Generation of Einstein-Podolsky-Rosen-Entangled Radiation through an Atomic Reservoir

We propose a scheme for generating two-mode squeezing in high-$Q$ resonators using a beam of atoms with random arrival times, which acts as a reservoir for the field. The scheme is based on four-wave mixing processes leading to emission into two cavity modes, which are resonant with the Rabi sidebands of the atomic dipole transition, driven by a saturating classical field. At steady state the cavity modes are in an Einstein-Podolsky-Rosen state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, does not require atomic detection nor velocity selection, and can be realized by presently available experimental setups with microwave resonators.

Figure 1

Setup of the system. Atoms from a beam are prepared in a coherent superposition of two Rydberg states $|g⟩$ and $|e⟩$ by a combination of laser and microwave fields. The atoms have random arrival times, and a low pumping rate warrants that at most one atom is inside the resonator at a time [9, 10]. While in the cavity, the dipole transition $|g⟩\to |e⟩$ is saturated by a transverse microwave field, thereby pumping on resonance two nondegenerate modes of the resonator, which are led asymptotically to a two-mode squeezed state.

Figure 2

(a) Dipole transition $|g⟩\to |e⟩$ at frequency ${\omega }_0$ coupling to the classical field at frequency ${\omega }_L$. (b) Resulting ladder of the semiclassical dressed states $|\pm ⟩$. A transition $|+⟩\to |-⟩$ is accompanied by absorption (emission) of a photon of frequency ${\omega }_1$ (${\omega }_2$), and vice versa; see text.

Figure 3

(a) Schematic representation of the two-step procedure. In the plot, the expectation values of the operators ${\widehat{b}}_1^{†}{\widehat{b}}_1$ and ${\widehat{b}}_2^{†}{\widehat{b}}_2$ are shown as a function of time, in units of ${\tau }_0={\gamma }^{-1}$, for $\mu =0.97$. After a sufficiently long time $T$ the steady state $|0,0{⟩}_b$, corresponding to the two-mode squeezed state of the cavity modes, is reached with fidelity $F=0.98$. (b) Average photon number (dashed line) and total experimental time $T$, in seconds, as a function of $\mu$.