High Quality of Electromagnetically Induced Transparency Spectroscopy of 87Rb in a Buffer Gas Cell with Magnetic Field

TL;DR

This study demonstrates high-resolution electromagnetically induced transparency spectroscopy of 87Rb vapor in a buffer gas cell under magnetic fields, enabling precise Zeeman splitting measurements and laser frequency locking.

Contribution

It introduces a spectral method with Doppler broadening removal for high-resolution Zeeman splitting measurement in 87Rb vapor with buffer gas and magnetic field.

Findings

EIT spectral lines become weaker and wider with buffer gas.

Doppler broadening can be fully removed using a weighted least-square fit.

The method allows high-resolution Zeeman splitting measurement and laser frequency locking.

Abstract

We have studied the phenomenon of electromagnetically induced transparency (EIT) of 87Rb vapor with a buffer gas in a magnetic field at room temperature. It is found that the spectral lines caused by the velocity selective optical pump effects get much weaker and wider when the sample cell mixed with a 5-Torr N2 gas while the EIT signal kept almost unchanged. A weighted least-square fit is also developed to remove the Doppler broadening completely. This spectral method provides a way to measure the Zeeman splitting with high resolution, for example, the {\Lambda}-type EIT resonance splits into four peaks on the D2 line of 87Rb in the thermal 2-cm vapor cell with a magnetic field along the electric field of the linearly polarized coupling laser. The high resolution spectrum can be used to lock the laser to a given frequency by tuning the magnetic field.

Full text

Electromagnetically induced transparency, Zeeman effect, rubidium atom

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I Introduction

The interesting coherent interaction of atoms with laser fields in three level $\Lambda$ configurations has attracted increasing attention in studies of nonlinear and quantum optics and spectroscopy recently. Electromagnetically induced transparency (EIT) is a quantum coherence effect which has a number of important applications such as laser cooling 975 , lasing without inversion 1121 , information storage 976 and magnetometry 1080 .

EIT resonance line-shape and line-width are of interest for many EIT applications. A narrow and high contrast EIT resonance is useful for many fields, especially for the study of spectroscopy 1531 ; 1397 and precision metrology 795 ; 1196 . In a three-level $\Lambda$ scheme, the line-width caused by the nonlinear effects in EIT is governed by the relaxation rate of ground state coherence, which is predominantly determined by the interaction time of the atom with the applied laser fields, i.e, by the average time-of-flight of an atom through the laser beam 1162 ; 1089 . To get a narrower EIT resonance, a buffer gas can be added to the atomic vapor to prolong the interaction time 1162 ; 1424 . The addition of a buffer gas slows the diffusion of the coherently prepared atoms through the laser beam by simultaneously preserving the ground state coherence as a result of the collisions over millions of buffer-gas 1068 . The line-width can be reduced by several orders of magnitude 1062 ; 1471 ; 1052 .

The line-shape of EIT resonance is also affected by the thermal motion of atoms in a vapor cell filled with a mixture of alkali atoms and inert gas at several Torr 1103 ; 1051 ; 1044 ; 483 ; 1489 . For example, Sarkisyan studied the effect of different pressure of buffer gas on the EIT resonances 1103 while Eugeniy et al. studied the influence of the laser detuning on the line shape of the EIT and observed that in the presence of a buffer gas an absorption resonance appears, which is different to the Lorentzian shape of the usual EIT resonance 1051 ; 1216 .

What’s more, compared to the case without buffer gas, the velocity selective optical pump (VSOP) effects when the vapor cell filled with a buffer gas will disappear due to the pumping process overridden by velocity-changing. Therefore, the EIT resonance will grow up on a broaden Gaussian background, which simplifies the analysis of the spectra and supplies a good way for us to study the EIT splitting with a high resolution spectrum in a magnetic field 1077 .

The EIT resonance in the $\Lambda$-system of the $D_{1}$ or $D_{2}$ line of Rb atoms in a magnetic field has been studied a lot both theoretically and experimentally 1102 ; 504 ; 1451 ; 1203 . In most cases, the magnetic field is either parallel to the laser propagation direction, where both coupling and probe fields are seen as combination of left- and right-circularly polarized ones, or orthogonal to the laser propagation direction but along the electric field of the probe laser, where only the coupling beam is seen as combined fields 1498 .

However, for the case with the magnetic field along the electric field of the coupling laser the Zeeman-splitting in magnetic fields is rarely studied. In our work, we use a vapor cell filled with 87Rb and 5 torr N2 to remove the VSOP peaks in the $\Lambda$-type EIT for $D_{2}$ line at room temperature and present an experimental observation of $\Lambda$-type EIT by applying an external magnetic field along the electric field of the coupling laser. A skill of weighted least-square fit is used to remove the Doppler broadening background. The observed spectrum is well explained by our theoretical simulation.

