Sub-natural width N-type resonance in cesium atomic vapour: splitting in magnetic fields

Dimitar Slavov; Armen Sargsyan; David Sarkisyan; Rafayel Mirzoyan; Anna Krasteva; Arlene D Wilson-Gordon; Stefka Cartaleva

doi:10.1088/0953-4075/47/3/035001

1. Introduction

Although the coherent population trapping (CPT) and electromagnetically induced transparency (EIT) resonances have been successfully used for designing highly sensitive magnetometers and highly accurate atomic clocks, various research groups are still exploring suitable approaches aimed at a profitable combination of the advantages of CPT/EIT with other processes, in order to solve the problems associated with slow light, optical recording of information, quantum communication, etc [1, 2]. As an alternative, optical systems in which narrow-band N-type resonances appear, have been extensively studied recently (for simplicity, we will refer to them as N-resonances). The N-resonance can be considered as a type of three-photon resonance where a two-photon Raman excitation is combined with a resonant optical pumping field. A resonance of this type was first demonstrated [3] in hot Rb vapour as a Doppler-free sub-natural width absorption peak. There, Rb atoms are irradiated by a fixed-frequency coupling field and a scanning probe field. The resonance occurs when the frequency difference between the coupling and probe fields is equal to the hyperfine splitting of the ground state of Rb (while the coupling frequency is detuned from the corresponding transition by the value of the hyperfine splitting) and the probe field is tuned to the Doppler broadened atomic transition. In its characteristics, the N-resonance resembles the 'bright' resonance caused by electromagnetically induced absorption in a degenerate two-level system [4]. In [3, 4] the Λ system in the D₁ or D₂ line of rubidium atoms was used for N-resonance preparation.

One of the main advantages of this approach consists in the easy experimental formation of a high contrast N-resonance [5]. As shown in [6], high N-resonance contrast is achieved on the D₂ line of rubidium atoms due to strong collisional mixing of Zeeman sublevels in the electronic excited state, which suppresses the Zeeman optical pumping in the ground electronic state. In contrast, the CPT difference is smaller for the D₂ line than for the D₁ line, due to pressure broadening of the excited state hyperfine levels, as well as the existence of cycling transitions [7].

The authors of [8] describe the possibility of cancelling the frequency shift of the N-resonance induced by the electric field of the laser radiation, which is important for creating atomic clocks. The asymmetry of the N-resonance profile was studied in [9]. The authors of [10] showed that the N-resonance parameters can be improved by using three lasers due to a decrease in the frequency detuning of the coupling laser from the corresponding transition. Note that a buffer gas with pressure of 3–30 Torr was used in [5, 6, 8–10] to the form the N-resonance.

In this paper we report the first observation of an N-resonance in Cs atomic vapour. The previous experimental studies were done for Rb atoms where the frequency difference between the two hyperfine ground levels is significantly less than in the case of Cs.

To clarify the importance of the value of the ground-state hyperfine level splitting, a schematic diagram of N-resonance formation in ¹³³Cs atoms (D₂ line) is shown in figure 1. The lower levels used for formation of the Λ system are the ground F_g = 3, 4 levels and the upper level is 6P_3/2, which consists of four hyperfine levels F_e = 2, 3, 4, 5. The probe laser frequency ν_P is scanned over the F_g = 4 → F_e = 3, 4, 5 set of transitions and the coupling laser frequency ν_C is fixed. In the probe beam transmission spectrum, an N-resonance involving a two-photon process will be observed if the two-field frequency difference is ν_P − ν_C = Δ₀, where Δ₀ is the splitting (Δ₀ = 9.2 GHz) of the 6S_1/2 electronic ground-state hyperfine levels with no external magnetic field applied. Thus, as the coupling laser frequency decreases to ν_C = ν_P − Δ₀, a bright N-resonance occurs, characterized by an increase in absorption. Note that the efficiency of the two-photon transition strongly decreases with an increase in the value of Δ₀. Thus, the preparation of N-resonance on the D₂ line of Cs is a challenging task.

