Possibility of the use of the magnetic field for creating a quantum filter on the <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript><Superscript>87</Superscript>Rb line

The possibility of the use of the F = 2?F = 1 transition of the D ₁ absorption line of the ⁸⁷Rb atom for creating of a single-photon quantum filter based on coherent population trapping (CPT) has been analyzed. It has been shown that the external magnetic field is necessary for ensuring the creation of the quantum filter on boson isotopes of alkali atoms. The field strength should be enough for the manifestation of the splitting of the Zeeman CPT resonances that is much larger than their spectral widths. The splittings of the CPT resonances, which characterize the nonlinearity of the Zeeman effect, have been measured for the ⁸⁷Rb atom and the possibility of the use of this system for the quantum filter is concluded.     

Tracking interacting dark states through higher order absorption resonances

A three photon resonance arising due to coherent population trapped (CPT) states in multi-level systems, is experimentally shown to be a powerful spectral marker to detect interacting CPT states. In systems showing N type or double Λ type level configurations, these absorption resonances can be used to identify spectral positions of maximal interactions between competing CPT ground states. The contrast of the absorption resonance serves to identify even partially destructive interactions between the CPT states, eliminating the need for strong resonant changes of ground state coherence for identification. We demonstrate this effect in a room temperature, gaseous collection of ⁸⁷Rb. atoms. Three laser fields interact with a double Λ configuration in the Zeeman degenerate levels of the ground state 5S_1/2S_{1/2}, F = 1 and those of the excited states 5P_3/2P_{3/2}, F = 0,1, around the D2 line. The three-photon resonance is studied in the counter-propagating third field when the other two co-propagating fields satisfy the two-photon resonance condition necessary for creation of CPT states. We envisage that this absorption feature in the third field, can become a veritable tool to quantify degradation of CPT induced effects in engineered quantum states using multi-level systems.     

Saturated absorption spectroscopy: Elimination of crossover resonances with the use of a nanocell

It is demonstrated that the velocity-selective optical pumping/saturation resonances of the reduced absorption in a Rb vapor nanocell with thickness L = λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow for the complete elimination of crossover (CO) resonances. We observe well-pronounced resonances corresponding to the F _g = 3 → F _e = 2, 3, and 4 hyperfine transitions of the ⁸⁵Rb D₂ line with line widths close to the natural width. A small CO resonance located midway between F _g = 3 → F _e = 3 and F _g = 3 → F _e = 4 transitions appears only for L ≥ 4λ. The D₂ line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances, it is possible to determine the thickness of the column of alkali vapor in the range of 1–1000 μm. The absence of the CO resonances for nanocells with L ～ λ is attractive for the frequency reference application and for studying the transitions between the Zeeman sublevels in external magnetic fields.     

The role of a dipole-coupled but not dipole-probed state in probe absorption with multilevel coupling

We study the impact on weak-probe spectra from the presence of a state for which the electric-dipole transition is allowed for coupling but forbidden for probing. Such is the ⁸⁵Rb ²P_3/2(F′ = 1) state, providing D2-line hfs transitions in Λ-configurations are considered with the 5²S_1/2(F = 2) and 5²S_1/2(F = 3) states in the role of the ground-states for coupling and probing, respectively. The multilevel EIT/Autler-Townes spectra were simulated with coupling field frequency fixed at various values in the range encompassing the atomic resonances. Collisionless (cold) atoms are assumed, and all decoherence rates, other than those related to the natural decay rates, are neglected. The general conclusion is that a state which is not directly involved in probe absorption can still considerably shape absorption spectra (due to multiphoton transitions), and its influence (negative for some applications) has to be carefully considered, even for the coupling-field-induced Rabi frequency values not exceeding the natural linewidth. A particular attention is paid to how the F′ = 1 state effects the narrow resonances, such as those of EIT origin or a “distant wing” of the Autler-Townes splitting, because resonances of these types are of interest, e.g., for developing quantum memory protocols [Sheremet et al., PRA82 (2010) 033838].     

