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This article is the second in a pair of articles on the topic of the generation of a two-color artificial star (which we term a "laser photometric ratio star," or LPRS) of de-excitation light from neutral sodium atoms in the mesosphere, for use in precision telescopic measurements in astronomy and atmospheric physics, and more specifically for the calibration of measurements of dark energy using type Ia supernovae. The two techniques respectively described in both this and the previous article would each generate an LPRS with a precisely 1:1 ratio of yellow (589/590 nm) photons to near-infrared (819/820 nm) photons produced in the mesosphere. Both techniques would provide novel mechanisms for establishing a spectrophotometric calibration ratio of unprecedented precision, from above most of Earth's atmosphere, for upcoming telescopic observations across astronomy and atmospheric physics. The technique described in this article has the advantage of producing a much brighter (specifically, brighter by approximately a factor of 1000) LPRS, using lower-power (<30 W average power) lasers, than the technique using a single 500 W average power laser described in the first article of this pair. However, the technique described here would require polarization filters to be installed into the telescope camera in order to sufficiently remove laser atmospheric Rayleigh backscatter from telescope images, whereas the technique described in the first article would only require more typical wavelength filters in order to sufficiently remove laser Rayleigh backscatter., Comment: The first article in this pair of articles is at arXiv:2001.10958 . This article has 15 pages and 3 figures. Both articles are published in MNRAS

The largest uncertainty on measurements of dark energy using type Ia supernovae is presently due to systematics from photometry; specifically to the relative uncertainty on photometry as a function of wavelength in the optical spectrum. We show that a precise constraint on relative photometry between the visible and near-infrared can be achieved in upcoming surveys (such as in LSST at the Vera C. Rubin Observatory) via a mountaintop-located laser source tuned to the 342.78 nm vacuum excitation wavelength of neutral sodium atoms. Using a high-power (500 W) laser modified from laser guide star studies, this excitation will produce an artificial star (which we term a "laser photometric ratio star," or LPRS) of de-excitation light in the mesosphere that is observable from the ground at approximately 20 magnitude (i.e., well within the expected single-image magnitude limit of LSST) at wavelengths in vacuum of 589.16 nm, 589.76 nm, 818.55 nm, and 819.70 nm, with the sum of the numbers of 589.16 nm and 589.76 nm photons produced by this process equal to the sum of the numbers of 818.55 nm and 819.70 nm photons, establishing a precise calibration ratio between, for example, the LSST r and z filters. This technique can thus provide a novel mechanism for establishing a spectrophotometric calibration ratio of unprecedented precision, from above most of the Earth's atmosphere, for upcoming telescopic observations across astronomy and atmospheric physics. This article is the first in a pair of articles on this topic. The second article of the pair describes an alternative technique to achieve a similar, but brighter, LPRS than the technique described in this paper, by using two mountaintop-located lasers, at optical frequencies approximately 4 GHz away from resonances at wavelengths in vacuum of 589.16 nm and 819.71 nm respectively., Comment: The second article in this pair of articles is at arXiv:2010.08683 . This article has 14 pages & 7 figures. Both articles are published in MNRAS. This most recent arXiv version fixes a minor error in the caption of Figure 4

The Thirty Meter Telescope (TMT) has been designed to include an adaptive optics system and associated laser guide star (LGS) facility to correct for the image distortion due to Earth's atmospheric turbulence and achieve diffraction-limited imaging. We have calculated the response of mesospheric sodium atoms to a pulsed laser that has been proposed for use in the LGS facility, including modeling of the atomic physics, the light-atom interactions, and the effect of the geomagnetic field and atomic collisions. This particular pulsed laser format is shown to provide comparable photon return to a continuous-wave (cw) laser of the same average power; both the cw and pulsed lasers have the potential to satisfy the TMT design requirements for photon return flux., Comment: 16 pages, 20 figures

The relationship between orientation-to-alignment conversion (a form of atomic polarization evolution induced by an electric field) and the phenomenon of spin squeezing is demonstrated. A "stretched" state of an atom or molecule with maximum angular-momentum projection along the quantization axis possesses orientation and is a quantum-mechanical minimum-uncertainty state, where the product of the equal uncertainties of the angular-momentum projections on two orthogonal directions transverse to the quantization axis is the minimum allowed by the uncertainty relation. Application of an electric field for a short time induces orientation-to-alignment conversion and produces a spin-squeezed state, in which the quantum state essentially remains a minimum-uncertainty state, but the uncertainties of the angular-momentum projections on the orthogonal directions are unequal. This property can be visualized using the angular-momentum probability surfaces, where the radius of the surface is given by the probability of measuring the maximum angular-momentum projection in that direction. Brief remarks are also given concerning collective-spin squeezing and quantum nondemolition measurements., Comment: 7 pages, 6 figures

