A new submicron thin cell (STC) filled with Rb and neon gas is developed and comparison of resonant absorption with STC containing pure Rb is provided. The effect of collapse and revival of Dicke-type narrowing is still observable for the thickness L = λ/2 and L = λ, where λ is a resonant laser wavelength 794 nm (D1 line). For an ordinary Rb cm-size cell with addition of buffer gas, the velocity selective optical pumping/saturation (VSOP) resonances in saturated absorption spectra are fully suppressed if neon pressure > 0.5 Torr. A spectacular difference is that for L = λ, VSOP resonances are still observable even when neon pressure is ≥ 6 Torr. Narrow fluorescence spectra at L = λ/2 allow one to realize online buffer gas pressure monitoring. A good agreement with theoretical model is observed.
© 2010 Optical Society of America
Recently it has been demonstrated that sealed-off submicron-thin cell containing atomic vapor of Rb, Cs, etc. with the thickness of the vapor column L comparable or smaller than resonant optical wavelength λ, is a very promising tool for fundamental studies of atom-light, atom-atom, atom-surface and atom-external magnetic field interactions [1–9]. Dramatically different behavior of resonant absorption, fluorescence and resonant magneto-optical processes compared to that obtained with the help of ordinary (cm-long) optical cells have been demonstrated.The absorption and fluorescence spectra for D1 and D2 lines of Rb and Cs in a STC as a function of L = λ ratio, with L being in the range of 50 – 3000 nm, have been published in [2, 4, 6–8].It was revealed that for low laser intensity (< 1 mW/cm2), the absorption linewidth of optical hyperfine transition between ground and excited levels exhibits oscillating behavior and has the minimum value when L = (2n+1)λ/2, and the maximum value when L = nλ (n is integer). This is the manifestation of collapse and revival of Dicke-type coherent narrowing effect (CRDN) . For higher excitation intensity (~ 10 mW/cm2), VSOP resonances appear in the transmission spectrum when L = nλ. Narrow-band VSOP resonances are located exactly at the atomic transitions, which was already used to form frequency reference for Rb and Cs atomic transitions [2, 5, 6].
One could expect that the presence of a buffer gas can substantially alter the mentioned effects. For these studies we have developed special multi-region cells (MRC) with buffer gas. In this paper we present new peculiarities that we have observed for the first time in MRC and compare them with the results for an ordinary-length buffered cell. The presented results are important for a further development of a nanometric size devices.
MRC consists of two interconnected cells and a side-arm containing metal. The STC region (shown in the upper part of Fig. 1) has a wedged thickness of the gap between the windows that allows one to exploit atomic vapor column thickness in the range of 0.1 - 4 µm. The STC is connected through a thin sapphire pipe with the 1 cm-long cell region (the lower part of Fig. 1) with 2 sapphire windows. The 1 cm-long cell is terminated by a sapphire side-arm containing metallic Rb. We have used 2 MRCs, filled with 6 Torr and 20 Torr of neon gas. Such design of MRC allows one to compare absorption and fluorescence signals simultaneously recorded for STC and 1 cm-long ordinary cell. The MRC is placed in the oven with openings, which allow passing the laser radiation and registration of fluorescence in the direction perpendicular to the laser beam. The temperature of the MRC was kept at ~ 120 °C at the side-arm (the latter defines Rb atomic vapor pressure), and somewhat (20 °C) higher at the windows in order to prevent Rb vapor condensation at the windows. This regime corresponds to the number density of Rb atoms N ~ 1013 at/cm3. The sketch of the experimental setup is presented in Fig. 2. To measure the transmission and fluorescence spectra at different STC thicknesses, the oven with MRC was smoothly translating vertically as indicated by an arrow in Fig. 2. Note that although it is technically easier to move only the STC, in this case the temperature regime of the cell will be changed during