Search

The original version of this chapter was published with incorrect text on page 48 last paragraph 8th and 9th lines

Many theories predict that ultralight bosonic dark matter (UBDM) can couple to photons and thus generate electromagnetic signals. In such scenarios, UBDM can be searched for using a radio: an antenna connected to a tunable LC circuit that is in turn connected to an amplifier. Such “dark matter radios” are particularly useful tools to search the broad range of UBDM wavelengths where resonant cavity dimensions are too large to be practical. In this chapter, we discuss how dark matter radios can be used to search for UBDM, focusing on the case of hidden photons.

Self-compensated comagnetometers, employing overlapping samples of spin-polarized alkali and noble gases (for example K-$^3$He) are promising sensors for exotic beyond-the-standard-model fields and high-precision metrology such as rotation sensing. When the comagnetometer operates in the so-called self-compensated regime, the effective field, originating from contact interactions between the alkali valence electrons and the noble-gas nuclei, is compensated with an applied magnetic field. When the comagnetometer begins operation in a given magnetic field, spin-exchange optical pumping establishes equilibrium between the alkali electron-spin polarization and the nuclear-spin polarization. Subsequently, when the magnetic field is tuned to the compensation point, the spin polarization is brought out of the equilibrium conditions. This causes a practical issue for long measurement times. We report on a novel method for closed-loop control of the compensation field. This method allows optimization of the operating parameters, especially magnetic field gradients, in spite of the inherently slow (hours to days) dynamics of the system. With the optimization, higher stable nuclear polarization, longer relaxation times and stronger electron-nuclear coupling are achieved which is useful for nuclear-spin-based quantum memory, spin amplifiers and gyroscopes. The optimized sensor demonstrates a sensitivity comparable to the best previous comagnetometer but with four times lower noble gas density. This paves the way for applications in both fundamental and applied science.

In our recent companion paper [arXiv:2106.00022], we pointed out a novel signature of ultralight kinetically mixed dark-photon dark matter. This signature is a quasi-monochromatic, time-oscillating terrestrial magnetic field that takes a particular pattern over the surface of the Earth. In this work, we present a search for this signal in existing, unshielded magnetometer data recorded by geographically dispersed, geomagnetic stations. The dataset comes from the SuperMAG Collaboration and consists of measurements taken with one-minute cadence since 1970, with $\mathcal{O}(500)$ stations contributing in all. We aggregate the magnetic field measurements from all stations by projecting them onto a small set of global vector spherical harmonics (VSH) that capture the expected vectorial pattern of the signal at each station. Within each dark-photon coherence time, we use a data-driven technique to estimate the broadband background noise in the data, and search for excess narrowband power in this set of VSH components; we stack the searches in distinct coherence times incoherently. Following a Bayesian analysis approach that allows us to account for the stochastic nature of the dark-photon dark-matter field, we set exclusion bounds on the kinetic mixing parameter in the dark-photon dark-matter mass range $2\times10^{-18}\,\text{eV} \lesssim m_{A'} \lesssim 7\times10^{-17}\,\text{eV}$ (corresponding to frequencies $6\times 10^{-4}\,\text{Hz}\lesssim f_{A'} \lesssim 2\times 10^{-2}\,\text{Hz}$). These limits are complementary to various existing astrophysical constraints. Although our main analysis also identifies a number of candidate signals in the SuperMAG dataset, these appear to either fail or be in tension with various additional robustness checks we apply to those candidates. We report no robust and significant evidence for a dark-photon dark-matter signal in the SuperMAG dataset., Comment: 41 pages, 11 figures. Published version

A host of astrophysical and cosmological measurements have established that the majority of matter in the Universe is dark matter. Understanding its nature is of paramount importance to astrophysics, cosmology, and particle physics. A well-motivated possibility is that the dark matter consists of ultralight bosons such as axions, with masses far smaller than 1 eV, in which case they are well-described as a classical field. Due to topology or self-interactions, ultralight bosonic fields can form stable, macroscopic configurations in the form of boson stars or topological defects (domain walls). Even in the absence of topological defects or self-interactions, bosonic dark matter fields exhibit stochastic fluctuations. Furthermore, cataclysmic astrophysical events (like black hole mergers) could produce intense bursts of exotic low-mass fields (ELFs). In any of these scenarios, instead of being bathed in a uniform flux, terrestrial detectors will witness transient events when the exotic bosonic fields pass through Earth. The Global Network of Optical Magnetometers to search for Exotic physics (GNOME): an international collaboration to search for such transient events with a worldwide network of more than a dozen time-synchronized optical atomic magnetometers, with stations in Europe, North America, Asia, the Middle East, and Australia. We will report on our latest results and future directions.

