Dark Raman resonances due to Ramsey interference in vacuum vapor cells

We investigate the evolution of the atomic coherence between Zeeman sublevels with $\Delta m_F=2$ in the region between pump and probe laser beams, in a Rb vapor cell using the Hanle configuration. The transmission of the probe beam, placed inside the hollow pump beam, shows the narrowing of the Hanle resonance (at external magnetic field $B=0$) by Ramsey fringes whose separation from the central peak depends on the distance between the beams. The temporal evolution of the pump induced alignment is evident from the changes of the probe transmission spectra with increasing the angle between linear polarizations of each beam. Experimental results are in agreement with the results of the model which calculates probe fluorescence by solving time-dependent optical Bloch equations, from the time when atom enters the pump beam to the time when it leaves the probe beam. The results for total excited state populations were averaged over atomic velocities distribution.

Figure 1

(a) Schematic of atomic energy level diagram for ${}^{87}\mathrm{Rb}$ $D1$ line ground and excited levels, (b) the energy level diagram for magnetic sublevels of the $F_g=2\to F_e=1$ transition, and (c) pump and probe laser beam radial profiles used in the theoretical model. In (a) and (b) solid lines represent laser light coupling energy levels and dotted lines show the deexcitation paths from excited levels.

Figure 2

(Color online) Calculated dependence of spontaneous emission and of ground state coherence between Zeeman sublevels as a function of radial position of an atom (as atom passes through the pump beam, the “dark region,” and the probe region) for different values of $B$. First column: Spontaneous emission from the excited $F_e=2$ hyperfine level. Second column: the real (solid line) and imaginary (dashed line) parts of Zeeman coherence induced between $m_F=0$ and $m_F=-2$ Zeeman sublevels of $F_g=2$. Results are given for the magnetic field values of 0, 50, 170, and $290\mathrm{mG}$, for four rows top to bottom and average pump and probe powers of $2\mathrm{mW}$ and $20\mu \mathrm{W}$, respectively. Polarizations of the pump and probe beam are linear and parallel to each other. The results are for the atom velocity of $260\mathrm{m}∕\mathrm{s}$ and its trajectory is along the probe beam diameter. The distances which atoms travel through the pump, “dark” and probe regions are 3.5, 1.7, $1.5\mathrm{mm}$, respectively.

Figure 3

Experimental setup. ECDL: external cavity diode laser, OI: optical isolator, DDAVLL: Doppler free dichroic atomic laser lock, BS: beam splitter, I: iris, P: polarizer, VNDF: variable neutral-density filter, BE: beam expander, M: mirrors, $\lambda ∕2$: retardation plate, D: photodiode detector.

Figure 4

(Color online) Calculated (a) and measured (b) probe transmission for the $F_g=2\to F_e=1$ transition in ${}^{87}\mathrm{Rb}$ as a function of the axial magnetic field. Dashed and dotted lines are for two inner pump beam diameters 5 and $7\mathrm{mm}$ (corresponding to the “dark region” length of 1.7 and $2.7\mathrm{mm}$), respectively. The broad resonance in (b) is for the pump beam turned off (solid line). Both pump and probe beams have the same linear polarization. The probe laser power is $10\mu \mathrm{W}$, while the pump laser power is $0.55\mathrm{mW}$.

Figure 5

(Color online) Theoretical (a) and experimental (b) results of probe transmission spectra for the $F_g=2\to F_e=1$ transition in ${}^{87}\mathrm{Rb}$, for linearly polarized pump and probe beams and different probe beam polarization angles in respect to the pump beam polarization (0° solid, 20° dash-dot-dot, 45° dotted, 70° dash-dot, and 90° dashed lines). The probe and pump powers are $20\mu \mathrm{W}$ and $1.8\mathrm{mW}$, respectively.

Figure 6

Theoretical (a) and experimental (b) values of $B$ required to obtain the first transmission peak as a function of the angle of the probe beam polarization. Solid lines are used to guide the eye. Theoretical (c) and experimental (d) variation of EIT amplitude as a function of angle of the probe polarization.