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

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2014 J. Phys. B: At. Mol. Opt. Phys. 47 035001

(http://iopscience.iop.org/0953-4075/47/3/035001)

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Journal of Physics B: Atomic, Molecular and Optical Physics

J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 035001 (8pp) doi:10.1088/0953-4075/47/3/035001

Sub-natural width N-type resonance incesium atomic vapour: splitting inmagnetic fields

Dimitar Slavov1, Armen Sargsyan2, David Sarkisyan2,Rafayel Mirzoyan2,4, Anna Krasteva1, Arlene D Wilson-Gordon3

and Stefka Cartaleva1

1 Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko Shosse boulevard,1784 Sofia, Bulgaria2 Institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak-2, 0203, Armenia3 Department of Chemistry, Bar-Ilan University, Ramat Gan 52900, Israel

E-mail: rafayelm@gmail.com and stefka_cartaleva@yahoo.com

Received 27 September 2013, revised 4 December 2013Accepted for publication 18 December 2013Published 10 January 2014

AbstractThe sub-natural width N-type resonance in a �-system, on the D2 line of Cs atoms is studiedfor the first time in the presence of a buffer gas (neon) and the radiations of two continuousnarrow-band diode lasers. A L = 1 cm long cell is used to investigate the N-type process. TheN-type resonance in a magnetic field for 133Cs atoms is shown to split into seven or eightcomponents, depending on the magnetic field and laser radiation directions. The resultsobtained indicate that the levels Fg = 3, 4 are the initial and final ones in the N-resonanceformation. The experimental results with magnetic field agree well with theoreticaldescriptions.

Keywords: N-type resonance, sub-natural resonance, bright resonance, coherent process,two-photon Raman process

(Some figures may appear in colour only in the online journal)

1. Introduction

Although the coherent population trapping (CPT) andelectromagnetically induced transparency (EIT) resonanceshave been successfully used for designing highly sensitivemagnetometers and highly accurate atomic clocks, variousresearch groups are still exploring suitable approaches aimedat a profitable combination of the advantages of CPT/EITwith other processes, in order to solve the problems associatedwith slow light, optical recording of information, quantumcommunication, etc [1, 2]. As an alternative, optical systemsin which narrow-band N-type resonances appear, have beenextensively studied recently (for simplicity, we will refer tothem as N-resonances). The N-resonance can be considered asa type of three-photon resonance where a two-photon Ramanexcitation is combined with a resonant optical pumping field.

4 Author to whom any correspondence should be addressed.

A resonance of this type was first demonstrated [3] in hot Rbvapour as a Doppler-free sub-natural width absorption peak.There, Rb atoms are irradiated by a fixed-frequency couplingfield and a scanning probe field. The resonance occurs when thefrequency difference between the coupling and probe fields isequal to the hyperfine splitting of the ground state of Rb (whilethe coupling frequency is detuned from the correspondingtransition by the value of the hyperfine splitting) and theprobe field is tuned to the Doppler broadened atomic transition.In its characteristics, the N-resonance resembles the ‘bright’resonance caused by electromagnetically induced absorptionin a degenerate two-level system [4]. In [3, 4] the � system inthe D1 or D2 line of rubidium atoms was used for N-resonancepreparation.

One of the main advantages of this approach consists in theeasy experimental formation of a high contrast N-resonance[5]. As shown in [6], high N-resonance contrast is achievedon the D2 line of rubidium atoms due to strong collisional

0953-4075/14/035001+08$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK

J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 035001 D Slavov et al

Figure 1. The � system of D2 line 133Cs atoms. The probe laserfrequency νP scans the transitions Fg = 4 → Fe = 3, 4, 5 while theνc is fixed.

mixing of Zeeman sublevels in the electronic excited state,which suppresses the Zeeman optical pumping in the groundelectronic state. In contrast, the CPT difference is smaller forthe D2 line than for the D1 line, due to pressure broadening ofthe excited state hyperfine levels, as well as the existence ofcycling transitions [7].

The authors of [8] describe the possibility of cancellingthe frequency shift of the N-resonance induced by the electricfield of the laser radiation, which is important for creatingatomic clocks. The asymmetry of the N-resonance profilewas studied in [9]. The authors of [10] showed that theN-resonance parameters can be improved by using three lasersdue to a decrease in the frequency detuning of the couplinglaser from the corresponding transition. Note that a buffer gaswith pressure of 3–30 Torr was used in [5, 6, 8–10] to the formthe N-resonance.