**Figure 1.** The Λ system of D₂ line ¹³³Cs atoms. The probe laser frequency ν_P scans the transitions *F_g* = 4 → *F_e* = 3, 4, 5 while the ν_c is fixed.
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2. Experimental results

2.1. Arrangement of the experiment

Figure 2 shows a schematic diagram of the experimental setup. Two narrow-band distributed feedback diode-laser (DFB) systems, used in our experiment, were built using: (i) a DFB diode produced by Eagleyard and (ii) a DFB diode produced by Toptica Photonics AG. The first system provides laser radiation tunable in the range between 851 and 853 nm, while the second one is tunable in the range between 851.2 and 853.7 nm, both with an emission spectral width less than 2 MHz (FWHM).

Typically, the two laser systems show mode-hopping free frequency detuning which largely exceeds the width of the absorption spectrum of the Cs D₂ line. The coupling laser has a fixed frequency ν_C, while the probe frequency ν_P is tuned over the D₂ line. Both laser beams have a spot size of 2 mm in diameter and are carefully superimposed on polarization beam splitter-PBS 3 and then directed at the cell containing the atomic vapour. The polarizations of the coupling and probe lasers are linear and mutually orthogonal. The L = 10 mm long cell is filled with atomic cesium with 20 Torr of neon gas added that serves as a buffer gas. Part of the probe radiation is directed to an additional cell with thickness L = 6 λ, which was used as a frequency [11].

The transmitted probe beam is detected by a silicon photodiode and recorded by a four-channel TDS2014B digital oscilloscope. An interference filter at λ = 852 nm was placed in front of the photodiode detecting the probe radiation. In order to cancel the laboratory magnetic field, a magnetic shield was used. In order to apply a longitudinal magnetic field, a set of Helmholtz coils (HC) was inserted inside the magnetic shield. The cell with atomic vapour is placed inside the HC. The probe and the coupling laser radiations were separated using the PBS 4 cube placed after the cell. The probe radiation is mainly detected, but in some experiments the coupling beam is recorded as well.

2.2. N-resonance formation in a cell with cesium vapour and a buffer gas

Here we illustrate the N-resonance in a thermal cell of L = 10 mm thickness filled with Cs vapour and buffered by 20 Torr of Ne. A good contrast up to 30% and sub-natural ∼1.5 MHz line width of the resonance were observed during the experiments. For the measurement of the line width, a much shorter frequency scan was used, and the optimal experimental conditions were chosen.

The probe and the coupling beams were brought into coincidence and directed at the buffered L = 10 mm cell. The probe laser power was 12 mW and the coupling laser power was ∼10 mW. The atomic source temperature was kept at ∼70 °C. Under this condition the density of the cesium atom was approximately 8 × 10¹¹ atoms cm⁻³. The coupling beam was fixed at a lower frequency (ν_C = −9193 MHz) than that of the maximum of the absorption profile of the F_g = 4 set of transitions. The probe beam frequency was scanned in a spectral region broader than 25 GHz, thereby providing the absorption spectrum of the D₂ line and the frequency position of the coupling beam. The absorption spectrum of the L = 6 λ cell was recorded simultaneously and used as a frequency [11].

The narrow, enhanced absorption N-resonance, superimposed on the absorption profile of the F_g = 4 set of transitions, is clearly seen in figure 3. Note that the amplitude of the resonance in absolute absorption is about 15%, which shows a very good signal-to-noise ratio and is promising for further applications of the resonance. The N-resonance frequency position is shifted from that of the coupling laser by the electronic ground-state hyperfine level splitting of Δ₀ = 9.2 GHz. In figure 3, only one N-resonance within the F_g = 4 set of transitions is observed, which is determined by the frequency position of the coupling laser. A similar resonance is also observable in the absorption profile of the F_g = 3 set, providing the coupling laser frequency is higher than that of the F_g = 3 set absorption profile by Δ₀ = 9.2 GHz. In figure 4, we present the N-resonance profile in more detail, obtained by the probe beam scanning over a much shorter frequency interval than in figure 3.