We report measurements of nonlinear magneto-optical rotation (NMOR) for the D2 line of $^{87}$Rb atoms in an antirelaxation-coated vapor cell in the presence of a radio-frequency (rf) field. The experimental NMOR signals as a function of rf field frequency for various rf field powers are compared to a theoretical model based on the density-matrix formalism. The comparison between experiment and theory enables understanding of the ground-state atomic spin polarization dynamics, illustrated using plots of the probability distribution of the atomic angular momentum., Comment: 14 pages, 7 figures. Associated media files hosted at http://budker.berkeley.edu/rfnmor-movies/

Measurement of magnetic fields on the few-hundred-kilometer length scale is significant for a variety of geophysical applications including mapping of crustal magnetism and ocean-circulation measurements, yet available techniques for such measurements are very expensive or of limited accuracy. We propose a scheme for remote detection of magnetic fields using the naturally occurring atomic-sodium-rich layer in the mesosphere and existing high-power lasers developed for laser guide-star applications. The proposed scheme offers dramatic reduction in cost, opening the way to large-scale magnetic mapping missions., Comment: 5 pages, 3 figures

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

Context: Sodium laser guide stars (LGS) are about to enter a new range of laser powers. Previous theoretical and numerical methods are inadequate for accurate computations of the return flux and hence for the design of the next-generation LGS systems. Aims: We numerically optimize the cw (continuous wave) laser format, in particular the light polarization and spectrum. Methods: Using Bloch equations, we simulate the mesospheric sodium atoms, including Doppler broadening, saturation, collisional relaxation, Larmor precession, and recoil, taking into account all 24 sodium hyperfine states and on the order of 100 velocity groups. Results: LGS return flux is limited by "three evils": Larmor precession due to the geomagnetic field, atomic recoil due to radiation pressure, and transition saturation. We study their impacts and show that the return flux can be boosted by repumping (simultaneous excitation of the sodium D2a and D2b lines with 10-20% of the laser power in the latter). Conclusions: We strongly recommend the use of circularly polarized lasers and repumping. As a rule of thumb, the bandwidth of laser radiation in MHz (at each line) should approximately equal the launched laser power in Watts divided by six, assuming a diffraction-limited spot size., Comment: 15 pages, 12 figures, to be published in Astronomy & Astrophysics, AA/2009/13108

Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground-states in alkali atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called "heading errors" of alkali-vapor atomic magnetometers operating in the geophysical field range (B approx. 0.2-0.7 G). Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization and frequency, a technique that can be readily applied in practical situations., Comment: 5 pages, 5 figures, to be published in PRA

Atomic-vapor density change due to light induced atomic desorption (LIAD) is studied in paraffin-coated rubidium, cesium, sodium and potassium cells. In the present experiment, low-intensity probe light is used to obtain an absorption spectrum and measure the vapor density, while light from an argon-ion laser, array of light emitting diodes, or discharge lamp is used for desorption. Potassium is found to exhibit significantly weaker LIAD from paraffin compared to Rb and Cs, and we were unable to observe LIAD with sodium. A simple LIAD model is applied to describe the observed vapor-density dynamics, and the role of the cell's stem is explored through the use of cells with lockable stems. Stabilization of Cs vapor density above its equilibrium value over 25 minutes is demonstrated. The results of this work could be used to assess the use of LIAD for vapor-density control in magnetometers, clocks, and gyroscopes utilizing coated cells., Comment: 10 pages, 11 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

We demonstrate a magnetometric technique based on nonlinear magneto-optical rotation using amplitude modulated light. The magnetometers can be operated in either open-loop (typical nonlinear magneto-optical rotation with amplitude-modulated light) or closed-loop (self-oscillating) modes. The latter mode is particularly well suited for conditions where the magnetic field is changing by large amounts over a relatively short timescale., Comment: 8 pages, 6 figures, Submitted to Proc. of SPIE, Proceedings of XIVth International School on Quantum Electronics, Sunny Beach, Bulgaria 2006