Frequency-modulation spectroscopy of coherent dark resonances in <Superscript>87</Superscript>Rb atoms

The results of frequency-modulation (FM) spectroscopy of coherent dark resonances from the Zeeman sublevels of the transition F=2↔ F=1 of D ₁ line in absorption of ⁸⁷Rb atoms are presented and discussed in detail. By contrast with the conventional spectroscopy of coherent dark resonances employing two laser beams, relative frequency of which can be varied, these data has been obtained with the help of a single frequency-modulated laser field. Variation of the modulation frequency plays then a similar role as the variation of the relative frequency in conventional spectroscopy. Experimental data are fit to the theoretical calculations, which are based on the theory of FM spectroscopy of coherent dark resonances recently developed by us. Feasibility of using such experimental technique for accurate measurements of magnetic fields is also discussed.     

Measurement of the quadratic Zeeman shift of Rb hyperfine sublevels using stimulated Raman transitions

We demonstrate a technique for directly measuring the quadratic Zeeman shift using stimulated Raman transitions. The quadratic Zeeman shift has been measured yielding Δν=1296.8±3.3 Hz/G² for magnetically insensitive sublevels (5S_1/2,F=2,m_F=0→5S_1/2,F=3,m_F=0) of ⁸⁵Rb by compensating the magnetic field and cancelling the ac Stark shift. We also measured the cancellation ratio of the differential ac Stark shift due to the imbalanced Raman beams by using two pairs of Raman beams (σ⁺, σ⁺) and it is 1:3.67 when the one-photon detuning is 1.5 GHz in the experiment.     

Effect of Zeeman Depopulation Pumping on Cycling Atomic Transitions

The results of an investigation of fluorescence signal at 6S_1/2 (F_g = 4) → 6P_3/2 (F_e = 5) transition of D₂ line of atomic Cs vapor versus the magnetic field (up to B = 90 G), directed along the linear polarization of exciting light are presented. The recorded reduction of fluorescence in the magnetic field, which is especially strong at high intensity of laser radiation, is explained by conversion of the Zeeman optical pumping (the alignment) into the depopulation pumping under conditions, when the Zeeman frequency shift of individual transitions between magnetic sublevels exceeds the homogeneous width of transition. In consequence, the cycling hyperfine transition F_g = 4 → F_e = 5 is transformed into an open one.     

The influence of the spectral properties of human skin on the resolution of a Linnik interference microscope

We have studied the Zeeman structure of the 3p5f configuration of SiI and revealed its particular features in the range of variation of the magnetic field from 0 to 60 kOe. In this range, we have found 71 crossings of Zeeman sublevels with ΔM = ±1 and ±2 (M is the magnetic quantum number) and 4 anticrossings of lower F levels with j ₁ = 1/2 (j ₁ is the total angular momentum of the p electron). From splittings of levels in the assured linear range up to 40 Oe, we have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field.     

Zeeman effect on the hyperfine structure of the D 1 line of a submicron layer of 87Rb vapor

An extremely thin cell with a wedge gap was developed that makes it possible to form a column of Rb atom vapor with thickness in the range from 100 to 600 nm. It is experimentally shown that the use of this cell, along with commercially available diode lasers, allows one to spectrally resolve individual transitions between the Zeeman sublevels of the hyperfine structure of the ⁸⁷Rb D ₁ line (transitions F _g =1, 2→F _e =1, 2) in the resonance fluorescence spectrum in the presence of an external magnetic field (B≈200 G). This makes it possible to realize systems consisting of nondegenerate atomic levels. For comparison, it is shown that transitions between the Zeeman sublevels in the fluorescence spectrum obtained with the aid of a conventional cell (1–10 cm long) in an external magnetic field with B～200 G remain completely masked by the Doppler-broadened profile. The results obtained can be used for the creation of a simple magnetometer based on an extremely thin cell with Rb vapor for the measurement of magnetic fields with a submicron local spatial resolution.     

