Collective Quantum Jumps of Rydberg Atoms

We study an open quantum system of atoms with a long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective, and in fact, exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.

Figure 1

Two atoms. (a) When $\Delta =0$, $|ee⟩$ is uncoupled from the other states. (b) When $\Delta =V/2$, there is a resonant two-photon transition between $|gg⟩$ and $|ee⟩$. (c) Quantum trajectory simulation with $\Omega =1.5\gamma$, $\Delta =V/2=5\gamma$, showing Rydberg population of each atom over time. Atom 1 (solid blue line) emits at $t=14.4/\gamma$, which causes $⟨E_2⟩$ (dashed red line) to suddenly increase. Atom 2 then emits at $t=14.7/\gamma$. When no photons have been emitted for a while, the wave function approaches a steady state.

Figure 2

Photon correlation for two atoms with $V=10\gamma$. (a) Correlation vs $\Delta$ for $\Omega =0.5\gamma$. (b) Correlation as a function of $\Omega$ and $\Delta$ using color scheme on right.

Figure 3

(a) Fixed points of mean-field model as function of detuning for $\Omega =1.5\gamma$ and $V=10\gamma$. Stable (unstable) fixed points are denoted by solid (dashed) lines. (b) Mean-field bistable region (black) for $V=10\gamma$. (c) Photon correlation $g_{ij}^{(2)}$ for 16 atoms with same parameters as (b), using color scheme on right.

Figure 4

Quantum trajectory of 16 atoms showing average Rydberg population over time with $\Omega =1.5\gamma$, $V=10\gamma$, $\Delta =3.4\gamma$. (a) Quantum jumps between two metastable collective states. Red arrows point at the stable fixed points of mean-field theory. (b) and (c) are zoomed-in views, and red lines mark photon emissions. (b) Rapid succession of emissions around $t=232/\gamma$ causes a jump up. (c) Absence of emissions around $t=313/\gamma$ causes a jump down.

Figure 5

Statistics for $\Omega =1.5\gamma$, $V=10\gamma$, $\Delta =3.4\gamma$ comparing $N=4$, 8, 16. (a) Rydberg population $⟨E⟩$ after a number of simultaneous emissions from the steady-state wave function $|\psi {⟩}_{ss}$. (b) Length distribution of bright periods (in units of $1/\gamma$), using arbitrary threshold of $⟨E⟩=0.2$ and sampling rate of $10\gamma$. (c) Distribution of $⟨E⟩$. Red arrows point at stable fixed points of mean-field theory.