We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. We demonstrate a sensitivity of $100\thinspace{\rm pG/\sqrt{Hz}\thinspace(RMS)}$ in a 3.5 cm diameter, paraffin coated cell. Based on detection at the photon shot-noise limit, we project a sensitivity of $20\thinspace{\rm pG/\sqrt{Hz}\thinspace(RMS)}$., Comment: 6 pages, 6 figures

We demonstrate the detection of magnetic particles carried by water in a continuous flow using an atomic magnetic gradiometer. Studies on three types of magnetic particles are presented: a single cobalt particle (diameter ~150 um, multi-domain), a suspension of superparamagnetic magnetite particles (diameter \~1 um), and ferromagnetic cobalt nanoparticles (diameter ~10 nm, 120 kA/m magnetization). Estimated detection limits are 20 um diameter for a single cobalt particle at a water flow rate 30 ml/min, 5x10^3 magnetite particles at 160 ml/min, and 50 pl for the specific ferromagnetic fluid at 130 ml/min. Possible applications of our method are discussed., Comment: 10 pages, 4 figures

In this work, a sensitivity of the rate of relaxation of ground-state atomic coherences to magnetic-field inhomogeneities is studied. Such coherences give rise to many interesting phenomena in light-atom interactions, and their lifetimes are a limiting factor for achieving better sensitivity, resolution or contrast in many applications. For atoms contained in a vapor cell, some of the coherence-relaxation mechanisms are related to magnetic-field inhomogeneities. We present a simple model describing relaxation due to such inhomogeneities in a buffer-gas-free anti-relaxation coated cell. A relation is given between relaxation rate and magnetic-field inhomogeneities including the dependence on cell size and atomic spices. Experimental results, which confirm predictions of the model, are presented. Different regimes, in which the relaxation rate is equally sensitive to the gradients in any direction and in which it is insensitive to gradients transverse to the bias magnetic field, are predicted and demonstrated experimentally., Comment: 6 pages, 4 figures, Submitted to Phys. Rev. A

Larmor precession of laser-polarized atoms contained in anti-relaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR) is a promising technique for a new generation of ultra-sensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency- or amplitude-modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. New NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These new resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method for NMOR-based vector magnetometry., Comment: Submitted to Phys. Rev. A, 6 pages, 9 figures

Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived ($\tau\ts{rel} \sim 1 {\rm s}$) ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding $10^{-11} {\rm G/\sqrt{Hz}}$ for small ($\lesssim 1 {\rm \mu G}$) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range ($\sim 500 {\rm mG}$), of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered., Comment: 8 pages, 8 figures

We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parameterizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light-wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced \mbox{${\rm 6s^2}~ ^1{\rm S}_0~\to ~{\rm 5d6s}~ ^3{\rm D}_1\:$} transition at 408 nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the ${\rm 6s^2 \:} ^1{\rm S}_0\:$ ground state. A detailed description of the experiment and analysis is presented. A bi-product of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb., Comment: 15 pages, 11 figs

Specific types of atomic coherences between Zeeman sublevels can be generated and detected using a method based on nonlinear magneto-optical rotation with frequency modulated light. Linearly polarized, frequency modulated light is employed to selectively generate ground-state coherences between Zeeman sublevels for which $\Delta m=2$ and $\Delta m=4$ in $^{85}$Rb and $^{87}$Rb atoms, and additionally $\Delta m=6$ in $^{85}$Rb. The atomic coherences are detected with a separate, unmodulated probe light beam. Separation of the pump and probe beams enables independent investigation of the processes of creation and detection of the atomic coherences. With the present technique the transfer of the Zeeman coherences, including high-order coherences, from excited to ground state by spontaneous emission has been observed., Comment: 12 pages, 17 figures

The relaxation of atomic polarization in buffer-gas-free, paraffin-coated cesium vapor cells is studied using a variation on Franzen's technique of ``relaxation in the dark'' [Franzen, Phys. Rev. {\bf 115}, 850 (1959)]. In the present experiment, narrow-band, circularly polarized pump light, resonant with the Cs D2 transition, orients atoms along a longitudinal magnetic field, and time-dependent optical rotation of linearly polarized probe light is measured to determine the relaxation rates of the atomic orientation of a particular hyperfine level. The change in relaxation rates during light-induced atomic desorption (LIAD) is studied. No significant change in the spin relaxation rate during LIAD is found beyond that expected from the faster rate of spin-exchange collisions due to the increase in Cs density., Comment: 14 pages, 14 figures