In this paper we report the first observation of anN-resonance in Cs atomic vapour. The previous experimentalstudies were done for Rb atoms where the frequency differencebetween the two hyperfine ground levels is significantly lessthan 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 infigure 1. The lower levels used for formation of the � systemare the ground Fg = 3, 4 levels and the upper level is 6P3/2,which consists of four hyperfine levels Fe = 2, 3, 4, 5. Theprobe laser frequency νP is scanned over the Fg = 4 →Fe = 3, 4, 5 set of transitions and the coupling laser frequencyνC is fixed. In the probe beam transmission spectrum, anN-resonance involving a two-photon process will be observedif the two-field frequency difference is νP − νC = �0, where�0 is the splitting (�0 = 9.2 GHz) of the 6S1/2 electronicground-state hyperfine levels with no external magnetic fieldapplied. Thus, as the coupling laser frequency decreases toνC = νP − �0, a bright N-resonance occurs, characterized byan increase in absorption. Note that the efficiency of the two-photon transition strongly decreases with an increase in the

Figure 2. Schematic diagram of the experiment: DFB—distributedfeedback diode—laser, PBS—polarization beam splitter,HC—Helmholtz coils, (3)—photo diodes, M—mirror, F—neutraloptical filters, interference filter of a wavelength of 852 nm, anddigital oscilloscope; magnetic shielding was used in the case of thelongitudinal magnetic field measurement.

value of �0. Thus, the preparation of N-resonance on the D2

line of Cs is a challenging task.

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 DFBdiode produced by Eagleyard and (ii) a DFB diode produced byToptica Photonics AG. The first system provides laser radiationtunable in the range between 851 and 853 nm, while the secondone is tunable in the range between 851.2 and 853.7 nm, bothwith an emission spectral width less than 2 MHz (FWHM).

Typically, the two laser systems show mode-hopping freefrequency detuning which largely exceeds the width of theabsorption spectrum of the Cs D2 line. The coupling laser hasa fixed frequency νC, while the probe frequency νP is tunedover the D2 line. Both laser beams have a spot size of 2 mmin diameter and are carefully superimposed on polarizationbeam splitter-PBS 3 and then directed at the cell containingthe atomic vapour. The polarizations of the coupling and probelasers are linear and mutually orthogonal. The L = 10 mmlong cell is filled with atomic cesium with 20 Torr of neon gasadded that serves as a buffer gas. Part of the probe radiationis directed to an additional cell with thickness L = 6 λ, whichwas used as a frequency [11].

The transmitted probe beam is detected by a siliconphotodiode and recorded by a four-channel TDS2014B digitaloscilloscope. An interference filter at λ= 852 nm was placed infront of the photodiode detecting the probe radiation. In orderto cancel the laboratory magnetic field, a magnetic shield wasused. In order to apply a longitudinal magnetic field, a set ofHelmholtz coils (HC) was inserted inside the magnetic shield.The cell with atomic vapour is placed inside the HC. Theprobe and the coupling laser radiations were separated usingthe PBS 4 cube placed after the cell. The probe radiation is

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Figure 3. Large detuning of the probe beam frequency over thecouple-probe beating signal (showing the fixed-frequency positionof the coupling beam) and both sets of hyperfine transitions startingfrom Fg = 4 and Fg = 3 levels. (1) Absorption spectrum of the D2

line involving the N-resonance situated within the Fg = 4 set oftransitions. (2) Absorption spectrum of the L = 6 λ cell, used as afrequency reference.

mainly detected, but in some experiments the coupling beamis recorded as well.

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

Here we illustrate the N-resonance in a thermal cell ofL = 10 mm thickness filled with Cs vapour and buffered by20 Torr of Ne. A good contrast up to 30% and sub-natural∼1.5 MHz line width of the resonance were observed duringthe experiments. For the measurement of the line width, a muchshorter frequency scan was used, and the optimal experimentalconditions were chosen.

The probe and the coupling beams were brought intocoincidence and directed at the buffered L = 10 mm cell.The probe laser power was 12 mW and the coupling laserpower was ∼10 mW. The atomic source temperature was keptat ∼70 ◦C. Under this condition the density of the cesiumatom was approximately 8 × 1011 atoms cm−3. The couplingbeam was fixed at a lower frequency (νC = −9193 MHz) thanthat of the maximum of the absorption profile of the Fg =4 set of transitions. The probe beam frequency was scannedin a spectral region broader than 25 GHz, thereby providingthe absorption spectrum of the D2 line and the frequencyposition of the coupling beam. The absorption spectrum ofthe L = 6 λ cell was recorded simultaneously and used as afrequency [11].

