Selective reflection from Rb vapor in half- and quarter-wave cells: Features and possible applications

The features of the effect of selective reflection from rubidium vapor in a nanocell with the thickness L ≈ λ/2 and L ≈ λ/4, where λ = 795 nm is the wavelength of laser radiation resonant with the Rb D₁ line, are studied. It is shown that, because of the behavior of the nanocell as a low-Q-factor Fabry–Pérot etalon, the sign of the derivative of the selective reflection spectra changes near L ≈ λ/2 from negative at L > λ/2 to positive at L < λ/2. The simplicity of the experimental implementation, large amplitude, and sub-Doppler width (40MHz) of a detected signal at an atomic transition frequency are appropriate for applications in metrology and magnetometry. In particular, selective reflection from the nanocell is a convenient frequency marker of atomic transitions; in this case, the amplitudes of peaks are proportional to the transition probabilities. The remote optical monitoring of a magnetic field with a spatial resolution L = λ/4 ≈ 199 of nm is possible on the basis of the splitting of selective reflection peaks in a strong magnetic field (up to 3 kG). A theoretical model describes well the experimental results.     

Selective reflection of laser radiation from submicron layers of Rb and Cs atomic vapors: Applications in atomic spectroscopy

We studied selective reflection (SR) of laser radiation from a window of a nanocell with thickness L ~ λ_1,2/2 filled with Rb and Cs atoms, where λ₁ = 780 nm and λ₂ = 852 nm are the wavelengths resonant with the D₂ laser lines for Rb and Cs, respectively. It is demonstrated that the negative derivative of the SR signal profile for L > λ/2 changes to the positive one for L < λ/2. It is shown that the real-time formation of the SR signal profile derivative (SRD) with the spectral width 30–40 MHz and located at the atomic transition is, in particular, a convenient frequency marker of D₂ transitions in Rb and Cs. The amplitudes of SRD signals are proportional to the atomic transition probabilities. A comparison with the known saturated absorption (SA) method demonstrated a number of advantages, such as the absence of cross-over resonances in the SRD spectrum, the simplicity of realization, a low required power, etc. An SRD frequency marker also operates in the presence of the Ne buffer gas at a pressure of 6 Torr, which allowed us to determine the Ne–Rb collisional broadening, whereas the SA method is already inapplicable at buffer gas pressures above 0.1 Torr. The realization simplicity makes the SRD method a convenient tool for atomic spectroscopy. Our theoretical model well describes the SRD signal.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

V.L. Ginzburg’s elliptic screw polarization modes in an optical medium with linear birefringence and twist: Determination of their parameters by the method of Jones matrices

The effect of electromagnetically induced transparency (EIT) has been experimentally implemented for the first time for the (4S _1/2–4P _1/2–4S _1/2) Λ-system of potassium atom levels in a nanocell with a 770-nm-thick column of atomic vapor. It is shown that, at such a small thickness of the vapor column, the EIT resonance can be observed only when the coupling-laser frequency is in exact resonance with the frequency of the corresponding atomic transition. The EIT resonance disappears even if the coupling-laser frequency differs slightly (by ~50 MHz) from that of the corresponding atomic transition, which is due to the high thermal velocity of K atoms. The EIT resonance and related velocity selective optical pumping resonances caused by optical pumping (formed by the coupling) can be simultaneously recorded because of the small (~462 MHz) hyperfine splitting of the lower 4S _1/2 level.     

EIT resonance features in strong magnetic fields in rubidium atomic columns with length varying by 4 orders

Electromagnetically induced transparency (EIT) resonances are investigated with the ⁸⁵Rb D₁ line (795 nm) in strong magnetic fields (up to 2 kG) with three different types of spectroscopic vapor cells: the nano-cell with a thickness along the direction of laser light L ≈ 795 nm, the micro-cell with L = 30 μm with the addition of a neon buffer gas, and the centimeter-long glass cell. These cells allowed us to observe systematic changes of the EIT spectra when the increasing magnetic field systematically decoupled the total atomic electron and nuclear angular moments (the Paschen-Back/Back-Goudsmit effects). The observations agree well with a theoretical model. The advantages and disadvantages of a particular type of cell are discussed along with the possible practical applications.     

Phonon and electronic properties of the LiCaAlF<Subscript>6</Subscript> crystal: Experiment and ab initio calculations

The results obtained in a cell with a distance between windows on the order of several hundreds of nanometers (the so-called “nanocell”) are presented. The nanocell thickness L in the vertical direction changes from 100 to 900 nm. It is shown that the use of a nanocell with thickness L = λ/2, where λ is a laser wavelength resonant to the atomic transition D2 in sodium atoms, provides sub-Doppler resolution of transmission and fluorescence spectra.     

