Angular momentum alignment-to-orientation conversion in the ground state of Rb atoms at room temperature

We investigated experimentally and theoretically angular momentum alignment-to-orientation conversion created by the joint interaction of laser radiation and an external magnetic field with atomic rubidium at room temperature. In particular, we were interested in alignment-to-orientation conversion in the atomic ground state. In the experiment the laser frequency was fixed to the hyperfine transitions of the $D_1$ line of rubidium. To simulate the measured signals we used a theoretical model that takes into account all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. The experiments were carried out by exciting the atoms with linearly polarized laser radiation. Two orthogonal circularly polarized laser induced fluorescence (LIF) components were detected and afterward their difference was taken. The combined LIF signals originating from the hyperfine magnetic sublevel transitions of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ rubidium isotopes were included. The alignment-to-orientation conversion can be incontrovertibly identified in the difference signals for various laser frequencies, and a change in signal shapes can be observed when the laser power density is increased. We studied the formation of and the underlying physical processes behind the observed signals of the LIF components and their difference by performing an analysis of the influence of incoherent and coherent effects. We performed simulations of theoretical signals that showed the influence of ground-state coherent effects on the LIF difference signal.

Figure 1

Frequency shifts of the magnetic sublevels $m_F$ of the excited-state fine-structure level $5^2{P}_{1/2}$ as a function of magnetic field for ${}^{85}\mathrm{Rb}$. Zero frequency shift corresponds the excited-state fine-structure level $5^2{P}_{1/2}$.

Figure 2

Frequency shifts of the magnetic sublevels $m_F$ of the ground-state fine-structure level $5^2{S}_{1/2}$ as a function of magnetic field for ${}^{85}\mathrm{Rb}$. Zero frequency shift corresponds to the ground-state fine-structure level $5^2{S}_{1/2}$.

Figure 3

Excitation and observation geometry. The linearly polarized excitation laser light $\vec{E}$ can be split into two circularly polarized excitation light components ${\sigma }_{\mathrm{Exc}}^{\pm }$ and one linearly polarized excitation light component ${\pi }_{\mathrm{Exc}}^0$.

Figure 4

Side view of the experimental setup. The beam enters the coils at an angle of ${45}^{\circ }$ with respect to the $y$ axis in the $yz$ plane (axes shown in the inset).

Figure 5

LIF of a single circularly polarized light component ($I_L$). Black dots: experimental data; red dashed curve: theoretical data (left axis); colored lines: theoretical data without averaging over the Doppler profile (right axis). Magenta solid curve (dark gray): central velocity group of ${}^{85}\mathrm{Rb}$; orange curve (light gray): central velocity group of ${}^{87}\mathrm{Rb}$; blue short-dashed curves: negative velocity shift; green short-dotted curves: positive velocity shift.

Figure 6

The colored lines represent the dependence of the energy difference between various pairs of magnetic sublevels on magnetic field. $\mathrm{\Delta }\nu =0$ corresponds to laser frequency equal to the $F_g=2\to F_e=2$ hyperfine transition of the ${}^{85}\mathrm{Rb}$. (Only pairs crossing $\mathrm{\Delta }\nu =0$ are shown.)

Figure 7

Dependence of the Rabi frequency squared ${\mathrm{\Omega }}_R^2$ on the laser power density $I$ together with a linear fit for all the fixed laser frequencies used in the experiment (colored data points).

Figure 8

The dependence of the difference between the two LIF components on the hyperfine transitions to which the laser frequency was fixed. The laser frequency was fixed to (a) $F_g=2\to F_e=3$, (b) $F_g=2\to F_e=2$, (c) $F_g=3\to F_e=3$, (d) $F_g=3\to F_e=2$ hyperfine transition of ${}^{85}\mathrm{Rb}$. (a)–(d) laser frequencies are in descending order.

Figure 9

The first row (a)–(c) shows the signal of a single circularly polarized LIF component $I_L$ as a function of laser power density. The second row (d)–(f) shows the corresponding circularity dependence on laser power density for the case when the laser frequency was fixed to the $F_g=2\to F_e=3$ hyperfine transition of ${}^{85}\mathrm{Rb}$. Black dots: experimental data; red curve: theoretical calculation.

Figure 10

Red dashed curve (left axis): theoretical data of the difference between two circularly polarized light components ($I_L-I_R$) with averaging over the Doppler profile. Colored curves (right axis): theoretical data of the difference between two circularly polarized light components without averaging over the Doppler profile. Different colors represent various velocity groups from the Doppler profile. Magenta solid curve (dark gray): central velocity group; blue short-dashed curves: negative velocity shift; green short-dotted curves: positive velocity shift.

Figure 11

$I_L-I_R$ dependence on the magnetic field from the central velocity group; averaging over the Doppler profile is omitted. Red curve: theoretical data from ${}^{85}\mathrm{Rb}$ with Rabi frequency 100 MHz with large ${\gamma }_{\text{nondiagonal}}$; black curve: theoretical data from ${}^{85}\mathrm{Rb}$ with Rabi frequency 100 MHz with normal ${\gamma }_{\text{nondiagonal}}$.