The narrow, enhanced absorption N-resonance,superimposed on the absorption profile of the Fg = 4 set oftransitions, is clearly seen in figure 3. Note that the amplitudeof the resonance in absolute absorption is about 15%, whichshows a very good signal-to-noise ratio and is promising forfurther applications of the resonance. The N-resonancefrequency position is shifted from that of the coupling laser

Figure 4. Probe beam scanning in smaller frequency interval,involving only the N-resonance. (1) Probe laser absorption spectrumwith enhanced absorption N-type resonance; (2) probe beamabsorption only—the coupling beam is blocked; (3) narrow reducedabsorption N-type resonance observed in the absorption of thefixed-frequency coupling beam, for the scanned probe; (4) referencespectrum obtained by means of L = 6 λ cell. Only the Fg = 4 → Fe =4, 5 transitions are situated in the range of the probe beam scan. Thecoupling laser frequency is fixed. The cell temperature is T ∼ 70 ◦C.The powers of the coupling and probe lasers are 10 mW. Here theabsorption is presented in arbitrary units and the correspondingcurves are shifted for the reader’s convenience.

by the electronic ground-state hyperfine level splitting of�0 = 9.2 GHz. In figure 3, only one N-resonance within theFg = 4 set of transitions is observed, which is determinedby the frequency position of the coupling laser. A similarresonance is also observable in the absorption profile of theFg = 3 set, providing the coupling laser frequency is higherthan that of the Fg = 3 set absorption profile by �0 = 9.2 GHz.In figure 4, we present the N-resonance profile in more detail,obtained by the probe beam scanning over a much shorterfrequency interval than in figure 3.

The probe laser frequency νP was scanned only overthe Fg = 4 → Fe = 3, 4, 5 transitions and the couplinglaser frequency νC was fixed (figure 1). Figure 4, curve(1), shows the N-type resonance detected in the absorptionspectrum of the probe radiation. Here, the contrast of theresonance reaches ∼7% (it was determined as the ratio ofthe resonance amplitude to the peak absorption in the absenceof the coupling radiation). The spectral width of the N-typeresonance is ∼2 MHz. When the coupling or probe laserpower increases, the N-resonance width also increases, butis accompanied by a significant enhancement of the resonancecontrast, up to ∼30%. For comparison, curve (2) in figure 4shows the absorption spectrum of the probe beam, when thecoupling laser is off. In the experiment, the absorption signalfrom 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 inthe coupling beam absorption is also of sub-natural width.Moreover, it is superimposed on a very low-level constantbackground as the coupling frequency is situated in the far

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Figure 5. N-resonance profile at (1) B = 0. N-resonance splittinginto seven components in longitudinal magnetic fields (2) B = 7 Gand (3) B = 26 G.

wing of the absorption profile of the Fg = 4 set of transitions(see figure 3). Note that the coupling beam absorption isreduced, which can be attributed to the new photon emissionduring the Raman process (see figure 1). In figure 4 (curve4), the absorption spectrum from the L = 6 λ cell isshown. This spectrum contains sub-Doppler-width, velocityselective optical pumping resonances, which are locatedexactly at the frequencies of hyperfine optical transitions of Csvapour [11, 12].

2.3. N-resonance behaviour in an applied magnetic field

The good contrast and signal-to-noise ratio we obtainedmotivated us to study the splitting of the N-resonancein magnetic fields, for the D2 line of 133Cs atoms. Ourexperimental measurements have shown that the high contrastand the symmetric profile of the N-resonance can be usedwith very good accuracy to trace its behaviour in an appliedmagnetic field, starting from several gauss to several hundredgauss. In a magnetic field, the N-resonance splits into seven oreight components, depending on the mutual orientation of thefield 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 longitudinalmagnetic field B || k, where the magnetic field is orientedalong the direction of propagation of both laser beams. Thetop curve (1) in figure 5 presents the N-resonance profile (ofline width 1.8 MHz) in the case of vanishing magnetic fieldB ≈ 0. The curves (2) and (3) demonstrate the splitting of theN-resonance into seven components in magnetic fields B =7 G and 26 G, respectively. The powers of the coupling laseris Pc = 8 mW and the power of the probe laser is Pp = 12 mW.As can be seen from figure 5, all seven components havevery good contrast and a width of approximately ∼1 MHz,which is smaller by a factor of 1.4 than the width of the initialN-resonance at B = 0. Similar narrowing was reported in [13],where the EIT resonance splitting in a magnetic field wasstudied.

