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$^{39}$K atoms have the smallest ground state ($^2S_{1/2}$) hyperfine splitting of all the most naturally abundent alkali isotopes and, consequently, the smallest characteristic magnetic field value $B_0 = A_{^2S_{1/2}}/\mu_B \approx 170$ G, where $A_{^2S_{1/2}}$ is the ground state's magnetic dipole interaction constant. In the hyperfine Paschen-Back regime ($B \gg B_0$, where $B$ is the magnitude of the external magnetic field applied on the atoms), only 8 Zeeman transitions are visible in the absorption spectrum of the $D_1$ line of $^{39}$K, while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of $^{39}$K, this behavior is reached already at relatively low magnetic field $B > B_0$. For each circular polarization ($\sigma^-,\sigma^+$), 4 spectrally resolved atomic transitions having a sub-Doppler width are recorded using a sub-microsized vapor cell of thickness $L = 120 - 390$ nm. We present a method that allows to measure the magnetic field in the range $0.1 - 10$ kG with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with a large gradient (up to 3 G$/\mu$m). The theoretical model describes well the experimental results., Comment: 7 pages, 5 figures

We investigated experimentally and theoretically angular momentum alignment-to-orientation conversion created by the joint interaction of laser radiation and an external magnetic field with atomic rubidium at room temperature. In particular we were interested in alignment-to-orientation conversion in atomic ground state. Experimentally the laser frequency was fixed to the hyperfine transitions of $D_1$ line of rubidium. We used a theoretical model for signal simulations that takes into account all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. The experiments were carried out by exciting the atoms with linearly polarized laser radiation. Two oppositely circularly polarized laser induced fluorescence (LIF) components were detected and afterwards their difference was taken. The combined LIF signals originating from the hyperfine magnetic sublevel transitions of $^{85}$Rb and $^{87}$Rb rubidium isotopes were included. The alignment-to-orientation conversion can be undoubtedly identified in the difference signals for various laser frequencies as well as change in signal shapes can be observed when the laser power density is increased. We studied the formation and the underlying physical processes of the observed signal of the LIF components and their difference by performing the analysis of the influence of incoherent and coherent effects. We performed simulations of theoretical signals that showed the influence of ground-state coherent effects on the LIF difference signal., Comment: 11 pages, 11 figures

In this letter we demonstrate universal symmetry breaking by means of magnetically induced circular dichroism. Magnetic field induces forbidden at zero field atomic transitions between $\Delta F = \pm2$ hyperfine levels. In a particular range of magnetic field, intensities of these transitions experience significant enhancement. We have deduced a general rule applicable for the $D_2$ lines of all bosonic alkali atoms, that is transition intensity enhancement is larger for the case of $\sigma^+$ than for $\sigma^-$ excitation for $\Delta F = +2$, whereas it is larger (e.g. up to $10^{11}$ times for $^{85}$Rb atoms) in the case of $\sigma^-$ than for $\sigma^+$ polarization for $\Delta F = -2$. This asymmetric behaviour results in an explicit circular dichroism. For experimental verification we employed half-wavelength-thick atomic vapor nanocells using a derivative of selective reflection technique, which provides sub-Doppler spectroscopic linewidth ($\sim$50 MHz). The presented theoretical curves well describe the experimental results. This effect can find applications particularly in parity violation experiments., Comment: 5 pages, 5 figures

We present systematic measurements of longitudinal relaxation rates ($1/T_1$) of spin polarization in the ground state of the nitrogen-vacancy (NV$^-$) color center in synthetic diamond as a function of NV$^-$ concentration and magnetic field $B$. NV$^-$ centers were created by irradiating a Type 1b single-crystal diamond along the [100] axis with 200 keV electrons from a transmission electron microscope with varying doses to achieve spots of different NV$^-$ center concentrations. Values of ($1/T_1$) were measured for each spot as a function of $B$., Comment: 4 pages, 8 figures

We present experimental and numerical studies of nonlinear magneto-optical rotation (NMOR) in rubidium vapor excited with resonant light tuned to the $5^2\!S_{1/2}\rightarrow 6^2\!P_{1/2}$ absorption line (421~nm). Contrary to the experiments performed to date on the strong $D_1$ or $D_2$ lines, in this case, the spontaneous decay of the excited state $6^2\!P_{1/2}$ may occur via multiple intermediate states, affecting the dynamics, magnitude and other characteristics of NMOR. Comparing the experimental results with the results of modelling based on Auzinsh et al., Phys. Rev. A 80, 1 (2009), we demonstrate that despite the complexity of the structure, NMOR can be adequately described with a model, where only a single excited-state relaxation rate is used., Comment: 10 pages, 7 figures