The Global Network of Optical Magnetometers for Exotic physics searches (GNOME) conducts an experimental search for certain forms of dark matter based on their spatiotemporal signatures imprinted on a global array of synchronized atomic magnetometers. The experiment described here looks for a gradient coupling of axion-like particles (ALPs) with proton spins as a signature of locally dense dark matter objects such as domain walls. In this work, stochastic optimization with machine learning is proposed for use in a search for ALP domain walls based on GNOME data. The validity and reliability of this method were verified using binary classification. The projected sensitivity of this new analysis method for ALP domain-wall crossing events is presented.

Nuclear magnetic resonance is a promising experimental approach to search for ultra-light axion-like dark matter. Searches such as the cosmic axion spin-precession experiments (CASPEr) are ultimately limited by quantum-mechanical noise sources, in particular, spin-projection noise. We discuss how such fundamental limits can potentially be reached. We consider a circuit model of a magnetic resonance experiment and quantify three noise sources: spin-projection noise, thermal noise, and amplifier noise. Calculation of the total noise spectrum takes into account the modification of the circuit impedance by the presence of nuclear spins, as well as the circuit back-action on the spin ensemble. Suppression of the circuit back-action is especially important in order for the spin-projection noise limits of searches for axion-like dark matter to reach the quantum chromodynamic axion sensitivity.

Physical review letters 126(14), 141802 (2021). doi:10.1103/PhysRevLett.126.141802, Published by APS, College Park, Md.

An overview of our experimental program to search for axion and axion-like-particle (ALP) dark matter using nuclear magnetic resonance (NMR) techniques is presented. An oscillating axion field can exert a time-varying torque on nuclear spins either directly or via generation of an oscillating nuclear electric dipole moment (EDM). Magnetic resonance techniques can be used to detect such an effect. The first-generation experiments explore many decades of ALP parameter space beyond the current astrophysical and laboratory bounds. It is anticipated that future versions of the experiments will be sensitive to the axions associated with quantum chromodynamics (QCD) having masses \({\lesssim }10^{-9}\,\mathrm {eV}/c^2\).

The Global Network of Optical Magnetometers for Exotic physics searches (GNOME) is a network of time-synchronized, geographically separated, optically pumped atomic magnetometers that is being used to search for correlated transient signals heralding exotic physics. GNOME is sensitive to exotic couplings of atomic spins to certain classes of dark matter candidates, such as axions. This work presents a data analysis procedure to search for axion dark matter in the form of topological defects: specifically, walls separating domains of discrete degenerate vacua in the axion field. An axion domain wall crossing the Earth creates a distinctive signal pattern in the network that can be distinguished from random noise. The reliability of the analysis procedure and the sensitivity of the GNOME to domain-wall crossings are studied using simulated data.

Physical review letters 122(19), 191302 (2019). doi:10.1103/PhysRevLett.122.191302, Published by APS, College Park, Md.

Report of the first workshop to identify approaches and techniques in the domain of quantum sensing that can be utilized by future High Energy Physics applications to further the scientific goals of High Energy Physics.