Figure 6 shows a diagram related to the splitting of theFg = 3 and Fg = 4 levels into 2F + 1 Zeeman sublevels

Figure 6. Diagram of the Fg = 3 and Fg = 4 level splitting inlongitudinal magnetic field into 7 (with mF = 0, 1, 2, 3) and 9 (withmF = 0, 1, 2, 3, 4 ) sublevels, respectively. Respective pairs ofcoupling (νC) and probe (νP) laser frequency components are shown,forming seven N resonances. For simplicity, the splitting of theupper 6P levels is not shown.

(7 and 9 sublevels, respectively) in an applied longitudinalmagnetic field. For clarity, the splitting of the upper 6P3/2 levelis not shown. The effect of the upper level manifests itselfas a change in the detuning �, determined by the magneticfield splitting of the ground-state hyperfine levels. The changein � mainly affects the N-resonance amplitude but not itsposition. In figure 6, we show the pairs of coupling (νC)and probe (νP) laser frequencies that are involved in two-photon absorption starting from the lower Fg = 3 level to theupper Fg = 4 level of the electronic ground state. As is seenfrom the diagram, the frequency shift between neighbouringN-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 valuesdetermining the shifts of Zeeman sublevels with magneticquantum number mF in a magnetic field are given in [14].Using the value of the splitting of the N-type resonance, wemeasured the magnetic field B = 7 G for the middle curve infigure 5. The value of the higher magnetic field (figure 5, thelowest curve) was estimated to be 26 G.

We now discuss the resonance splitting in a transversemagnetic field where the field is oriented orthogonally tothe direction of propagation of both laser beams B ⊥ k(no magnetic shield was used). Strong transverse magneticfields were produced by two disc-shaped permanent magnetswith diameter � = 50 mm, and a width of ∼30 mm. Thepermanent magnets were mounted on two nonmagnetic stageswith the possibility of gradually adjusting the distance betweenthem. The magnetic field in the cell increased when thepermanent magnets approached each other (the techniqueof the measurement of the inhomogeneous magnetic fieldis described elsewhere [15]). Inside the laser beam thevariation of magnetic field was of several gauss. The maximumavailable magnetic field value was 650 G (after some technicalimprovements it will be possible to reach more than 2 kG).

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Figure 7. N-type resonance at (1) B = 0. The splitting of theN-resonance into eight components in transverse magnetic fields(2) B ∼ 632 G, (3) B ∼ 378 G and (4) ∼ 273 G. Frequencyreference spectrum for the Fg = 4 set of transitions (5). The bufferedcell temperature T = 74 ◦C. The power of the coupling and probelasers is 50 mW. Different curves are shifted for the convenience ofthe readers.

For this measurement, the N-resonances formed on theFg = 4 → Fe = 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 measuringlarger magnetic fields. In a vanishing magnetic field (B =0, curve 1), a single N-resonance is measured with 9 MHzline width. In an orthogonal magnetic field, the N-resonancesplits into eight components (as for the dark resonances in Csvapour [14]). Note, that for simple estimations of the frequencyseparation between neighbouring components the value of0.702 MHz G−1 can be used for B < 67 G (with an inaccuracyof 2%), while for B ∼ 650 G the inaccuracy increases up to∼15% (this is simply caused by a fact that the shift of theground levels is not linear in B), thus for large magnetic fieldsone must use the theoretical curves presented in figure 10(the curves coincide with the experimental results with aninaccuracy of 3%, see below). The N-type resonances in anexternal magnetic field occur when the frequency differencebetween the coupling and probe fields [1] is given as

νP − νC = [E(F = 4, mF ) − E(F = 3, mF ′ ))](h)−1. (1)

The theoretical dependence of the energies E(F = 4, mF )

and E(F = 3, mF ) of the hyperfine levels of Fg = 3, 4 of Csatoms on the magnetic field have been calculated accordingto the known model described, e.g. in [16]), and is shown infigure 8. Note, that for the calculations of Fg = 3, 4 energylevels as a function of magnetic field the Breit–Rabi formulacan also be used (see formula (74) in [1]).