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

We report the use of an atomic magnetometer based on nonlinear magneto-optical rotation with frequency modulated light (FM NMOR) to detect nuclear magnetization of xenon gas. The magnetization of a spin-exchange-polarized xenon sample ($1.7 $cm$^3$ at a pressure of $5 $bar, natural isotopic abundance, polarization 1%), prepared remotely to the detection apparatus, is measured with an atomic sensor (which is insensitive to the leading field of 0.45 G applied to the sample; an independent bias field at the sensor is $140 \mu$G). An average magnetic field of $\sim 10 $nG induced by the xenon sample on the 10-cm diameter atomic sensor is detected with signal-to-noise ratio $\sim 10$, limited by residual noise in the magnetic environment. The possibility of using modern atomic magnetometers as detectors of nuclear magnetic resonance and in magnetic resonance imaging is discussed. Atomic magnetometers appear to be ideally suited for emerging low-field and remote-detection magnetic resonance applications., Comment: 4 pages, 4 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

Recent work on Lambda-resonances in alkali metal vapors (E. Mikhailov, I. Novikova, Yu. V. Rostovtsev, and G. R. Welch, quant-ph/0309171, and references therein) investigated a type of electromagnetically induced absorption resonance that occurs in three-level systems under specific conditions normally associated with electromagnetically induced transparency. In this note, we show that these resonances have a direct analog in nonlinear magneto-optics, and support this conclusion with a calculation for a J=1->J'=0 system interacting with a single nearly circularly polarized light field in the presence of a weak longitudinal magnetic field., Comment: 4 pages, 2 figures v2. revised for clarity and completeness

A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J=1->J'=0 transition is presented. The theory is developed for a Doppler-free transition, and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1 line., Comment: 11 pages, 5 figures, v.2 edited for clarity

Electric polarizabilities of four low-J even-parity states and three low-J odd-parity states of atomic barium in the range $35,600 $ to $36,000\ $cm$^{-1}$ are investigated. The states of interest are excited (in an atomic beam) via an intermediate odd-parity state with a sequence of two laser pulses. The odd-parity states can be excited due to the Stark-induced mixing with even-parity states. The polarizabilities are measured via direct spectroscopy on the second-stage transition. Several states have tensor and scalar polarizabilities that exceed the values that might be expected from the known energy levels of barium by more than two orders of magnitude. Two of the Stark-induced transitions cannot be identified from the known energy spectrum of barium. The observations suggest the existence of as yet unidentified odd-parity energy states, whose energies and angular momenta are determined in the present experiment. A tentative identification of these states as [Xe]$6s8p ^3P_{0,2}$ is suggested., Comment: 29 pages, 12 figures

The role of alignment-to-orientation conversion (AOC) in nuclear quadrupole resonance (NQR) is discussed. AOC is shown to be the mechanism responsible for the appearance of macroscopic orientation in a sample originally lacking any global polarization. Parallels are drawn between NQR and AOC in atomic physics., Comment: 4 pages, 3 figures, v2: reorganized, Appendix added

We describe a method of selective generation and study of polarization moments of up to the highest rank $\kappa=2F$ possible for a quantum state with total angular momentum $F$. The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of $^{87}$Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultra-narrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances has important applications in quantum and nonlinear optics and in magnetometry., Comment: 5 pages, 6 figures

In this article, we review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. We begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances, and contrast these effects with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultra-narrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms., Comment: 51 pages, 23 figures, to appear in Rev. Mod. Phys. in Oct. 2002, Figure added, typos corrected, text edited for clarity

Nonlinear magneto-optical rotation is a sensitive technique for measuring magnetic fields. Here, the shot-noise-limited magnetometric sensitivity is analyzed for the case of optically-thick media and high light power, which has been the subject of recent experimental and theoretical investigations., Comment: 7 pages, 4 figures

When linearly polarized light propagates through a medium in which elliptically polarized light would undergo self-rotation, squeezed vacuum can appear in the orthogonal polarization. A simple relationship between self-rotation and the degree of vacuum squeezing is developed. Taking into account absorption, we find the optimum conditions for squeezing in any medium that can produce self-rotation. We then find analytic expressions for the amount of vacuum squeezing produced by an atomic vapor when light is near-resonant with a transition between various low-angular-momentum states. Finally, we consider a gas of multi-level Rb atoms, and analyze squeezing for light tuned near the D-lines under realistic conditions., Comment: 10 pages, 6 figures; Submitted to PRA