the movement. Extended cavity cw tunable diode laser (ECDL) with λ = 794 nm was used for the case of Rb D1 line. The laser radiation is branched to two beams: the main beam is directed to STC (MRC) for studying the absorption and fluorescence processes, while the second beam is used to form a reference spectrum by saturation absorption (SA) technique in a separate Rb cell. Atomic transitions of 85Rb and 87Rb D1 line are shown in Fig. 3. Transmission spectra for 85Rb D1 line Fg = 3 → Fe = 2,3 and 87Rb Fg = 2 → Fe = 2 transitions recorded in STC filled with pure Rb (for L = λ/2 and L = λ) are shown in Fig. 4(a) for laser intensity < 0.1 mW/cm2. Dicke-type coherent narrowing (DCN) effect is well seen: the spectral linewidth for L = λ/2 (~ 150 MHz) is narrower by factor of 3 than that for L = λ (~ 450 MHz). Transmission spectra for the STC filled with Rb and 6 Torr of neon are shown in Fig. 4(b) for the same thicknesses. Dicke-type coherent narrowing effect is still well seen . The further increase of buffer gas pressure [Fig. 4(c)] results in broadening and contrast reduction of DCN dips. We should note that transmission for L = λ in Fig. 4(b), c is more sensitive to IL as compared with the case of L = λ/2. Particularly, at IL ~ 1mW/cm2 transmission for L = λ can be higher (the absorption is lower) than for L = λ/2, which is caused by stronger influence of an optical pumping for L = λ . For this reason, in order to get graphs visually comparable with those presented in Fig. 4(a) we have adjusted IL (~ 0.2 mW/cm2) for L = λ.
Figure 5 presents theoretically calculated spectra corresponding to those presented in Fig. 4, preserving the labeling (only transitions Fg = 3 → Fe = 2,3 are considered in the model). A good agreement with experimental results is seen. The striking point is that even with neon gas pressure up to 20 Torr the CRDN is still observable [graphs (c)], though less pronounced as compared with (a) and (b).
It is important to note that in the case of an ordinary 0.1 – 10 cm-long alkali metal vapor cell, the addition of > 0.5 Torr of (any) buffer gas leads to disappearance of all the sub-Doppler features in the saturated absorption spectrum. Curve 1 in Fig. 6 shows the well-known SA spectrum obtained with 3-cm long ordinary cell with pure Rb. The VSOP and crossover (CO) resonances are well seen. The same spectrum recorded with 1-cm long Rb cell with 6 Torr of neon is shown by curve 2. One can see that here all the VSOP and CO resonances are completely vanished. This is caused by the fact that in the case of buffer gas use there is no anymore selected group of atoms (due to the frequent collisions of Rb atoms with Ne gas), which is necessary to form sub-Doppler resonances in the transmission spectrum inside the Doppler-broadened one.
Figure 7 shows transmission spectra for STCs with L = λ on 85Rb Fg = 3→Fe = 2,3 and 87Rb Fg = 2 → Fe = 2 transitions (IL ~ 10 mW/cm2) for the following cases: curve 1 - STC with pure Rb: the linewidth of VSOP resonances ~ 25 MHz; curve 2- STC with Rb and 6 Torr Ne: VSOP linewidth is ~ 90 MHz; curve 3 - STC with Rb and 20 Torr Ne: VSOP resonances are absent.
The comparison of Fig. 6 and Fig. 7 shows a striking peculiarity: the VSOPs still exist for the STC with Rb + 6 Torr neon when L = λ. This important difference in behavior as compared with ordinary 1 cm-long cell can be explained as follows. The free path length of Rb atom for 6 Torr Ne is somewhat less than 10 µm, so the atoms flying parallel to the windows inside the laser beam of 2 mm diameter experience hundreds of collisions with Ne atoms causing just additional broadening of VSOP. Meanwhile collisions of Rb atoms wih longitudinal velocity with Ne atoms have a negligible impact since the thickness of STC for L = λ is less than 1 µm. It is important to note that the observed peculiarities of VSOPs formation presented in Fig. 7 are well described by the theoretical model (the graphs are not shown). Namely, the theory predicts i) formation of narrow VSOPs with linewidth of ~ γN in the case of pure Rb; ii) VSOP broadening for the case illustrated by curve 2; iii) absence of VSOPs for the case illustrated by curve 3.