Figure 9 shows the theoretical curves for the frequencyshifts of the N-resonance components (1–7) versus thelongitudinal external magnetic field with those obtained inthe experiment indicated by black squares. The mF sublevelsparticipating in the formation of the N-resonance components1–7 for the case of longitudinal magnetic field are shown in

Figure 8. Theoretical magnetic field dependence of the hyperfinestructure of 133Cs atoms with Fg = 3, 4. The numbers indicate thevarious mF sublevels participating in the formation of theN-resonance components 1–8, for the case of a transverse magneticfield. The sublevels of Fg = 4 and Fg = 3 in high magnetic fields aredetermined by the projection mJ of the total angular momentum J ofan electron and are equal to mJ = +1/2 and m + J = −1/2,respectively. The frequency slopes for the magnetic sublevels ofFg = 4 and Fg = 3 in high magnetic fields (B > 10 kG)asymptotically approach +1.39 MHz G−1 and −1.38 MHz G−1,respectively.

Figure 9. Magnetic field dependence of the frequency shifts of theN-resonance components 1–7 in a longitudinal magnetic field (fielddirection is parallel to the laser beam direction). Solid lines aretheoretical curves. Black squares indicate the experimental results(the size of the squares represents an experimental error of ∼3%).

figure 6. As can be seen in figure 9, the experimental resultsare in good agreement with the theory.

Figure 10 shows the theoretical curves for the frequencyshifts of the N-resonance (1–8) components in the transversemagnetic field. The experimental results are shown by blacksquares. As can be seen from figure 10, the experimental resultsare in good agreement with the theory. Note that for the largemagnetic fields the satellites located near the N-resonancecomponents (i.e. the existence of a double structure) couldappear, 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 1–8N-resonance components versus magnetic field is presented.

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Figure 10. Magnetic field dependence of the frequency shifts of theN-resonance 1–8 components. Field direction is perpendicular to thelaser beam direction (the B-field direction is along the linearpolarization of the probe radiation). Solid lines are the theoreticalcurves. Closed black squares are the experimental points and thesize of the squares represents an experimental error of ∼3%.Although experimental results are presented for low magnetic fields,nevertheless the theoretical curves are presented up to 3000 G, inorder to show that the hyperfine Paschen–Back regime (HPB)begins at higher magnetic fields [18].

Figure 11. Frequency slope (s) in MHz G−1 of eight componentsversus magnetic field. The slopes of 1–7 curves at B > 1.1 kG arepositive and asymptotically approach s = 2.77 MHz G−1 forB > 10 kG. For the same conditions, the slope for the componentlabelled 8 approaches s = 0.

As can be seen, the slopes for 1–7 curves becomes positiveat 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 amanifestation of the hyperfine Paschen–Back regime (HPB)[16, 18–20]. The slope for the component labelled 8 (forB > 10 kG) approaches s = 0. As can be seen from figure 8,the energies of the sublevels (Fg = 4, mF = −4) and (Fg = 3,mF = −3) that participate in the formation of the component8 at high magnetic field become parallel to each other, and thefrequency distance between them becomes constant. In thisway, the slope of the eighth component (figure 11) approacheszero.

Figure 12. Illustration related to the N-resonance formation. Theprobe radiation in resonance with the transition Fg = 4 → 6P3/2

transfers atoms from level Fg = 4 to level Fg = 3, increasing itspopulation (large circle) and decreasing the population of the Fg = 4level (small circle). Thus, significant difference between the groundlevel populations (N3 > N4) occurs. When the condition νP − νC =�0 is satisfied, a strong absorption of the probe radiation νP occursvia a two-photon process Fg = 3 → Fg = 4, resulting in N-resonanceformation detected in the νP field.