Heretofore undiscovered spin-0 or spin-1 bosons can mediate exotic spin-dependent interactions between standard-model particles. Here we carry out the first search for semileptonic spin-dependent interactions between matter and antimatter. We compare theoretical calculations and spectroscopic measurements of the hyperfine structure of antiprotonic helium to constrain exotic spin- and velocity-dependent interactions between electrons and antiprotons., 10 pages, 6 figures, 3 appendices

Under conditions where the angular momentum of a ferromagnetic particle is dominated by intrinsic spin, applied torque is predicted to cause gyroscopic precession of the particle. If the particle is sufficiently isolated from the environment, a measurement of spin precession can potentially yield sensitivity to torque beyond the standard quantum limit. Levitation of a micron-scale ferromagnetic particle above a superconductor is a possible method of near frictionless suspension enabling observation of ferromagnetic particle precession and ultrasensitive torque measurements. We experimentally investigate the dynamics of a micron-scale ferromagnetic particle levitated above a superconducting niobium surface. We find that the levitating particles are trapped in potential minima associated with residual magnetic flux pinned by the superconductor and, using an optical technique, characterize the quasiperiodic motion of the particles in these traps., Comment: 9 pages, 10 figures

Results of a search for a long-range monopole-dipole coupling between the mass of the Earth and rubidium (Rb) nuclear spins are reported. The experiment simultaneously measures the spin precession frequencies of overlapping ensembles of $^{85}$Rb and $^{87}$Rb atoms contained within an evacuated, antirelaxation-coated vapor cell. The nuclear structure of the Rb isotopes makes the experiment particularly sensitive to spin-dependent interactions of the proton. The spin-dependent component of the gravitational energy of the proton in the Earth's field is found to be smaller than $3 \times 10^{-18}~{\rm eV}$, improving laboratory constraints on long-range monopole-dipole interactions by over three orders of magnitude., 10 pages, 8 figures

Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, constraints on dipole-dipole interactions associated with the exchange of pseudoscalar bosons (such as axions or axion-like particles) with masses ${10}^{\ensuremath{-}2}\ensuremath{\lesssim}m\ensuremath{\lesssim}{10}^{4}\mathrm{eV}$ are improved by a factor of $\ensuremath{\sim}100$. The first atomic-scale constraints on several exotic velocity-dependent dipole-dipole interactions are established as well.

The Cosmic Axion Spin Precession Experiment (CASPEr) is a nuclear magnetic resonance experiment (NMR) seeking to detect axion and axion-like particles which could make up the dark matter present in the universe. We review the predicted couplings of axions and axion-like particles with baryonic matter that enable their detection via NMR. We then describe two measurement schemes being implemented in CASPEr. The first method, presented in the original CASPEr proposal, consists of a resonant search via continuous-wave NMR spectroscopy. This method offers the highest sensitivity for frequencies ranging from a few Hz to hundreds of MHz, corresponding to masses $ m_{\rm a} \sim 10^{-14}$--$10^{-6}$ eV. Sub-Hz frequencies are typically difficult to probe with NMR due to the diminishing sensitivity of magnetometers in this region. To circumvent this limitation, we suggest new detection and data processing modalities. We describe a non-resonant frequency-modulation detection scheme, enabling searches from mHz to Hz frequencies ($m_{\rm a} \sim 10^{-17}$--$10^{-14} $ eV), extending the detection bandwidth by three decades.

New constraints on exotic dipole-dipole interactions between electrons at the micrometer scale are established, based on a recent measurement of the magnetic interaction between two trapped $^{88}$Sr$^+$ ions. For light bosons (mass $\le$ 0.1 eV) we obtain a $90\%$ confidence interval on axial-vector mediated interaction strength of $\left|g_A^eg_A^e/4\pi\hbar c\right|\le 1.2\times 10^{-17}$. Assuming CPT invariance, this constraint is compared to that on anomalous electron-positron interactions, derived from positronium hyperfine spectroscopy. We find that the electron-electron constraint is six orders of magnitude more stringent than the electron-positron counterpart. Bounds on pseudo-scalar mediated interaction as well as on torsion gravity are also derived and compared with previous work performed at different length scales. Our constraints benefit from the high controllability of the experimental system which contained only two trapped particles. It therefore suggests a useful new platform for exotic particle searches, complementing other experimental efforts., Comment: 5 pages, 1 figure

Author(s): Budker, D; Kimball, DJ | Abstract: Several years ago, one of us, having noticed that inexperienced scientists tend to make largely the same mistakes while writing their first papers, was compelled to write a one-page note summarizing some dos and don'ts intended to help take care of common problems before they occur. Since these days the majority of research papers are written collaboratively by groups of co-authors, we are compelled to extend these recommendations to collaborative writing as we observe groups of co-authors falling into the same traps again and again.

