Spatial correlations between Rydberg atoms in an optical dipole trap

We use direct spatial ion imaging of cold ${}^{85}$Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function, with and without light-shift potentials generated by an optical dipole trap. We find that the blockade radius depends on laser detunings and spatially varying light shifts. At certain laser detunings the probability of exciting Rydberg atoms at particular separations is enhanced, which we interpret to be a result of direct two-photon excitation of Rydberg atom pairs. The results are in accordance with predictions [F. Robicheaux and J. V. Hernández, Phys. Rev. A 72, 063403 (2005)] and a model we develop that accounts for a one-dimensional dipole-trap potential.

Figure 1

Experimental geometry: (a) A top view showing the crossed 780- and 480-nm excitation beams and the 1064-nm trap beam, with the $2w_0$ widths marked for the 480- and 1064-nm beams. The circle shows an estimate of the field of view of the microchannel plate (MCP) in the excitation plane (radius 25 $\mu$m). (b) A shadow image of the ODT above the tip imaging probe (TIP), and a sketch of the ion trajectories toward the MCP.

Figure 2

(a) Excitation spectrum without ODT for $66S_{1/2}$. Note the line asymmetry, with interaction-induced broadening for $\Delta >0$. The vertical lines show frequencies at which correlation functions are measured. Panels (b) and (c): Pair correlations for excitation of $66S_{1/2}$ at the indicated detunings. (d) Level diagrams for off-resonant excitation without ODT. The laser frequency is $f$, and the frequency to excite one Rydberg atom without interactions is $f_0$. Dotted lines indicate energy levels without interactions. Solid lines are energy levels with interactions. The diagram is for the case of blue detuning from $f_0$ ($\Delta >0$). The “two-photon resonance” for the direct excitation of two Rydberg atoms occurs when the interaction energy $V_{\mathrm{int}}/h=2\Delta$.

Figure 3

(a) Correlation function for resonant excitation of $59S_{1/2}$ without ODT. Panels (b)–(d): Correlation functions for excitation in the ODT, at the indicated detunings. (e) Spectra for excitation of $59S_{1/2}$ without ODT (black dashed curve) and with ODT (red [gray] solid curve). Vertical lines indicate the excitation frequencies used to acquire the correlation functions in panels (a)–(d). The 0-MHz line is for excitation without ODT; for the other lines the ODT is on. (f) Angular averages, $I\left(r\right)$, for the correlation functions in panels (a)–(d). The curves correspond to correlation functions as follows: black solid (a), red (gray) dashed (b), green (gray) dotted (c), and purple (dark gray) dot-dash (d). The vertical scale is labeled for the black solid curve; a vertical offset of 0.1 is applied between subsequent curves to allow visual discrimination. For $r$ less than the imaging resolution, each curve $I\left(r\right)$ drops to zero.

Figure 4

Measurements and predictions of the blockade radius $r_b$ for several $n{S}_{1/2}$ and $n{D}_{5/2}$ states, for zero detuning without ODT. Error bars on measurements are $\pm 10\%$ of the measured value, due to uncertainty in the magnification ratio calibration.

Figure 5

Blockade radius $r_b$ as a function of $\Delta$, the laser detuning from the trap-free transition. Measurements are for exciting states $59S_{1/2}$ [run 1 ($+$), run 2 ($\times$)] and $57D_{5/2}$ ($*$). Measurements at $\Delta =0$ are without ODT as in Fig. 4; other measurements are with ODT. Uncertainties are $\pm 10\%$. Predictions are lines, using the same excitation bandwidths as in Fig. 4. The light shift of the ground-Rydberg transition at the center of the ODT is $s_{\max }\approx 30$ MHz.

Figure 6

(a) Spatially dependent light shifts of the ground and Rydberg states, with $x$, $s_1$, and $s_2$, defined in text. Panels (b)–(d): Level diagrams for excitation of two Rydberg atoms from the ODT with the first step (b) on-resonant ($f_1=f$) for $S$ states and [(c), (d)] off-resonant ($f_1<f$) for (c) $S$ states and (d) $D$ states.