Dephasing dynamics of Rydberg atom spin waves

A theory of Rydberg atom interactions is used to derive analytical forms for the spin-wave pair correlation function in laser-excited cold-atom vapors. This function controls the quantum statistics of light emission from dense, inhomogeneous clouds of cold atoms of various spatial dimensionalities. The results yield distinctive scaling behaviors on the microsecond time scale, including generalized exponential decay. A detailed comparison is presented with a recent experiment on a cigar-shaped atomic ensemble [Y. Dudin and A. Kuzmich, Science 336, 887 (2012)], in which Rb atoms are excited to a set of Rydberg levels.

Figure 1

Behavior of the spin-wave pair correlation function $g^{\left(2\right)}$ vs $n$ for an asymmetrical cloud having $(w_z,w_{\perp })=(15,6.4)\mu \mathrm{m}$, compared with the experimental data from Ref. [8] (black dots). Also shown are results from the double-spin-wave model (blue, dashed line). Experimental data are reprinted with permission from The American Association for the Advancement of Science (AAAS) and authors.

Figure 2

Asymptotic behavior of atom-pair interference function for double excitations of the $100s$ level. (a) Isotropic dipole-dipole interactions: Solid lines are numerical simulation for $D=1$ [blue (black)], 2 [red (dark gray)], and 3 [green (light gray)], compared with the long-time asymptotic behavior given by the modulus square of Eq. (10) (dashed lines). The green (light gray) dotted-dashed line includes the first asymptotic correction for $D=3$. (b) vdW interactions [color legend as in (a)]: The long-time behavior shows the square modulus of formula (12). The first-order asymptotic correction for $D=3$ is indistinguishable from the solid line. Parameters are given in the text.