The probe laser frequency ν_P was scanned only over the F_g = 4 → F_e = 3, 4, 5 transitions and the coupling laser frequency ν_C was fixed (figure 1). Figure 4, curve (1), shows the N-type resonance detected in the absorption spectrum of the probe radiation. Here, the contrast of the resonance reaches ∼7% (it was determined as the ratio of the resonance amplitude to the peak absorption in the absence of the coupling radiation). The spectral width of the N-type resonance is ∼2 MHz. When the coupling or probe laser power increases, the N-resonance width also increases, but is accompanied by a significant enhancement of the resonance contrast, up to ∼30%. For comparison, curve (2) in figure 4 shows the absorption spectrum of the probe beam, when the coupling laser is off. In the experiment, the absorption signal from the fixed-frequency coupling beam was also measured, while scanning the frequency of the probe beam (figure 4, curve 3). It can be seen that the resonance observed in the coupling beam absorption is also of sub-natural width. Moreover, it is superimposed on a very low-level constant background as the coupling frequency is situated in the far wing of the absorption profile of the F_g = 4 set of transitions (see figure 3). Note that the coupling beam absorption is reduced, which can be attributed to the new photon emission during the Raman process (see figure 1). In figure 4 (curve 4), the absorption spectrum from the L = 6 λ cell is shown. This spectrum contains sub-Doppler-width, velocity selective optical pumping resonances, which are located exactly at the frequencies of hyperfine optical transitions of Cs vapour [11, 12].

2.3. N-resonance behaviour in an applied magnetic field

The good contrast and signal-to-noise ratio we obtained motivated us to study the splitting of the N-resonance in magnetic fields, for the D₂ line of ¹³³Cs atoms. Our experimental measurements have shown that the high contrast and the symmetric profile of the N-resonance can be used with very good accuracy to trace its behaviour in an applied magnetic field, starting from several gauss to several hundred gauss. In a magnetic field, the N-resonance splits into seven or eight components, depending on the mutual orientation of the field B and the direction k of the propagation of laser radiation. The B-field strength was measured by a calibrated Hall gauge. First we consider the resonance splitting in a longitudinal magnetic field B∣∣k, where the magnetic field is oriented along the direction of propagation of both laser beams. The top curve (1) in figure 5 presents the N-resonance profile (of line width 1.8 MHz) in the case of vanishing magnetic field B ≈ 0. The curves (2) and (3) demonstrate the splitting of the N-resonance into seven components in magnetic fields B = 7 G and 26 G, respectively. The powers of the coupling laser is P_c = 8 mW and the power of the probe laser is P_p = 12 mW. As can be seen from figure 5, all seven components have very good contrast and a width of approximately ∼1 MHz, which is smaller by a factor of 1.4 than the width of the initial N-resonance at B = 0. Similar narrowing was reported in [13], where the EIT resonance splitting in a magnetic field was studied.

**Figure 5.** N-resonance profile at (1) B = 0. N-resonance splitting into seven components in longitudinal magnetic fields (2) B = 7 G and (3) B = 26 G.
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Figure 6 shows a diagram related to the splitting of the F_g = 3 and F_g = 4 levels into 2F + 1 Zeeman sublevels (7 and 9 sublevels, respectively) in an applied longitudinal magnetic field. For clarity, the splitting of the upper 6P_3/2 level is not shown. The effect of the upper level manifests itself as a change in the detuning Δ, determined by the magnetic field splitting of the ground-state hyperfine levels. The change in Δ mainly affects the N-resonance amplitude but not its position. In figure 6, we show the pairs of coupling (ν_C) and probe (ν_P) laser frequencies that are involved in two-photon absorption starting from the lower F_g = 3 level to the upper F_g = 4 level of the electronic ground state. As is seen from the diagram, the frequency shift between neighbouring N-resonance components is 0.351 + 0.351 = 0.702 MHz G⁻¹ (note that this value is correct with an inaccuracy of 2% for longitudinal magnetic field B ⩽ 108 G). The values determining the shifts of Zeeman sublevels with magnetic quantum number m_F in a magnetic field are given in [14]. Using the value of the splitting of the N-type resonance, we measured the magnetic field B = 7 G for the middle curve in figure 5. The value of the higher magnetic field (figure 5, the lowest curve) was estimated to be 26 G.