The electromagnetically induced transparency (EIT) phenomenon has been investigated in a $\Lambda$-system of the $^{87}$Rb D$_1$ line in an external transverse magnetic field. Two spectroscopic cells having strongly different values of the relaxation rates $\gamma_{rel}$ are used: a Rb cell with antirelaxation coating ($L\sim$1 cm) and a Rb nanometric-thin cell (nano-cell) with thickness of the atomic vapor column $L$=795nm. For the EIT in the nano-cell, we have the usual EIT resonances characterized by a reduction in the absorption (i.e. dark resonance (DR)), whereas for the EIT in the Rb cell with an antirelaxation coating, the resonances demonstrate an increase in the absorption (i.e. bright resonances). We suppose that such unusual behavior of the EIT resonances (i.e. the reversal of the sign from DR to BR) is caused by the influence of alignment process. The influence of alignment strongly depends on the configuration of the coupling and probe frequencies as well as on the configuration of the magnetic field., Comment: 9 pages,23 figures

We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the $D_2$ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments laser induced fluorescence (LIF) components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components we were able to see structures not visible in the difference graphs, which yields deeper insight into the processes responsible for these signals. We studied how these signals are dependent on laser power density and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions., Comment: 11 pages, 13 figures

We have measured magneto-optical signals obtained by exciting the $D_1$ line of cesium atoms confined to an extremely thin cell (ETC), whose walls are separated by less than one micrometer, and developed an improved theoretical model to describe these signals with experimental precision. The theoretical model was based on the optical Bloch equations and included all neighboring hyperfine transitions, the mixing of the magnetic sublevels in an external magnetic field, and the Doppler effect, as in previous studies. However, in order to model the extreme conditions in the ETC more realistically, the model was extended to include a unified treatment of transit relaxation and wall collisions with relaxation rates that were obtained directly from the thermal velocities of the atoms and the length scales involved. Furthermore, the interaction of the atoms with different regions of the laser beam were modeled separately to account for the varying laser beam intensity over the beam profile as well as saturation effects that become important near the center of the beam at the relatively high laser intensities used during the experiments in order to obtain measurable signals. The model described the experimentally measured signals for laser intensities for magnetic fields up to 55~G and laser intensities up to 1~W/cm$^2$ with excellent agreement., Comment: 9 pages, 7 figures

Simple and efficient "\lambda-method" and "\lambda/2-method" (\lambda is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D_1 line in an external magnetic field in the range of B = 0.5 - 0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of \sigma+ polarized laser radiation, only 6 (4) remain at B > 0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen-Back regime). The expressions derived in the frame of completely uncoupled basis (J, m_J ; I, m_I) describe very well the experimental results for 85Rb transitions at $B > 0.6 T (that is a manifestation of hyperfine Paschen-Back regime). A remarkable result is that the calculations based on the eigenstates of coupled (F, m_F) basis, which adequately describe the system for low magnetic field, also predict reduction of number of transition components from 20 to 6 for 85Rb, and from 12 to 4 for 87Rb spectrum at B > 0.5 T. Also, the Zeeman transitions frequency shift, frequency interval between the components and their slope versus $B$ are in agreement with the experiment., Comment: 10 pages, 13 figures

We present the results of an experimental as well as theoretical study of nonlinear magneto-optical resonances in diatomic potassium molecules in the electronic ground state with large values of the angular momentum quantum number J~100. At zero magnetic field, the absorption transitions are suppressed because of population trapping in the ground state due to Zeeman coherences between magnetic sublevels of this state along with depopulation pumping. The destruction of such coherences in an external magnetic field was used to study the resonances in this work. K2 molecules were formed in a glass cell filled with potassium metal at a temperature above 150C. The cell was placed in an oven and was located in a homogeneous magnetic field B, which was scanned from zero to 0.7 T. Q-type and R-type transitions were excited with a tunable, single-mode diode laser with central wavelength of 660 nm. Well pronounced nonlinear Hanle effect signals were observed in the intensities of the linearly polarized components of the laser-induced fluorescence (LIF) detected in the direction parallel to the (B)-field with polarization vectors parallel (I_par) and perpendicular (I_per) to the polarization vector of the exciting laser radiation, which was orthogonal to (B). The intensities of the LIF components were detected for different experimental parameters, such as laser power density and vapor temperature, in order to compare them with numerical simulations that were based on the optical Bloch equations for the density matrix. We report good agreement of our measurements with numerical simulations. Narrow, subnatural line width dark resonances in I_per(B) were detected and explained.