II Experimental setup

Our experimental setup for the $\Lambda-$type EIT of 87Rb in magnetic field is shown in Fig. 1(a) and the relative transition energy level diagram shown in Fig. 1(b). The arrangement for the optical elements is also detailed in our previous work 1496 . The coupling laser frequency is locked to a saturation absorption spectroscopy (SAS) system and the probe laser is scanned across the $D_{2}$ line levels.

The polarizations of the coupling and probe lasers are linear and mutually orthogonal. The beam size is around $1$ mm2 for each laser. The coupling and probe laser beams are carefully superimposed on one polarization beam splitter (PBS) and then adjusted to overlap almost completely throughout the cell. The spherical shaped Rb vapor cell is made of pyrex glass and has a size of diameter $2$ cm. The cell is filled with pure 87Rb and N2 buffer gas at a pressure of $5$ Torr at room temperature. There is no magnetic field shielding outside the Rb vapor cell. A long permanent magnet is placed near the cell to apply a magnetic field for the Rb atoms. The magnetic field direction is along the $y-$axis, which is parallel to the electric field of the coupling laser, and the strength can be controlled by changing the distance between the magnet and the cell. The strongest magnitude can be up to $500$ Gauss. The coupling field couples the hyperfine level $F=2$ of the ground state ${5}S_{1/2}$ and $F^{\prime}=2$ of the excited state ${5}P_{3/2}$ while the probe laser scans over the transitions from the ground state $F=1$ to the excited states ${5}P_{3/2}$ $F^{\prime}=0,1$ and $2$.

III Results and discussion

In fact, the $D_{2}$ line of 87Rb atoms are of multi-levels, and there will be some satellite peaks along with the EIT line due to the Doppler effect in the $\Lambda$ configuration 473 , which causes the observed spectrum very complicated. In our work, we use a pure 87Rb vapor cell filled with N2 buffer gas to decrease or remove this effect and only keep the EIT signal for high spectroscopy, which further helps us to study the EIT splitting in the magnetic field.

Figure 2 shows the observed EIT spectra without and with N2 buffer gas under no magnetic field. The coupling laser is locked to the transition $F=2$ to $F^{\prime}=1\&2$, where $F^{\prime}=1\&2$ means the cross-over peak between $F^{\prime}=1$ and $2$ due to the Doppler broadening in SAS configuration. In the case without buffer gas we can see an EIT peak with several VSOP peaks. Obviously, the EIT signal is much narrower than that of VSOP. However, if we fill the cell with 5 Torr N2, all the VSOP peaks will get much broadened and its magnitude also decreases greatly. This feature keeps the EIT peak to emerge on a very broadened background and therefore the effects of VSOP will not affect our observation for the spectral change of atom in external field in the ground state.

To remove the Doppler broadening background, we developed a numerical skill based on the least-square fit. The main idea is to set the weights of data points around the EIT peaks to zero and a fit of the data gives a Gaussian background which we can remove from the experimental data by a subtraction. Shown in Figs. 3(a)(b) are the experimental spectra without and with the magnetic field and their numerical processes, where we can see that the Doppler broadening is removed completely. In Fig. 3(b), the magnetic field is $B=44.3$ Gauss and along the $y-$axis, where the EIT spectral line splits into four peaks.

As observed in many previous works 1525 ; 1051 ; 1212 ; 1193 , the EIT spectral line-shape becomes asymmetric when the coupling laser detuned far away from resonance, which is re-investigated in our experiment as shown in Fig. 4. The detuning of the coupling laser varying from $-78.5$ to $346$ MHz causes the EIT resonance shifting within the absorption profile of the probe laser and the lineshape of the detuned EIT resonance becomes asymmetric and non-Lorentzian. In addition, an increasing detuning of the coupling frequency leads to a significant reduction of the amplitude of the EIT peaks 1451 , even inducing a dispersive line shape. For example, when the coupling field frequency detuned to $346$ MHz, an obvious dispersion-like resonant absorption peak appears. Our simulation considering the detuning coincides well with the experimental spectrum. If we apply a magnetic field to the atom, the hyperfine energy levels will split and the coupling laser detunes away from the resonant energies as well. It also causes the EIT spectral lines shows an asymmetric structure as shown in Fig. 3(b).