We now discuss the resonance splitting in a transverse magnetic field where the field is oriented orthogonally to the direction of propagation of both laser beams B⊥k (no magnetic shield was used). Strong transverse magnetic fields were produced by two disc-shaped permanent magnets with diameter ⊘ = 50 mm, and a width of ∼30 mm. The permanent magnets were mounted on two nonmagnetic stages with the possibility of gradually adjusting the distance between them. The magnetic field in the cell increased when the permanent magnets approached each other (the technique of the measurement of the inhomogeneous magnetic field is described elsewhere [15]). Inside the laser beam the variation of magnetic field was of several gauss. The maximum available magnetic field value was 650 G (after some technical improvements it will be possible to reach more than 2 kG).

For this measurement, the N-resonances formed on the F_g = 4 → F_e = 3, 4, 5 set of transitions were used (figure 7). The highest possible power of both lasers (50 mW) was used, in order to obtain suitable resonance contrast for measuring larger magnetic fields. In a vanishing magnetic field (B = 0, curve 1), a single N-resonance is measured with 9 MHz line width. In an orthogonal magnetic field, the N-resonance splits into eight components (as for the dark resonances in Cs vapour [14]). Note, that for simple estimations of the frequency separation between neighbouring components the value of 0.702 MHz G⁻¹ can be used for B < 67 G (with an inaccuracy of 2%), while for B ∼ 650 G the inaccuracy increases up to ∼15% (this is simply caused by a fact that the shift of the ground levels is not linear in B), thus for large magnetic fields one must use the theoretical curves presented in figure 10 (the curves coincide with the experimental results with an inaccuracy of 3%, see below). The N-type resonances in an external magnetic field occur when the frequency difference between the coupling and probe fields [1] is given as

$\begin{equation} \nu _P - \nu _C = [E(F = 4, m_F) - E(F = 3, m_{F^{\prime }}))](h)^{-1}. \end{equation} \tag{ 1 }$

**Figure 7.** N-type resonance at (1) B = 0. The splitting of the N-resonance into eight components in transverse magnetic fields (2) B ∼ 632 G, (3) B ∼ 378 G and (4) ∼ 273 G. Frequency reference spectrum for the *F_g* = 4 set of transitions (5). The buffered cell temperature T = 74 °C. The power of the coupling and probe lasers is 50 mW. Different curves are shifted for the convenience of the readers.
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The theoretical dependence of the energies E(F = 4, m_F) and E(F = 3, m_F) of the hyperfine levels of F_g = 3, 4 of Cs atoms on the magnetic field have been calculated according to the known model described, e.g. in [16]), and is shown in figure 8. Note, that for the calculations of F_g = 3, 4 energy levels as a function of magnetic field the Breit–Rabi formula can also be used (see formula (74) in [1]).

**Figure 8.** Theoretical magnetic field dependence of the hyperfine structure of ¹³³Cs atoms with *F_g* = 3, 4. The numbers indicate the various *m_F* sublevels participating in the formation of the N-resonance components 1–8, for the case of a transverse magnetic field. The sublevels of *F_g* = 4 and *F_g* = 3 in high magnetic fields are determined by the projection *m_J* of the total angular momentum J of an electron and are equal to *m_J* = +1/2 and m + J = −1/2, respectively. The frequency slopes for the magnetic sublevels of *F_g* = 4 and *F_g* = 3 in high magnetic fields (B > 10 kG) asymptotically approach +1.39 MHz G⁻¹ and −1.38 MHz G⁻¹, respectively.
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Figure 9 shows the theoretical curves for the frequency shifts of the N-resonance components (1–7) versus the longitudinal external magnetic field with those obtained in the experiment indicated by black squares. The m_F sublevels participating in the formation of the N-resonance components 1–7 for the case of longitudinal magnetic field are shown in figure 6. As can be seen in figure 9, the experimental results are in good agreement with the theory.

Figure 10 shows the theoretical curves for the frequency shifts of the N-resonance (1–8) components in the transverse magnetic field. The experimental results are shown by black squares. As can be seen from figure 10, the experimental results are in good agreement with the theory. Note that for the large magnetic fields the satellites located near the N-resonance components (i.e. the existence of a double structure) could appear, similar to the results on double structure in the CPT-resonances detected in the paper [17].