It was demonstrated in  that under optimal experimental conditions, the FullWidth at Half Maximum (FWHM) of the fluorescence spectrum of an individual transition for L = λ/2 can be reduced down to ~ 70 MHz (in the case of ordinary cm-size cell the value is ~ 500 MHz). This striking feature of the STC offers an important benefit in the case of the STC filled with buffer gas, too. Figure 8 presents fluorescence spectrum when L = λ/2 for 3 cases (a - experiment, b - theory): curve 1 - STC with pure Rb vapor; curve 2 and 3 - STC containing Rb vapor + 6 Torr and 20 Torr Ne, correspondingly. For theory (b): Rabi frequency ΩL = 0.4γ, where γ = γN (5.7 MHz) + 2.5 MHz (the broadening caused by Rb-Rb collisions at 120 °C at the side-arm) + γL (laser linewidth ~ 0.8 MHz) = 9 MHz. For the calculations we used broadening rate of 7 MHz/Torr, thus for 6 Torr, G(total)/2π ~ 49 MHz, and for 20 Torr, Γ(total)/2π ~ 149 MHz, and Maxwellian velocity distribution with VT = 300 m/s. Laser intensity is ~ 10 mW/cm2. As it is seen, up to 20 Torr Ne the fluorescence spectrum has a sub-Doppler linewidth. As it is shown below, a tool for in situ pressure monitoring based on this effect can be developed.
3. Theoretical Consideration and Discussion
We consider a three-level atomic system (see Fig. 9) interacting with a linearly polarized laser radiation of frequency ω. The three levels under the consideration are: one ground hyperfine level F = 1 (∣1〉) and two excited levels F′ = 2,3 (∣2〉 and ∣3〉). For simplicity, we consider a one-dimensional situation, where the driving field is in the ±z-direction and the atom is moving along z-direction with a velocity vz. The detunings of the laser from the transitions ∣1〉 → ∣2〉 and ∣1〉 → ∣3〉 are Δ1 = ω 21 − ω −kvz and Δ2 = ω31 − ω − kvz, respectively, where kvz is the shift due to the Doppler effect, with k being the wave vector of the excitation light. We analyze the observed spectra of resonant absorption and fluorescence on the basis of a standard densitymatrix approach [10, 11].
The dynamical behavior of the density matrix ρ is given by the Liouville equation of motion
where Ĥ 0 is the unperturbed atomic Hamiltonian, and V̂ = −d̂E(t) is the atom-light interaction Hamiltonian in the electric-dipole approximation with d̂ being the electric dipole operator and E(t) the electric field of the radiation light. The components of the density-matrix elements of Eq. (1) can be represented by taking rotating-wave-approximation
where δ is the excited state hyperfine splitting, γ i1 is the rate of the spontaneous decay from the excited state ∣i〉 to the ground state ∣1〉, and 2Γ = γ 21+γ′1 = γ 31+γ′2. Here γ′1 and γ′2 are the rates of population lost from the system, responsible for the optical pumping of the other ground hyperfine level with F = 2 denoted as ∣1′〉 in Fig. 9. The Rabi frequencies of the corresponding transitions are defined as Ω1 = d 12 E/2h̄ and Ω2 = d 13 E/2h̄, respectively. As the atoms are in thermal motion, we take the average of all ρij values over the range of velocities, weighted by the one dimensional Maxwellian velocity distribution.