Unlike the case of atom in zero magnetic field, the degeneracy of the hyperfine levels is destroyed due to the Zeeman effect, forming 13 nondegenerate magnetic sublevels as shown in Fig. 1(b). Specially, for the case where the magnetic field is parallel to the electric field vector of the coupling laser along $y-$axis, we can simplify the complex transitions by decomposition. The coupling process corresponds to a $\pi$ transition while the probe beam has a $\sigma$ one which can be decomposed to be the combination of $\sigma^{+}$ and $\sigma^{-}$ transitions in the same weight. All possible transitions can form six $\Lambda-$type subsystems. The two sub-EIT peaks in the outside each contains one single subsystem, corresponding to the transitions from $F=1,m_{F}=1$ via $F^{\prime}=2,m_{F}^{\prime}=2$ to $F=2,m_{F}=2$ and $F=1,m_{F}=-1$ via $F^{\prime}=2,m_{F}^{\prime}=-2$ to $F=2,m_{F}=-2$, respectively. While the two sub-EIT peaks in the middle both contain two subsystems.

Shown in Fig. 5 is the spectrum of 87Rb in magnetic fields along the $y$-axis but at different magnetic field intensities. The magnetic field varies from $B=16$ Gauss to $B=98$ Gauss. Firstly, we can see that the four EIT peaks are linearly shifted away with the magnetic field increasing. Secondly, in the low magnetic field ($B=16$ Gauss), the amplitudes of the middle two peaks are smaller than the two peaks outside. An interesting phenomenon is that with the magnetic field increasing, the amplitudes of the two middle peaks become larger and larger than the ones outside. They do not keep a constant ratio at all as expected.

Usually the spectral line intensity is determined directly by the transition probability between different Zeeman sublevels, in our case, from $F=2$ to $F^{\prime}=2$. For example, the transition probabilities from $F=2,m_{F}=\pm 2$ to $F^{\prime}=2,m_{F}=\pm 2$ (corresponding to the two outside peaks) are two times larger than that of the transitions $F=2,m_{F}=\pm 1$ to $F^{\prime}=2,m_{F}=\pm 1$ (corresponding to the two inside peaks)1526 . It agrees with the observation at low magnetic field, i.e., at $B=16$ Gauss.

However, as discussed previously, the magnitude of the resonance is also dependent on the detuning of the coupling laser frequency from the corresponding atomic transition. To show the influence of the detuning caused by the magnetic field on the magnitude of the EIT resonance, we have a further comparison of with or without considering the detuning in our calculation, which is as shown in Fig. 6. The blue and red lines indicate the calculated results of considering or without considering the detuning, respectively. In the low magnetic field as shown in Fig. 6(a), the simulated spectral line intensity ratio $A_{1}^{\prime}/A_{2}^{\prime}$ having considered the detuning is almost the same with the ratio $A_{1}/A_{2}$ of the transition intensity, which indicates that in the low magnetic field, the amplitudes of EIT peaks are mainly determined by the transition intensities between different sub-levels and we can ignore the influence of the detuning on the amplitudes.

However, the detuning influence plays a more and more important role for the line intensity and position when the magnetic field increased. It is shown in Fig. 6(b), where we can see that the amplitude ratio $A_{1}^{\prime}/A_{2}^{\prime}$ considering the detuning decreased to $1$ from its original ratio $A_{1}/A_{2}=3.8$. This is because the outside EIT peaks own a much larger red- or blue-detuning, which distorts the resonant lineshape and reduces the amplitudes of their spectral line intensities significantly 1525 . For example, for the magnetic field of $B=98$ Gauss shown in Fig. 5(e), the detunings of the coupling laser for the peaks on the two outsides can reach more than $200$ MHz, resulting in a remarkable reduction of the spectral amplitudes. In addition, the simulated spectral line position also shifts a little. It also indicates that we have to choose a zero detuning line if this Doppler free technique is used for a laser frequency locking.

IV Conclusion

In this paper, we have observed a high resolution of EIT splittings in a Rb vapor cell with N2 buffer gas in a magnetic field at room temperature. With the additional 5 Torr N2, the VSOP peaks due to optical pumping almost disappeared and only the EIT signals were kept in the spectra due to the collision effects by the buffer gas. We present a method by a least-square fit to remove the Doppler broadening completely which keeps only the EIT peaks. These two techniques simplify the analysis of the observed EIT spectral splittings in the magnetic field. The dependence of splitting line shape and intervals of sub-EIT windows on the magnetic field have been investigated. When the applied magnetic field is along the polarization direction of the coupling laser, the EIT peak splits into four sub-ones. An asymmetric spectral lineshape can be observed for the deep detunings caused by the Zeeman level splitting. All experimental observations are well explained by a simulation considering the detuning effect. Our work provides a method to lock the laser to a given frequency by tuning the magnetic field.