We have implemented the so-called $\lambda$-Zeeman technique (LZT) to investigate individual hyperfine transitions between Zeeman sublevels of the Rb atoms in a strong external magnetic field $B$ in the range of $2500 - 5000$ G (recently it was established that LZT is very convenient for the range of $10 - 2500$ G). Atoms are confined in a nanometric thin cell (NTC) with the thickness $L = \lambda$, where $\lambda$ is the resonant wavelength 794 nm for Rb $D_1$ line. Narrow velocity selective optical pumping (VSOP) resonances in the transmission spectrum of the NTC are split into several components in a magnetic field with the frequency positions and transition probabilities depending on the $B$-field. Possible applications are described, such as magnetometers with nanometric local spatial resolution and tunable atomic frequency references., Comment: 12 pages

Measurements were made to determine the density of rubidium dimer vapor in paraffin-coated cells. The number density of dimers and atoms in similar paraffin-coated and uncoated cells was measured by optical spectroscopy. Due to the relatively low melting point of paraffin, a limited temperature range of 43-80 deg C was explored, with the lower end corresponding to a dimer density of less than 10^7 cm^(-3). With one-minute integration time, a sensitivity to dimer number density of better than 10^6 cm^(-3) was achieved. No significant difference in dimer density was observed between the cells., Comment: 5 pages, 2 figures, edited intro and minor misprints. To appear in NJP

Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground state total angular momentum F_g was greater than or equal to the excited state total angular momentum F_e. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. Although the values of certain model parameters in the ETC differed significantly from the case of ordinary cells, the same physical processes were used to model both cases. However, to describe the resonances in the ETC, key parameters such as the transit relaxation rate and Doppler width had to be modified in accordance with the ETC's unique features. Agreement between the measured and calculated resonance curves was satisfactory for the ETC, though not as good as in the case of ordinary cells., Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10 figures; accepted for publication in Physical Review A

The creation and detection of atomic polarization is examined theoretically, through the study of basic optical-pumping mechanisms and absorption and fluorescence measurements, and the dependence of these processes on the size of ground- and excited-state hyperfine splittings is determined. The consequences of this dependence are studied in more detail for the case of nonlinear magneto-optical rotation in the Faraday geometry (an effect requiring the creation and detection of rank-two polarization in the ground state) with alkali atoms. Analytic formulas for the optical rotation signal under various experimental conditions are presented., Comment: v2: Version to be published

Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. Great care was taken to obtain accurate experimental signals and avoid systematic errors. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the F_g=1 --> F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position of the transition due to the influence of the nearby F_g=2 --> F_e=2 transition, which is a dark resonance whose contrast is almost two orders of magnitude larger than the contrast of the bright resonance at the F_g=2 --> F_e=3 transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings., Comment: 11 pages, 9 figures

Anisotropy of atomic states is characterized by population differences and coherences between Zeeman sublevels. It can be efficiently created and probed via resonant interactions with light, the technique which is at the heart of modern atomic clocks and magnetometers. Recently, nonlinear magneto-optical techniques have been developed for selective production and detection of higher polarization moments, hexadecapole and hexacontatetrapole, in the ground states of the alkali atoms. Extension of these techniques into the range of geomagnetic fields is important for practical applications. This is because hexadecapole polarization corresponding to the $\Delta M=4$ Zeeman coherence, with maximum possible $\Delta M$ for electronic angular momentum $J=1/2$ and nuclear spin $I=3/2$, is insensitive to the nonlinear Zeeman effect (NLZ). This is of particular interest because NLZ normally leads to resonance splitting and systematic errors in atomic magnetometers. However, optical signals due to the hexadecapole moment decline sharply as a function of magnetic field. We report a novel method that allows selective creation of a macroscopic long-lived ground-state hexadecapole polarization. The immunity of the hexadecapole signal to NLZ is demonstrated with F=2 $^{87}$Rb atoms at Earth's field., Comment: 4 pages, 5 figures

Experimental and theoretical studies are presented related to the ground-state magneto-optical resonance prepared in Cesium vapour confined in an Extremely Thin Cell (ETC, with thickness equal to the wavelength of the irradiating light). It is shown that the utilization of the ETC allows one to examine the formation of a magneto-optical resonance on the individual hyperfine transitions, thus distinguishing processes resulting in dark (reduced absorption) or bright (enhanced absorption) resonance formation. We report on an experimental evidence of the bright magneto-optical resonance sign reversal in Cs atoms confined in the ETC. A theoretical model is proposed based on the optical Bloch equations that involves the elastic interaction processes of atoms in the ETC with its walls resulting in depolarization of the Cs excited state which is polarized by the exciting radiation. This depolarization leads to the sign reversal of the bright resonance. Using the proposed model, the magneto-optical resonance amplitude and width as a function of laser power are calculated and compared with the experimental ones. The numerical results are in good agreement with the experiment.

