State-selective imaging of cold atoms

Atomic coherence phenomena are usually investigated using single beam techniques without spatial resolution. Here we demonstrate state-selective imaging of cold ${}^{85}\text{R}\text{b}$ atoms in a three-level ladder system, where the atomic refractive index is sensitive to the quantum coherence state of the atoms. We use a phase-sensitive diffraction contrast imaging (DCI) technique which depends on the complex refractive index of the atom cloud. A semiclassical model allows us to analytically calculate the detuning-dependent refractive index of the system. The predicted Autler-Townes splitting and our experimental measurements are in excellent agreement. DCI provided a quantitative image of the distribution of the excited-state fraction, and compared with on-resonance absorption and blue cascade fluorescence techniques, was found to be experimentally simple and robust.

Figure 1

(Color online) Simplified Rb level scheme showing Rydberg states, ionization threshold, $5S\text{−}5P\text{−}5D$ ladder system used for state-selective imaging, and $6D$ state which leads to blue fluorescence at 420 nm. Atoms are cooled and maintained in the excited $5P$ state by the 780 nm laser. A 480 nm beam will excite to Rydberg states or photoionize the atoms, producing cold electrons. The excited-state atom distribution was determined by imaging the $5P\text{−}5D$ transition at 776 nm.

Figure 2

(Color online) Diffraction contrast imaging records the diffraction pattern of an off-resonant plane wave incident on a cold atom sample.

Figure 3

(Color online) Analytical result for the phase and absorption on the 776 nm transition for a three-level model of Rb, in the weak coupling limit on the 776 nm beam. The two-level results (dashed line) are clearly not valid for excited-state imaging.

Figure 4

(Color online) Calculated absorption and phase for the 776 nm transition, showing exact analytic (solid line) and first-order approximation [Eq. (6); dashed line], for typical experimental parameters (${\Delta }_{780}=-3\Gamma$, ${\Omega }_{780}=30\text{MHz}$).

Figure 5

(Color online) Simulation of diffraction contrast imaging, showing input excited-state column density (left-hand side), calculated excited-state diffraction pattern at $z=130\text{mm}$ (center), and retrieved column density (right-hand side). Vertical column density line profiles through the peak are shown below. The 776 nm probe beam was simulated with a Gaussian intensity profile of 5 mm FWHM, detuned $2{\Gamma }_{776}$ from absorption resonance. The retrieval was regularized with $\alpha =0.2$.

Figure 6

Normalized error (difference divided by sum) in the peak column density retrieved from simulated excited-state diffraction patterns at a propagation distance of 130 mm, for the object shown in Fig. 5.

Figure 7

(Color online) Simplified schematic of the imaging beam locking arrangement. Lenses, mirrors, wave plates omitted for clarity. The frequencies of the laser beams are given relative to the $F=3\to F^{\prime }=4$ (780 nm) and $F=4\to F^{\prime }=5$ (776 nm) transitions.

Figure 8

(Color online) Schematic of the imaging beam path and MOT vacuum chamber. Only two of the six cooling beams are shown.

Figure 9

(Color online) Attenuation of 780 nm and 776 nm light by a heated 10-cm-long vapor cell narrow-bandwidth atomic filter.

Figure 10

780 nm absorption images showing compression due to increase in magnetic field gradient. Uncompressed (left-hand side), field gradient 10 G/cm. Compressed (right-hand side), 100 ms at 50 G/cm. Cloud full width at half-maximum from Gaussian fit, $735\pm 20\mu \text{m}$ and $322\pm 12\mu \text{m}$, respectively. Both images: 10 ms exposure, $20\mu \text{s}$ pulse duration, 1.5 mW probe beam power.

Figure 11

(Color online) Theoretical (dashed line) and experimental (solid line) 420 nm fluorescence in the MOT for 780 nm cooling beam detunings of $-10.0\pm 0.5$ and $-20\pm 3\text{MHz}$.

Figure 12

(Color online) Blue fluorescence image (false color) of the uncompressed MOT for 780 nm excitation and 776 nm probe. 1 s exposure with 21 G/cm magnetic field gradient, $85°\text{C}$ vapor cell filter temperature. The fluorescence intensity is shown for a profile along the dashed line, with a Gaussian fit.

Figure 13

In-focus absorption image of atoms in the $5P$ state using 776 nm probe beam. Experimental parameters: 60 G/cm peak magnetic field gradient, 4 ms compression, $300\mu \text{W}$ probe beam power, $300\mu \text{s}$ pulse duration, 1 ms exposure, $85°\text{C}$ filter cell temperature. Line profile (right-hand side) and Gaussian best fit through the dashed line in the image.

Figure 14

Ground- and excited-state diffraction patterns, column density reconstructions, and column density line profiles. Experimental parameters for ground-state image: 60 G/cm peak magnetic field gradient, 4 ms field ramp, $-6\text{MHz}$ maximum cooling beam detuning, $850\mu \text{W}$ probe beam power, $30\mu \text{s}$ pulse duration, 1 ms exposure, $+2.5{\Gamma }_{780}$ probe detuning, 120 mm effective defocus. For excited-state image: 60 G/cm peak magnetic field gradient, 4 ms field ramp, $-6\text{MHz}$ maximum cooling beam detuning, $150\mu \text{W}$ probe beam power, $100\mu \text{s}$ pulse duration, 1 ms exposure, $+12.5\text{MHz}$ probe detuning ($+2{\Gamma }_{776}$ from absorption peak), 130 mm effective defocus.