The origin of this behaviour of the slopes of theN-resonances in the case of strong magnetic field lies in thefact that at fields B AHFS/μB ≈ 1700 G (where AHFS isthe hyperfine coupling coefficient for 6S1/2 and μB is the Bohrmagneton), there is decoupling of the total angular momentumJ of an electron and the nuclear magnetic moment I (for133Cs I = 7/2) and the sublevel splitting is described by theprojections mJ and mI (HPB regime [18, 19]). In this case,both groups of sublevels with mJ = +1/2 and mJ = −1/2(each group consisting of eight energy sublevels shown infigure 8) demonstrate simple linear dependence of the energyas a function of magnetic field [21]:

E|J,mj,I,mI〉 = AHFSmJmI + μB(gJmJ + gImI )B (2)

where the values for nuclear (gI) and fine structure (gJ) Landefactors, and hyperfine constants AHFS are given in [21]. Itshould be noted that accurate investigations of the splittingof the hyperfine structure of the Na and Li-D-lines in highmagnetic fields (including the observation of the Paschen–Back regime) using laser-atomic beam-spectroscopy wereperformed 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 areillustrated in figure 12. The probe radiation transfers atomsfrom the Fg = 4 level to the 6P3/2 level from which decay tothe Fg = 3, 4 levels takes place. This is the well known opticalpumping process [20]: the Fg = 4 level suffers populationloss (indicated by the small circle) while the population ofthe Fg = 3 level increases (indicated by the large circle).As a result, a two-photon Raman process occurs at a certain

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coupling laser frequency: an atom from level Fg = 3 absorbs aprobe photon at frequency νP, emits a photon at frequencyνC, and decays to the Fg = 4 level. This results in theformation of a narrow N-resonance feature in the proberadiation spectrum, characterized by enhanced absorption.The N-resonance amplitude is approximately exp[σTP(N3 −N4)L], where σTP is the cross section of the two-photonprocess (which depends on the detuning �0, the coupling laserradiation intensity, and the probabilities of the Fg = 3 → 6P3/2

and Fg = 4 → 6P3/2 transitions).Such a mechanism is supported by the substantial

improvement in the N-resonance contrast when a buffer gasis used. This can be explained as follows: it is known thatthe lower levels of a �-system are only weakly broadened bya buffer gas in the pressure range 10–100 Torr (see figure 8in review paper [1]). Thus, the dominating positive effect ofbuffer gas is an increase in atomic transit time t across thelaser 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 oflaser radiation with an atom increases). The atom velocity(diffusion rate) in the presence of a buffer gas is severalorders of magnitude lower than the atom velocity in purerubidium vapour. For the case of an exact resonance betweenprobe laser frequency νP and an atomic transition, the opticalpumping efficiency is proportional to the interaction time t[23]. Therefore, more efficient optical pumping and an increasein N4 are realized.

As mentioned in the introduction, the efficiency of thetwo-photon transition for Cs atoms is less than that ofRb atoms. Nevertheless, the N-resonance in our experimentis measured with very good resolution under typicalexperimental conditions. This could be attributed to the largerCs atomic vapour density than for Rb. Moreover, due to themuch higher value of �0 for Cs atoms more effective hyperfineoptical pumping is realized in a buffered cell containing Csvapour than in one with Rb vapour. Note that the resultspresented here for Cs atoms, related to the N-resonancesplitting in a magnetic field, are in a good agreement with theresults published in recent papers [24, 25] for Rb atoms. Herewe demonstrate the N-resonance formation mechanism for Csatoms as well. From the comparison of N- and EIT resonanceparameters (at various values of L), it can be deduced that it ispractically easier to obtain a very good contrast to width ratiofor the N-resonance than for the EIT resonance, for opticalcells of reduced thickness (centimeters or millimeters). In theN-system discussed here (see figures 1 and 12), the two lowerlevels and the two upper levels (one is virtual) are separatedby the hyperfine frequency. In the N-system discussed in[26, 27] which is the simplest model that can describe EIA, thelower two levels are Zeeman sublevels of the ground hyperfinestate whereas the upper two levels are Zeeman sublevels of anexcited hyperfine state. The mechanism for the formation ofthe sharp absorption peak in EIA is the spontaneous transferof coherence from the excited Zeeman sublevels to the groundZeeman sublevels. Here, such a mechanism cannot occur dueto the large value of �0.

4. Conclusions

We have recorded and studied for the first time the sub-naturalwidth N-resonance on the D2 line of Cs atoms in cells withthickness L = 10 mm in the presence of gaseous neon at apressure of 20 Torr. The detected N-resonance contrast canreach 30%.

The behaviour of the N-resonance was investigated in anapplied magnetic field showing that (i) when the field B issituated in the plane determined by electric field vectors ofcouple and probe radiations, the N-resonance splits into eightcomponents and (ii) in the case of a longitudinal magneticfield, seven components occur. The investigations performedin a magnetic field demonstrate that the ground Fg = 3, 4 levelsare involved in the N-resonance formation.