We have studied the resonance fluorescence of a room-temperature rubidium vapor exited to the atomic 5P3/2 state (D2 line) by powerful single-frequency cw laser radiation (1.25 W/cm^2) in the presence of a magnetic field. In these studies, the slow, linear scanning of the laser frequency across the hyperfine transitions of the D2 line is combined with a fast linear scanning of the applied magnetic field, which allows us to record frequency-dependent Hanle resonances from all the groups of hyperfine transitions including V- and Lambda - type systems. Rate equations were used to simulate fluorescence signals for 85Rb due to circularly polarized exciting laser radiation with different mean frequency values and laser intensity values. The simulation show a dependance of the fluorescence on the magnetic field. The Doppler effect was taken into account by averaging the calculated signals over different velocity groups. Theoretical calculations give a width of the signal peak in good agreement with experiment.

We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for these states are also presented and checked for consistency with experimental values., Comment: 12 pages, revtex4, 11 figure files

The pure electric field level-crossing of m_F Zeeman sublevels of hyperfine F levels at two-step laser excitation was described theoretically and studied experimentally for the nD_3/2 states in Cs with n = 7,9, and 10, by applying a diode laser in the first 6S_1/2 to 6P_3/2 step and a diode or dye laser for the second 6P_3/2 to nD_3/2 step. Level-crossing resonance signals were observed in the nD_3/2 to 6P_1/2 fluorescence. A theoretical model was developed to describe quantitatively the resonance signals by correlation analysis of the optical Bloch equations in the case when an atom simultaneously interacts with two laser fields in the presence of an external dc electric field. The simulations described well the experimental signals. The tensor polarizabilities (in Bohr radii cubed) were determined to be 7.45(20) x 10^4 for the 7D_3/2 state and 1.183(35) x 10^6 for the 9D_3/2 state; a well established tensor polarizability value for 10D_3/2 was used to calibrate the electric field. The tensor polarizability value for the 7D_3/2 state differed by ca. 15% from the existing experimentally measured value., Comment: 10 pages, 6 figures (10 eps files), revtex4, submitted to Optics Communications

In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization., Comment: This is a companion note to physics/0403097

A brief review is given of topics relating to dynamical processes arising in nonlinear interactions between light and resonant systems (atoms or molecules) in the presence of a magnetic field., Comment: 15 pages, 11 figures

Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. Fundamental noise sources include the quantum projection noise and the photon shot-noise. For measurement times much shorter than the spin-relaxation time observed in the absence of light ($\tau_{\rm rel}$) divided by $\sqrt{N}$, the optimal sensitivity of the magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity scaling as $N^{-1/2}$ can be achieved. However, at longer measurement times, the optimized sensitivity scales as $N^{-1/2}$, as for a usual shot-noise limited magnetometer. If strongly squeezed probe light is used, the Heisenberg uncertainty limit may, in principle, be reached for very short measurement times. However, if the measurement time exceeds $\tau_{\rm rel}/N$, the $N^{-1/2}$ scaling is again restored., Comment: Some details of calculations can be found in a companion note: physics/0407125

In this paper a new method is presented for particles in storage rings which could reach a statistical sensitivity of 10**(-27) e cm for the deuteron EDM. This implies an improvement of two orders of magnitude over the present best limits on the T-odd nuclear forces ksi parameter., Comment: 5 pages. Proceedings of a talk presented at CIPANP 2003, May 19-24, 2003

In this paper a coherent superposition of angular momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing spatial orientation of internuclear axis of diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing Zeeman effect and molecules absorbing light in a permanent electric field experiencing quadratic Stark effect. In a magnetic field we have a wave packet that evolves in time exactly as classical dipole oscillator in a permanent magnetic field. In the second case we have the wave packet that goes through periodical changes of a shape of the packet and revivals of initial shape. This is a pure quantum behavior. Classical motion of angular momentum in an electric field in case of quadratic Stark effect is known to be aperiodic. Obtained solutions for wave packet evolution are briefly compared with Rydberg state coherent wave packets and harmonic oscillator wave packets., Comment: LaTeX, 3 figures

A simple expression for a ground state energy for a two-electron atom is derived. For this, assumption based upon the Niels Bohr ''old'' quantum mechanics idea about electron correlation in a two-electron atom is exploited. Results are compared with experimental data and theoretical results based on a variation approach., Comment: LaTeX 5 pages, 1 figure, 1 table