Infrared diode laser spectroscopy of FCO: The ν1 and ν2 bands

The ν₁ (CO stretching) and ν₂ (CF stretching) bands of the FCO radical were observed with Doppler-limited resolution by an infrared diode laser spectrometer with Zeeman and source modulation. The FCO radical was generated by a 60-Hz discharge in one of the following three gas mixtures: O₂ + C₂F₄, CO + SF₆, and CO + C₂F₄, all diluted with He. The observed spectra were analyzed to determine the rotational constants, the centrifugal distortion constants, and the spin-rotation interaction constants. The band origins, 1861.6372(1) and 1026.1283(1) cm^?1 [with standard errors in parentheses], which were obtained, were found to agree well with matrix data, 1857 and 1023 cm^?1, respectively. The assignment of the observed spectra to the FCO radical was further supported by observing the ν₁ band of F¹³CO, which was obtained from ¹³CO and SF₆. The molecular structure and the force field of FCO are briefly discussed by using molecular constants obtained from the observed spectra.     

Mechanism of “GSI oscillations” in electron capture by highly charged hydrogen-like atomic ions

We suggest a qualitative explanation of oscillations in electron capture decays of hydrogen-like ¹⁴⁰Pr and ¹⁴²Pm ions observed recently in an ion experimental storage ring (ESR) of Gesellschaft für Schwerionenforschung (GSI) mbH, Darmstadt, Germany. This explanation is based on the electron multiphoton Rabi oscillations between two Zeeman states of the hyperfine ground level with the total angular momentum F = 1/2. The Zeeman splitting is produced by a constant magnetic field in the ESR. Transitions between these states are produced by the second, sufficiently strong alternating magnetic field that approximates realistic fields in the GSI ESR. The Zeeman splitting amounts to only about 10^?5 eV. This allows explaining the observed quantum beats with the period 7 s.     

Zeeman effect and stark splitting of the electronic states of the rare-earth ion in the paramagnetic terbium garnets Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> and Tb<Subscript>3</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript>

The Zeeman effect in the ⁷ F ₆ → ⁵ D ₄ absorption band of the Tb³⁺ ion in the paramagnetic garnets Tb₃Ga₅O₁₂ and Tb₃Al₅O₁₂ was studied. The field dependences of the Zeeman splitting of some absorption lines are found to exhibit unusual behavior: as the magnetic field increases, the band splitting decreases rather than increases. Symmetry analysis relates these lines to 4f → 4f electron transitions of the doublet-quasi-doublet or quasi-doublet-doublet type, for which the field dependences of the splitting differ radically from the well-known field dependences of the Zeeman splitting for quasi-doublet-quasi-doublet or quasi-doublet-singlet transitions in a longitudinal magnetic field.     

A new type of resonances in saturated absorption spectroscopy of 3-level systems

We report the experimental observation of new resonances in saturated absorption spectra of a J = 1 to J = 0 transition of Ne atoms in a static magnetic field. These resonances, which are distinct from the well-known Zeeman and cross-over resonances, result from the modification of stimulated Raman processes by the simultaneous resonant saturation of an optical transition. The light-shifts of the various resonances are also studied.     

A tunable laser at λ=3.39 μm with line width of 7 Hz used in investigating a hyperfine structure of theF 2 (2) line of methane

A laser spectrometer is described which was used in exploring resonance shapes of about 1000 Hz width in methane in the region of low absorption of about 10⁻⁶ cm⁻¹. We report on first measurements of relative intensities of hyperfine components of theF ₂ ⁽²⁾ line in methane, on direct observations of line splitting due to a recoil effect and of a non-linear dependence of collisional broadening of resonances in the transit region, and on observation of an anomalous Zeeman effect in hyperfine components in a longitudinal magnetic field. The results of this work were summarized by one of the authors (V.C.) at the 2nd Symposium on Frequency Standards and Metrology (Boulder, Colo., USA, July 1976) and at lectures in the School Enrico Fermi (Varenna, Italy, July 1976).     