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., 51 pages, 23 figures, to appear in Rev. Mod. Phys. in Oct. 2002, Figure added, typos corrected, text edited for clarity

The dynamics of resonant light propagation in rubidium vapor in a cell with antirelaxation wall coating are investigated. We change the polarization of the input light and measure the time dependence of the polarization after the cell. The observed dynamics are shown to be analogous to those in electromagnetically induced transparency. Spectral dependence of light pulse delays is found to be similar to that of nonlinear magneto-optic rotation. Delays up to [approx]13 ms are observed, corresponding to a 8 m/s group velocity. Fields of a few microgauss are used to control the group velocity. [copyright] [ital 1999] [ital The American Physical Society ]

Results of an investigation of collisional deexcitation of the metastable $6s6p{}^{3}{P}_{0}$ state in atomic ytterbium by helium and neon buffer gases are reported. We find upper limits for the quenching cross sections to be ${\ensuremath{\sigma}}_{\mathrm{He}}l13\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}{\mathrm{cm}}^{2}$ and ${\ensuremath{\sigma}}_{\mathrm{Ne}}l8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}{\mathrm{cm}}^{2}.$ The small cross sections may allow an ytterbium parity nonconservation experiment to be performed in a vapor cell. We have also measured the pressure broadening and shift of the $6s6p{}^{3}{P}_{0}\ensuremath{\rightarrow}6s7s{}^{3}{\mathrm{S}}_{1}$ and ${6s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}6s6p{}^{3}{P}_{1}$ transitions by helium and neon.

Resonant enhancement of optical Kerr and higher order nonlinearities in multilevel systems under the conditions of electromagnetically-induced transparency might be useful for quantum signal processing. The main problem with these schemes is related to the selective measurement of high-order atomic coherences that requires multiphoton interactions for the production and detection. In this paper we present a method in which a single laser beam is used for the creation of required nonlinear interactions. It is based on the nonlinear magneto-optical rotation with frequency-modulated light. Using this technique, we measure the nonlinear Faraday rotation caused by four-photon atomic coherence in M-type system. The method is also applicable to the selective control of higher order atomic coherences.

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., 14 pages, 14 figures

Using laser optical pumping, widths and frequency shifts are determined for microwave transitions between ground-state hyperfine components of {sup 85}Rb and {sup 87}Rb atoms contained in vapor cells with alkane anti-relaxation coatings. The results are compared with data on Zeeman relaxation obtained in nonlinear magneto-optical rotation (NMOR) experiments, a comparison important for quantitative understanding of spin-relaxation mechanisms in coated cells. By comparing cells manufactured over a forty-year period we demonstrate the long-term stability of coated cells, an important property for atomic clocks and magnetometers.

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

Erratum for paper "Light-induced desorption of alkali-metal atoms from paraffin coating" [Phys. Rev. A 66, 042903 (2002)., Comment: Erratum, 1 page

Observation of nonthermal, light-induced desorption of Cs and Rb atoms from paraffin coating is reported. Buffer-gas-free paraffin-coated cells containing Cs and Rb were exposed to laser light of various intensities and frequencies, and the change of the vapor densities as a function of time was investigated. Because atomic polarization relaxes very slowly in paraffin-coated cells (spin-relaxation times can be $\ensuremath{\gtrsim}1\mathrm{s}),$ they are applied in a variety of precision measurements (e.g., magnetometry, discrete symmetry tests, etc.). Light-induced desorption may be useful in such measurements as a method to control atomic density without changing the temperature of the cell.

Optical pumping of an atomic sample with narrow-band light can create sub-Doppler features, known as Bennett structures, in the velocity distribution of state populations. In the presence of static magnetic or electric fields, the corresponding sub-Doppler features in the index of refraction can cause nonlinear optical rotation and induced ellipticity of resonant light propagating through the atomic medium. Physical mechanisms causing Bennett-structure-related nonlinear electro- and magneto-optical effects are discussed in detail for transitions involving states with low angular momenta. Measurements of Bennett-structure-related nonlinear magneto-optical rotation and electric-field-induced ellipticity for the Rb D2 line are performed and compared to density-matrix calculations. The latter effect can he used for measuring electric fields applied to atoms.