Selective Reflection of Laser Radiation from Ultrathin Layers of Cesium Atomic Vapors Confined in a Nanocell

The effect of the van der Waals interaction of cesium atoms with the sapphire windows of a nanocell was experimentally investigated using the selective reflection process. The distance L between the windows varied in the range of 50–2000 nm and the nanocell was filled with the vapors of cesium atoms. For the Cs atoms (the transition 6S_1/2 → 6P_1/2), the C₃ coefficient of the van der Waals interaction with the sapphire windows of the nanocell is measured. It is shown that it is possible to determine the magnetic fields with the spatial resolution of 70 nm using the selective reflection spectrum and, consequently, both the homogeneous and highly gradient magnetic fields can be measured.     

Nanocell with a pressure-controlled Rb atomic vapor column thickness: Critical influence of the thickness on optical processes

A new device is designed: it consists of a nanocell (NC) filled with Rb atom vapors and placed in a vacuum chamber. When the pressure in the chamber changes in the range 0–1 atm, the NC thickness is smoothly varied in the range L = 140–1700 nm, which is caused by the pressure-induced deformation of thin garnet windows in the chamber. The pressure dependence has excellent reproducibility even after many hundreds of cycles of letting in of air and its complete pumping out from the chamber. The accuracy of setting required thickness L is much better than in the wedge-gap NCs to be moved mechanically that were used earlier. The processes of Faraday rotation (FR) of a polarization plane, resonance absorption, and fluorescence are studied using the D ₁-line narrow-band continuous laser radiation when the thickness changes from L = λ/2 (398 nm) to L = 2λ (1590 nm) at a step λ/2. The FR signal is shown to be maximal at L = λ/2 and 3λ/2 and to have the minimum spectral width (≈60 MHz). At L = λ and 2λ, the FR signal is minimal and has the maximum spectral width (≈200 MHz). The resonance absorption demonstrates the same oscillating behavior; however, the effect in the case of FR is much more pronounced. The oscillating effect is absent for resonance fluorescence: its spectral width and amplitude increase monotonically with L. The detected effects are explained and possible applications are noted.     

Features of faraday rotation in cs atomic vapor in a cell thinner than the wavelength of light

Features of the effect of Faraday rotation (the rotation of the radiation polarization plane) in a magnetic field of the D ₁ line in Cs atomic vapor in a nanocell with the thickness L varying in the range of 80–900 nm have been analyzed. The key parameter is the ratio L/λ, where λ = 895 nm is the wavelength of laser radiation resonant with the D ₁ line. The comparison of the parameters for two selected thicknesses L = λ and λ/2 has revealed an unusual behavior of the Faraday rotation signal: the spectrum of the Faraday rotation signal at L = λ/2 = 448 nm is several times narrower than the spectrum of the signal at L = λ, whereas its amplitude is larger by a factor of about 3. These differences become more dramatic with an increase in the power of the laser: the amplitude of the Faraday rotation signal at L = λ/2 increases, whereas the amplitude of the signal at L = λ almost vanishes. Such dependences on L are absent in centimeter-length cells. They are inherent only in nanocells. In spite of a small thickness, L = 448 nm, the Faraday rotation signal is certainly detected at magnetic fields ≥0.4 G, which ensures its application. At thicknesses L < 150 nm, the Faraday rotation signal exhibits “redshift,” which is manifestation of the van der Waals effect. The developed theoretical model describes the experiment well.     

Selective Reflection of Potassium Vapor Nanolayers in a Magnetic Field

The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the ³⁹K and ⁴¹K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ⁺ or σ^–. Different intensities (probabilities) of transitions for the σ⁺ and σ^– excitations are detected in magnetic field B₀ ≈ A _hfs /μ_B ≈ 165 G (A _hfs is the magnetic dipole constant for the ground state and μ_B is the Bohr magneton). A substantially different situation is observed at B ? B₀, since high symmetry appears for the two groups formed by radiation with circular polarization σ⁺ or σ^–. Each group is the mirror image of the other group with respect to the frequency of the 4²S_1/2–4²P_1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D₁ lines of ⁸⁷Rb and ²³Na.     

