0.5$, and $0.1$, respectively. Noninteger values for $N$ are possible if $N$ is a mean number of atoms, e.g., for atoms crossing a cavity field. Triangles (squares) denote bunching (antibunching). (b) $g_{11}^{\left(2\right)}\left(\tau \right)$ vs delay time $\tau$. (i) $N=15,{\eta }_1={\eta }_2=0.6$; (ii) $N=6,{\eta }_1=0.8,{\eta }_2=0.05$; (iii) $N=1,{\eta }_1={\eta }_2=0.2$.

Figure 4

The cross-correlation function $g_{12}^{\left(2\right)}\left(0\right)$ against bath parameters ${\eta }_1={\eta }_2$. The number of atoms in the sample is (i) $N=2$, (ii) $N=50$, and (iii) $N=150$. (a) ${\eta }_1={\eta }_2$, (b) ${\eta }_2$ chosen such that the SNR on both transitions is above 10.

Figure 5

The Cauchy-Schwarz parameters ${\chi }_1$ shown vs bath parameters ${\eta }_1={\eta }_2\equiv \eta$. The solid, long-dashed, and short-dashed curves are plotted for $N=4$, $10$, and $150$.