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

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

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

Taking into account the advantages provided by theN-resonance parameters and the simplicity of its experimentalrealization, the obtained results can be of interest for a largevariety of fundamental and applied problems in optics andlaser spectroscopy fields.

Acknowledgments

The research leading to these results has received funding fromthe European Union FP7/2007-2013 under grant agreementno 295025-IPERA. This work was partially supportedby a Marie Curie International Research Staff ExchangeScheme Fellowship within the 7th European CommunityFramework Programme: ‘Coherent optics sensors for medicalapplications-COSMA’ (grant agreement no PIRSES-GA-2012-295264). Co-authors AS, RM and DS note that this workwas also supported by State Committee Science MES RA, inframe of the research project no SCS 13-1C029.

References

[1] Wynands R and Nagel A 1999 Appl. Phys. B 68 1[2] Fleischhauer M, Imamoglu A and Marangos J P 2005 Rev.

Mod. Phys. 77 633[3] Zibrov A S, Ye C Y, Rostovtsev Y V, Matsko A B

and Scully M O 2002 Phys. Rev. A 65 043817[4] Lezama A, Barreiro S and Akulshin A M 1999 Phys. Rev. A

59 4732[5] Zibrov S, Novikova I, Phillips D F, Taichenachev A V,

Yudin V I, Walsworth R L and Zibrov A S 2005 Phys. Rev.A 72 011801

[6] Novikova I, Phillips D F, Zibrov A S, Walsworth R L,Taichenachev A V and Yudin V I 2006 Opt. Lett. 31 2353

7

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[7] Taichenachev A V, Yudin V I, Velichansky V L, Zibrov A Sand Zibrov S A 2006 Phys. Rev. A 73 013812

[8] Novikova I, Phillips D F, Zibrov A S, Walsworth R L,Taichenachev A V and Yudin V I 2006 Opt. Lett. 31 622

[9] Hancox C, Hohensee M, Crescimanno M, Phillips D Fand Walsworth R L 2008 Opt. Lett. 33 1536

[10] Ben-Aroya I and Eisenstein G 2011 Opt. Express 19 9956[11] Cartaleva S, Saltiel S, Sargsyan A, Sarkisyan D, Slavov D,

Todorov P and Vaseva K 2009 J. Opt. Soc. Am. B 26 1999[12] Sargsyan A, Leroy C, Pashayan-Leroy Y, Sarkisyan D,

Slavov D and Cartaleva S 2012 Opt. Commun. 285 2090[13] Iftiquar S M and Natarajan V 2009 Phys. Rev. A 79 013808[14] Wynands R, Nagel A, Brandt S, Meschede D and Weis A 1998

Phys. Rev. A 58 196[15] Sargsyan A, Hakhumyan G, Papoyan A, Sarkisyan D,

Atvars A and Auzinsh M 2008 Appl. Phys. Lett. 93 021119[16] Auzinsh M, Budker D and Rochester S M 2010 Optically

Polarized Atoms: Understanding Light–Atom Interactions(Oxford: Oxford University Press) ISBN978-0-19-956512-2

[17] Taichenachev A V, Yudin V I, Velichansky V Land Zibrov S A 2005 JETP Lett. 82 398

[18] Olsen B A, Patton B, Jau Y-Y and Happer W 2011 Phys. Rev.A 84 063410

[19] Sargsyan A, Hakhumyan G, Leroy C, Pashayan-Leroy Y,Papoyan A and Sarkisyan D 2012 Opt. Lett. 37 1379

[20] Weller L, Kleinbach K S, Zentile M A, Knappe S, AdamsCh S and Hughes I G 2012 J. Phys. B: At. Mol. Opt. Phys.45 215005

[21] Steck D A 1998 Cesium D Line Data http://steck.us/alkalidata[22] Umfer C, Windholz L and Musso M 1992 Z. Phys. D 25 23[23] Happer W 1972 Rev. Mod. Phys. 44 169[24] Sargsyan A, Mirzoyan R and Sarkisyan D 2012 J. Exp. Theor.

Phys. 115 769[25] Sargsyan A, Mirzoyan R, Papoyan A and Sarkisyan D 2012

Opt. Lett. 37 4871[26] Taichenachev A V, Tumaikin A M and Yudin V I 1999 Phys.

Rev. A 61 011802[27] Goren C, Wilson-Gordon A D, Rosenbluh M and

Friedmann H 2004 Phys. Rev. A 69 053818

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