Frequency reference for atomic transitions of Rb D<Subscript>2</Subscript>-line based on the effect of selective reflection

On an example of the D₂-line of the Rb atoms the work of the frequency reference of atomic transitions is demonstrated, based on the application of the spectrum of a selective reflectance (SR) from the boundary of atom vapors with the use of nano-cell (NC) with the thickness L ~ λ/2, where λ is the laser wavelength equal to 780 nm. When changing the thickness of the nano-cell near the thickness L ~ λ/2, we observe the inversion of sign of the SR slope profile which is positive when L < λ/2 and negative when L > λ/2. In the case when the incidence angle of the laser beam on the surface of the nano-cell is close to the normal, in real-time it is possible to form the derivative of the SR which represents a resonance peak with ~35 MHz spectral linewidth and located at the atomic transition. The phenomenon of oscillation of the sign of slope while changing the nano-cell thickness from L ~ λ/2 up to L ~ 3/2λ is demonstrated. The practical application of the SR is noted.     

Effect of photoions on the line shape of the Förster resonance lines and microwave transitions in cold rubidium Rydberg atoms

Experiments are carried out on the spectroscopy of the Förster resonance lines Rb(37P) + Rb(37P) → Rb(37S) + Rb(38S) and microwave transitions nP → n′S, n′D between Rydberg states of cold rubidium atoms in a magneto-optical trap (MOT). Under ordinary conditions, all spectra exhibit a linewidth of 2–3 MHz irrespective of the interaction time between atoms or between atoms and microwave radiation, although the limit resonance width should be determined by the inverse interaction time. The analysis of experimental conditions has shown that the main source of line broadening is the inhomogeneous electric field of cold photoions that are generated under the excitation of initial nP Rydberg states by broadband pulsed laser radiation. The application of an additional electric-field pulse that rapidly extracts photoions produced by a laser pulse leads to a considerable narrowing of lines of microwave resonances and the Förster resonance. Various sources of line broadening in cold Rydberg atoms are analyzed.     

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path L _e , the localization length ξ and the inelastic mean free path L _i . Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature T. In BLG an additional characteristic distance l ₁ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1%–2%, one has l ₁ ≤ L _e ? ξ and the BLG has transport properties that differ from those of the MLG independently of L _i (T). Whereas for larger concentration of defects L _e <l ₁ ? ξ, and depending on L _i (T), the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.     

Scaling of the conductance and resistance of square lattices with an exponentially wide spectrum of the resistances of links

The conductance G? and \(\overline {{G^{ - 1}}} \) resistance average over realizations of disorder have been calculated for various sizes of square lattices L. In contrast with different direction of change in the two quantities at percolation in lattices with the binary spread of conductances of links (g _i = 0 or 1), it has been found that the mean conductance and resistance of lattices decrease simultaneously with an increase in L in the case of an exponential distribution of local conductances g _i = exp(?kx_i), where x _i ∈ [0,1] are random numbers. When L is smaller than the disorder length L₀ = bk^v, G?(L) and \(\overline {{G^{ - 1}}} \)(L) are proportional to L^?n with n = k/5 and k/6, respectively. A similar behavior is characteristic of the distributions of conductances of links, which simulate a transition between the open and tunneling regimes in semiconducting lattices of antidots created in a two-dimensional electron gas.     

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.     

Band splitting and relative spin alignment in bilayer systems

It is shown that one-particle spectra of the lower Hubbard band of bilayer correlated 2D systems with different relative alignments of the spin systems in the layers differ significantly. In particular, the bilayer band splitting differs from zero for identically directed alternating spins of different layers (F _z configuration), but tends to zero for antiparallel alignment (AF _z configuration). It is found that the type of the alignment of the ground state changes upon an increase in the doping δ from the lower AF _z configuration to the F _z configuration of the alignment observed for large values of δ. The behavior of bilayer splitting in Bi₂Sr₂CaCu₂O_8+δ suggests that the configuration of the alignment may change from F _z →AF _z simultaneously with the superconducting transition. The effects associated with the influence of spin alignment on the magnetic excitation spectrum as a method of studying the spin structure of bilayer systems are considered for homogeneous solutions of effective spin models.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Das Auger-Spektrum derL III- Schale von Wismut

A thin Bi layer is irradiated by X-rays so thatL-Auger electrons are emitted. A magnetic lens spectrometer is used to measure the electron spectrum. Energy, transition, and relativ intensity are given for 14 lines. Under the most favourable conditions the number ofL _III ionisations is about ten times that ofL _II ionisations. In this case only a small intensity ofL _II-Auger electrons is superposed on theL _III-Auger spectrum. The ratiod of intensities of line groupL _III M N to line groupL _III M M is found by extrapolation to bed=0·46±0·02. This combined with earlier results gives anL _III-Auger yielda ₃= 0·64±0·04. TheL _III fluorescenc yield isω ₃=0·36±0·04, correspondingly. A further application of the experimental method is described.