In figure 11 the frequency slope in MHz G⁻¹ of 1–8 N-resonance components versus magnetic field is presented. As can be seen, the slopes for 1–7 curves becomes positive at B > 2.1 kG, and asymptotically approach s = 1.39 + 1.38 = 2.77 MHz G⁻¹ (see figure 8) at B > 10 kG, which is a manifestation of the hyperfine Paschen–Back regime (HPB) [16, 18–20]. The slope for the component labelled 8 (for B > 10 kG) approaches s = 0. As can be seen from figure 8, the energies of the sublevels (F_g = 4, m_F = −4) and (F_g = 3, m_F = −3) that participate in the formation of the component 8 at high magnetic field become parallel to each other, and the frequency distance between them becomes constant. In this way, the slope of the eighth component (figure 11) approaches zero.

The origin of this behaviour of the slopes of the N-resonances in the case of strong magnetic field lies in the fact that at fields B ≫ A_HFS/μ_B ≈ 1700 G (where A_HFS is the hyperfine coupling coefficient for 6S_1/2 and μ_B is the Bohr magneton), there is decoupling of the total angular momentum J of an electron and the nuclear magnetic moment I (for ¹³³Cs I = 7/2) and the sublevel splitting is described by the projections m_J and m_I (HPB regime [18, 19]). In this case, both groups of sublevels with m_J = +1/2 and m_J = −1/2 (each group consisting of eight energy sublevels shown in figure 8) demonstrate simple linear dependence of the energy as a function of magnetic field [21]:

$\begin{equation} E_{\mid J,m_j,I,m_I \rangle } = A_{{\rm HFS}}m_Jm_I + \mu _B (g_Jm_J + g_Im_I)B \end{equation} \tag{ 2 }$

where the values for nuclear (g_I) and fine structure (g_J) Lande factors, and hyperfine constants A_HFS are given in [21]. It should be noted that accurate investigations of the splitting of the hyperfine structure of the Na and Li-D-lines in high magnetic fields (including the observation of the Paschen–Back regime) using laser-atomic beam-spectroscopy were performed in [22, see citations therein].

3. Discussion of results

First we discuss the formation of the N-resonance (see [3, 5, 6, 8–10]). The processes behind the resonance are illustrated in figure 12. The probe radiation transfers atoms from the F_g = 4 level to the 6P_3/2 level from which decay to the F_g = 3, 4 levels takes place. This is the well known optical pumping process [20]: the F_g = 4 level suffers population loss (indicated by the small circle) while the population of the F_g = 3 level increases (indicated by the large circle). As a result, a two-photon Raman process occurs at a certain coupling laser frequency: an atom from level F_g = 3 absorbs a probe photon at frequency ν_P, emits a photon at frequency ν_C, and decays to the F_g = 4 level. This results in the formation of a narrow N-resonance feature in the probe radiation spectrum, characterized by enhanced absorption. The N-resonance amplitude is approximately exp[σ_TP(N₃ − N₄)L], where σ_TP is the cross section of the two-photon process (which depends on the detuning Δ₀, the coupling laser radiation intensity, and the probabilities of the F_g = 3 → 6P_3/2 and F_g = 4 → 6P_3/2 transitions).

Such a mechanism is supported by the substantial improvement in the N-resonance contrast when a buffer gas is used. This can be explained as follows: it is known that the lower levels of a Λ-system are only weakly broadened by a buffer gas in the pressure range 10–100 Torr (see figure 8 in review paper [1]). Thus, the dominating positive effect of buffer gas is an increase in atomic transit time t across the laser beam t = d/v, where d is the laser beam diameter and v is the atomic thermal velocity (i.e., the time t of interaction of laser radiation with an atom increases). The atom velocity (diffusion rate) in the presence of a buffer gas is several orders of magnitude lower than the atom velocity in pure rubidium vapour. For the case of an exact resonance between probe laser frequency ν_P and an atomic transition, the optical pumping efficiency is proportional to the interaction time t [23]. Therefore, more efficient optical pumping and an increase in N₄ are realized.