To take into account the laser bandwidth we use the phase diffusion model of Wigner-Levy [11, 12], in accordance with which it is assumed that the laser radiation has a Lorentzian spectrum with the FWHM of γL. The bandwidth is incorporated into Eqs. (2) as a relaxation term for the non-diagonal element of the density matrix in accordance to the procedure given in . The main assumptions made in the model are as follows: the atomic number density is assumed to be low enough so that the effect of collisions between the Rb-Rb atoms can be ignored; the atoms experience inelastic collisions with the cell walls, i.e. atoms lose completely their optical excitation; the incident beam diameter largely exceeds the cell thickness which allows one to neglect the relaxation of atoms travelling out of the diameter of the laser beam. These assumptions allow us to take into account the collisional relaxation of each atom by solving the temporal equations for the atomic density matrix with proper boundary conditions for each atom separately. The dephasing process due to collisions between buffer-gas and the Rb atoms is described through collision decay rate Γdeph entering as additional relaxation term for non-diagonal elements of the density matrix. The effect of the reflection of the radiation from the highly-parallel windows of the nano-cell behaving as aFabry-Perot cavity  is also taken into account. The model used here is on the lines of [3, 5].
Figure 10 presents the calculated dependence of the fluorescence linewidth and the amplitudes as a function of the neon pressure for Rb, D1 line, Fg = 3→Fe = 2,3, Ω = 0.4 γ, VT=300 m/s. Note that, the FWHM data coincide for Fg = 3 → Fe = 2 and Fg = 3 → Fe = 3 spectral lines. One of the possible applications using this dependence is development of an online pressure gauge. In [14, 15] it was demonstrated a simple way to separate alkali metal isotopes based on reactions studied in [16, 17]: hydrogen gas with a pressure of ~ 20 Torr is added to the cell containing alkali metal vapor. Then the needed isotope is excited by a narrow-band resonant laser radiation (for the case of Rb vapor confined in a cell of ordinary 1-5 cm length, the Doppler-broadened lines of 85Rb and 87Rb practically do not overlap). Selectively excited to 5P state isotope (e.g., 85Rb) even at room temperature easily undergoes two-step chemical reaction with hydrogen, 85Rb* + H2 → 85Rb + H† 2; 85Rb* + H† 2 → 85RbH† + H forming 85Rb hydride RbH. The reaction is more efficient when the cell is heated, so it is justified to use a sapphire cell which is resistive to chemically aggressive alkali vapor. The isotopic-selective hydride gets condensed on the cell walls. When the reaction is over, the residual non-reacted vapor can be driven out by freezing the cell side-arm, and the isotopic-pure hydride is easily dissociated by heating the cell body to > 300 °C. The pressure of gas (notably, H2) in the cell strongly varies in the course of chemical reaction; that is why it is important to have a tool for in situ pressure monitoring. The use of conventional room-temperature gas pressure gauges, especially for heated cell, is impossible because alkali metal vapor would condensate on a gauge. Alternatively, an STC can be soldered to the main separation cell as is shown in Fig. 1 and heated in the same oven up to needed temperature. The pressure in this case can be monitored online using measurement curves similar to those presented in Fig. 10.
Comparison of the resonant absorption in the STC filled with Rb vapor with another STC filled with Rb and neon gas with pressure 6 Torr and 20 Torr shows that the spectra of the resonant absorption demonstrate sub-Doppler narrowing for the thickness L = λ/2 and broadening for the thickness L = λ, thus manifesting the effect of collapse and revival of Dicke-type narrowing (λ = 794 nm is a resonant laser wavelength). In an ordinary Rb cell with L = 0.1 − 10 cm filled with buffer gas, in the saturated absorption spectra VSOP and CO resonances are washed out when pressure > 0.5 Torr. In contrast, for the STC with L = λ the VSOP resonances located at the atomic transition are still observable even when neon pressure is = 6 Torr. Narrow-band fluorescence spectra of the STC with L = λ/2 can be used as a convenient tool for online buffer gas pressure monitoring in the MRC in its several centimeter-long part, for the conditions when ordinary pressure gauges are unusable. Developed theoretical model well describes all experimentally observed peculiarities.
The authors thank A. Sarkisyan for his valuable participation in the fabrication of the MRC.Research conducted in the scope of the International Associated Laboratory IRMAS. Armenian team thanks for the ANSEF PS 1868 support.
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