A new scheme to measure parity-nonconserving effects in atomic ytterbium is proposed. This method entails measuring parity-nonconserving optical rotation on the $1.28 \ensuremath{\mu}\mathrm{m} 6s6p{ }^{3}{P}_{0}\ensuremath{\rightarrow}6s6p{}^{1}{P}_{1}$ transition, for which optical rotation per unit absorption length is predicted to be an order of magnitude larger than that for transitions experimentally studied in thallium, lead, and bismuth. In the proposed experiment using a vapor cell filled with buffer gas, the lifetime of the lower metastable $6s6p{ }^{3}{P}_{0}$ state is limited by collisional de-excitation. Atoms are excited to the lower metastable state by, e.g., short $(\ensuremath{\sim}10 \mathrm{ns})$ near-resonant light pulses and spurious optical rotation is subtracted on a pulse by pulse basis. The potential sensitivity of this technique may enable precise measurements of electroweak parameters.

Self-rotation (SR) of elliptically polarized light resonant with atoms in a collision-free vapor is investigated experimentally and theoretically. Results of density matrix calculations are compared to measurements of SR on the Rb D1 and D2 lines. It is noted that SR eects involving individual hyperne transitions are suppressed due to Doppler broadening, and so previously unrecognized eects arising from the interaction of light with multiple hyperne transitions can become dominant. PACS. 42.50.Gy, 42.50.Hz, 32.80.Bx Interaction with an elliptically polarized light eld can cause an initially isotropic medium to become dichroic and birefringent. The resultant circular birefringence and linear dichroism induce rotation of the polarization ellipse of the light. In the present work, we investigate this eect, known as self-rotation (SR), occurring in a rubidium vapor in which the eect of collisions can be neglected. The vapor is subject to narrow-band cw light near-resonant with the Rb D1 (795 nm, 2 S 1 ! 2 P 1 ) and D2 (780 nm, 2 S 1 ! 2 P 3 ) transitions. Under these conditions, as we discuss below, the previously unrecognized

Recent and ongoing experiments testing various fundamental discrete symmetries are discussed, including search for parity nonconservation in dysprosium and ytterbium, investigation of possibilities of searches for parity and time-reversal invariance violation in samarium, and a test of permutation properties of photons in a two-photon transition in barium.

Magneto-optical (Faraday) rotation is a process in which the plane of light polarization rotates as light propagates through a medium along the direction of a magnetic field. In atomic vapors where ground state atomic polarization relaxes very slowly (relaxation rates ≳1 Hz), there arise ultranarrow, light-power-dependent (nonlinear) features in the magnetic field dependence of Faraday rotation. The shot-noise-limited sensitivity of a magnetometer based on nonlinear Faraday rotation can exceed 10−11 G/Hz, corresponding to a sensitivity of ∼10−6 Hz/Hz to Zeeman sublevel shifts. Here we discuss recent progress in magnetometry based on nonlinear optical rotation and consider the application of these methods to searches for fundamental-symmetry-violating interactions.

Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $(\ensuremath{\sim}{10}^{\ensuremath{-}6} \mathrm{G})$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\ensuremath{\mu}\mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the $D1$ and $D2$ lines of ${}^{85}\mathrm{Rb}.$ It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$

Nonlinear magneto-optical rotation is investigated at high light powers where the rotation is significantly modified by ac Stark shifts. These shifts are shown to change the overall sign of rotation for closed F--F+1 transitions compared to the low light power limit. The effect is demonstrated by measurements in rubidium and density matrix calculations. The results are important for applications of nonlinear optical rotation such as sensitive magnetometry.

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., 15 pages, 11 figures

Collimated and conical emissions that appear when Yb vapor is illuminated by light pulses at 262 nm (near the one-photon Yb 6s2 1S0→6s7p 3P1 transition) are experimentally investigated. Conical emission is observed at multiple wavelengths. Parametric and nonparametric nonlinear optical processes are studied by investigation of the spatial distribution of generated light and the efficiency of light generation as a function of the incident light frequency.

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