Thermometry of ultracold atoms by electromagnetically induced transparency

We report on systematic numerical and experimental investigations of electromagnetically induced transparency (EIT) to determine temperatures in an ultracold atomic gas. The technique relies on the strong dependence of EIT on atomic motion (i.e., Doppler shifts), when the relevant atomic transitions are driven with counterpropagating probe and control laser beams. Electromagnetically induced transparency permits thermometry with satisfactory precision over a large temperature range, which can be addressed by the appropriate choice of Rabi frequency in the control beam. In contrast to time-of-flight techniques, thermometry by EIT is fast and nondestructive, i.e., essentially it does not affect the ultracold medium. In an experimental demonstration we apply both EIT and time-of-flight measurements to determine temperatures along different symmetry axes of an anisotropic ultracold gas. As an interesting feature we find that the temperatures in the anisotropic atom cloud vary in different directions.

Figure 1

Level scheme of ${}^{87}$Rb used for the calculation.

Figure 2

Calculated EIT spectra for Doppler-sensitive beam alignment. The parameters are ${\alpha }_0=10$, ${\Omega }_c=0.45\Gamma$, $\gamma =0$, $T=10\mu$K (red dotted line), $T=30\mu$K (blue dash-dotted line), $T=50\mu$K (magenta dashed line), and $T=100\mu$K (black solid line). The inset shows a close-up around zero probe detuning.

Figure 3

(a) Residual absorption at two-photon resonance vs width of single-photon Doppler shifts $\Delta {\omega }_{\mathrm{D}}$ and EIT bandwidth $\Delta {\omega }_{\text{EIT}}$. The other parameters in the simulation are ${\alpha }_0=10$ and $\gamma =0$. The amount of residual absorption is color coded from 100$\%$ (red) to 0$\%$ (blue). (b) Derivative of the residual absorption vs Doppler width for EIT bandwidths $\Delta {\omega }_{\text{EIT}}$ of 0.05$\Gamma$ (black solid line), 0.09$\Gamma$ (red dashed line), and 0.12$\Gamma$ (magenta dash-dotted line) as indicated by the horizontal lines in (a).

Figure 4

(a) and (b) Residual absorption at two-photon resonance vs temperature $T$ and control Rabi frequency ${\Omega }_c$ for (a) $\gamma =0$ and (b) $\gamma =0.008\Gamma$ at ${\alpha }_0=10$. The amount of residual absorption is color coded from 100$\%$ (red) to 0$\%$ (blue). (c) and (d) Relative attainable temperature precision $\Delta T/T$ as obtained from the data shown in (a) and (b) (see the text for an explanation). The Rabi frequencies are ${\Omega }_c=0.74\Gamma$ (magenta dotted lines), ${\Omega }_c=0.63\Gamma$ (blue dash-dotted lines), ${\Omega }_c=0.54\Gamma$ (red dashed lines), and ${\Omega }_c=0.41\Gamma$ (black solid lines).

Figure 5

Schematic setup of the relevant part of the experiment for anticollinear beam alignment: 1, vacuum cell; 2, laser-cooled rubidium atoms; L, lens; QWP, quarter-wave plate; G, glass plate; C, collimation optics; MMF, multimode fiber; and APD, avalanche photo diode. For collinear beam alignment we replace the glass plate by a polarizing beam-splitter cube.

Figure 6

(a) EIT spectrum for collinear probe and control beams. (b) EIT spectra for anticollinear probe and control beams for different control beam powers (i.e., Rabi frequencies). Symbols represent experimental data. Solid lines indicate numerical fits. The numerical fit of the data in the collinear geometry yields the parameters ${\alpha }_0=7.5$, ${\Omega }_c=0.74\Gamma$, and $\gamma =0.008\Gamma$. The parameters in the numerical fit of the data in anticollinear geometries are ${\Omega }_c=0\Gamma$ (black squares), ${\Omega }_c=0.55\Gamma$ (magenta diamonds), ${\Omega }_c=0.85\Gamma$ (red circles), and ${\Omega }_c=1.55\Gamma$ (blue triangles) as well as $\gamma =0.008\Gamma$ in all cases. The fits yield a temperature of $T=150\mu$K in all four cases. We note that for the experiment in the anticollinear geometry we increased the density to ${\alpha }_0=19$. For all simulations we assumed realistic Gaussian profiles of beam intensities and density in the medium, which affects the shape of the plateau region.

Figure 7

(a) EIT spectrum and (b) time-of-flight absorption signal, taken after a 10-ms period of optical molasses. Symbols represent experimental and lines calculated data. The calculation parameters are (a) ${\alpha }_0=5.3$, ${\Omega }_c=0.45\Gamma$, $\gamma =0.008\Gamma$, and $T_{\text{long}}=115\left(30\right)\mu$K and (b) $T_{\text{trans}}=21\left(5\right)\mu$K.