Structure of magnetic resonance in <Superscript>87</Superscript>Rb atoms

Magnetic resonance at the F_g = 1 \( \rightleftarrows \)F_e = 1 transition of the D₁ line in ⁸⁷Rb has been studied with pumping and detection by linearly polarized radiation and detection at the double frequency of the radiofrequency field. The intervals of allowed values of the static and alternating magnetic fields in which magnetic resonance has a single maximum have been found. The structure appearing beyond these intervals has been explained. It has been shown that the quadratic Zeeman shift is responsible for the three-peak structure of resonance; the radiofrequency shift results in the appearance of additional extrema in resonance, which can be used to determine the relaxation constant Γ₂. The possibility of application in magnetometry has been discussed.     

New projected range algorithm as derived from transport equations

The Zeeman effect in the 6s n d ^1'3 D ₂ sequences and their 5d7d ³ F ₂,¹ D ₂ perturbers was investigated. In total 26 states were studied using Zeeman quantum-beat-and rfspectroscopy techniques. Theoreticalg _J -values obtained from an extended multi-channel quantum-defect theory are in fair agreement with the experimental results.     

Luminescence and magnetic properties of europium(III) carboxylatodibenzoylmethanates

This paper reports on the results of an investigation of the luminescence and magnetic properties of europium(III) carboxylates, which are determined by the structure of the Stark and Zeeman sublevels. It has been established that the energy splittings λ_lum between the ⁷ F ₀ ground level and the ⁷ F ₁ term in the luminescence spectra of these compounds well correlate with the energy splittings λ_magn obtained from magnetochemical measurements.     

Spectroscopy of coherent dark resonances in multilevel atoms for the example of samarium vapor

A universal theory for calculating coherent population trapping resonances in multilevel atoms is suggested. The theory allows arbitrary schemes of multilevel atoms and their excitations to be calculated taking into account the influence of relaxation effects in atoms, applied magnetic field, and the Doppler effect. The experimental data obtained by high-precision diode spectroscopy of coherent dark resonances in samarium vapor are systematically analyzed using the suggested theory. In the absence of a magnetic field, the model of samarium is based on consideration of a degenerate Λ system of the 4f⁶6s²(⁷F₀) ? 4f⁶(⁷F)6s6p(³P⁰)⁹F ₁ ⁰ ?4f⁶6s²(⁷F₁) active transitions. If the fourth 4f⁶6s²(⁷F₂) level is taken into account, this Λ system becomes open. Numerical simulation of coherent population trapping resonances shows that the open character of the system decreases the contrast of resonance curves in absorption spectra without changing resonance widths. The system under applied external longitudinal and transverse magnetic fields is correctly described by 7-and 12-level models of atomic transitions, respectively.     

Precise measurement of the frequency separation between the F(2)2 and the E lines in methane

The methane E line at 2947.811 cm^-1 has been observed by the saturated absorption technique using a Zeeman shifted 3.39 μm He-Ne laser. The frequency separation between this line and the F(²)₂ line in methane, commonly used as an infrared frequency reference, is measured to be ν(F²₂) - ν(E) = 3032560 ± 5 kHz. It has been checked that the E line is free from power and Stark frequency shifts within our 5 kHz measurement precision.     

On the optical absorption due to particle-hole excitations in thin metal films

We present here a qualitative discussion on the optical absorption due to particle-hole excitations in thin metal films. We show that in sufficiently thin films, such excitations yield resonant absorption, when P-polarized light is obliquely incident on the metal surface. For instance, for frequency ω #62; ε_F where ε_F is the Fermi-energy, such resonances occur whenever ω satisfies the condition ω/ε_F = (1 + nπ/dq_F)² - 1, where n = 1,3,5,…,q_F is the Fermi wave-vector and d is the thickness of the film. The experimental observability of this effect is also discussed.