Dissipative light scattering by a trapped atom approaching electromagnetically-induced-transparency conditions

We study the time dependence of the spectrum of inelastically scattered radiation from a trapped atom. The atom is illuminated by two lasers tuned to the electromagnetically induced transparency (EIT) of the free atom. For counterpropagating laser beams, rapid removal of vibrational energy is observed as the atom approaches near-EIT conditions. We show that the imbalance in the sidebands of the scattered radiation spectrum explains quantitatively the cooling of the center-of-mass motion of the trapped atom. We also examine parameters critical for EIT cooling in situations far from the Lamb-Dicke limit.

Figure 1

Trapped three-level atom in the presence of two counterpropagating lasers at the frequencies ${\omega }_{L1}$ and ${\omega }_{L2}$. The trap frequency is $\omega$.

Figure 2

Strength of sideband transitions from $n=20$ for three values of $\eta$.

Figure 3

Close up of EIT-resonance line shape in the Lamb-Dicke limit for absorption of laser 2 at the parameters used in the simulations. Frequencies, given in units of $2\pi$ MHz, are $g_1=1.3$, $g_2=0.3$, $\Delta =15$, and $\Gamma =6$. The effective detuning of laser 2 from the EIT resonance is defined as ${\delta }_{\mathrm{eff}}={\Delta }_2-{\Delta }_1$.

Figure 4

Map of populations in the three electronic states for cooling from the initial Fock state ($n=10$) in state $|2\rangle$.

Figure 5

Interaction force terms from laser L1 (upper line) and laser L2 (lower line) are compared to the response in mean position $\langle \mathcal{Q}\rangle$ (full line) and momentum $\langle \mathcal{P}\rangle$ (dashed line). Also shown is the difference between mean kinetic and potential energy. The top row gives the result when the initial Fock state ($n=10$) is in the electronic state $|2\rangle$. In the bottom row, the system is initially in the electronic state $|1\rangle$.

Figure 6

Vibrational energy transfer rates from Eq. (34) are shown in the left and center images. The time-integrated loss rate is compared to the value of $\langle n\rangle$ in the right images Eq. (41). The top row gives the result when the initial Fock state ($n=10$) is in the electronic state $|2\rangle$. In the bottom row, the system is initially in the electronic state $|1\rangle$.

Figure 7

Steady-state spectral distribution of scattered radiation from the strong laser 1 (left) and from laser 2 (right) in the immediate vicinity of the elastic peaks.

Figure 8

Steady-state spectral distribution of scattered radiation from the strong laser 1 (left) and from laser 2 (right) including the Mollow contributions. The spectral contributions at frequencies ${\omega }^{\prime }<0$ are given by the dashed lines; the full lines refer to ${\omega }^{\prime }>0$.

Figure 9

Excitation profile and Mollow triplet under EIT conditions with blue detuning. In our example, the actual ratio of $\omega :\Delta =1:500$.

Figure 10

Temporal development of radiation scattered from each laser beam during the cooling process. The result for the strong laser 1 is given in the left figure, and that of laser 2 is given in the right figure. The spectra are calculated at the times indicated in each figure.

Figure 11

Summed spectra of scattered radiation show preferential blue emission at early times in the cooling process. As the cooling proceeds, the stationary-state spectrum predicted from Eq. (43) is reached. The spectra are calculated at the times indicated in the figure.

Figure 12

Cooling rate $\mathcal{R}(t)$ resulting from unbalanced scattering of laser radiation from Eq. (46) is given by the dots. It closely follows the predictions for the negative cooling rate $-d\langle {\stackrel{\wedge }{\mathcal{H}}}_{\mathrm{cm}}\rangle /\mathit{dt}$ obtained by adding Eqs. (37), (38), and (40), which is represented by the full line.