As mentioned in the introduction, the efficiency of the two-photon transition for Cs atoms is less than that of Rb atoms. Nevertheless, the N-resonance in our experiment is measured with very good resolution under typical experimental conditions. This could be attributed to the larger Cs atomic vapour density than for Rb. Moreover, due to the much higher value of Δ₀ for Cs atoms more effective hyperfine optical pumping is realized in a buffered cell containing Cs vapour than in one with Rb vapour. Note that the results presented here for Cs atoms, related to the N-resonance splitting in a magnetic field, are in a good agreement with the results published in recent papers [24, 25] for Rb atoms. Here we demonstrate the N-resonance formation mechanism for Cs atoms as well. From the comparison of N- and EIT resonance parameters (at various values of L), it can be deduced that it is practically easier to obtain a very good contrast to width ratio for the N-resonance than for the EIT resonance, for optical cells of reduced thickness (centimeters or millimeters). In the N-system discussed here (see figures 1 and 12), the two lower levels and the two upper levels (one is virtual) are separated by the hyperfine frequency. In the N-system discussed in [26, 27] which is the simplest model that can describe EIA, the lower two levels are Zeeman sublevels of the ground hyperfine state whereas the upper two levels are Zeeman sublevels of an excited hyperfine state. The mechanism for the formation of the sharp absorption peak in EIA is the spontaneous transfer of coherence from the excited Zeeman sublevels to the ground Zeeman sublevels. Here, such a mechanism cannot occur due to the large value of Δ₀.

4. Conclusions

We have recorded and studied for the first time the sub-natural width N-resonance on the D₂ line of Cs atoms in cells with thickness L = 10 mm in the presence of gaseous neon at a pressure of 20 Torr. The detected N-resonance contrast can reach 30%.

The behaviour of the N-resonance was investigated in an applied magnetic field showing that (i) when the field B is situated in the plane determined by electric field vectors of couple and probe radiations, the N-resonance splits into eight components and (ii) in the case of a longitudinal magnetic field, seven components occur. The investigations performed in a magnetic field demonstrate that the ground F_g = 3, 4 levels are involved in the N-resonance formation.

In the case of a transverse magnetic field, the frequency interval between the boundary components 1 and 8 is ∼4.914 MHz G⁻¹, which can be used to measure magnetic fields starting from ∼1 G.

In the future, we intend to fabricate and use a L = 30 μm thin cell filled with Cs and buffer gas that will allow us to use the permanent ring magnets and reach fields up to 2 kG, in order to realize and study in detail the hyperfine Paschen–Back regime.

The method presented here, based on the N-resonance, makes it possible to study in detail the behaviour of the ground-state levels of alkali atoms in a wide range of magnetic fields.

Taking into account the advantages provided by the N-resonance parameters and the simplicity of its experimental realization, the obtained results can be of interest for a large variety of fundamental and applied problems in optics and laser spectroscopy fields.

Acknowledgments

The research leading to these results has received funding from the European Union FP7/2007-2013 under grant agreement no 295025-IPERA. This work was partially supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme: 'Coherent optics sensors for medical applications-COSMA' (grant agreement no PIRSES-GA-2012-295264). Co-authors AS, RM and DS note that this work was also supported by State Committee Science MES RA, in frame of the research project no SCS 13-1C029.

Sub-natural width N-type resonance in cesium atomic vapour: splitting in magnetic fields

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Abstract

1. Introduction

2. Experimental results

2.1. Arrangement of the experiment

2.2. N-resonance formation in a cell with cesium vapour and a buffer gas

2.3. N-resonance behaviour in an applied magnetic field

3. Discussion of results

4. Conclusions

Acknowledgments

Sub-natural width N-type resonance in cesium atomic vapour: splitting in magnetic fields

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Submit

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Author e-mails

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Dates

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Abstract

1. Introduction

2. Experimental results

2.1. Arrangement of the experiment

2.2. N-resonance formation in a cell with cesium vapour and a buffer gas

2.3. N-resonance behaviour in an applied magnetic field

3. Discussion of results

4. Conclusions

Acknowledgments