Nonlinear Magneto-optical Rotation Research Articles

Features of two-photon resonances of nonlinear magnetooptical rotation of the plane of polarization for the initial population of fine-structure levels in alkali atoms

The features of nonlinear magnetooptical effects of fine-structure levels of an alkali atom, including effects in strong magnetic fields, as well as under conditions of two-photon resonance, are considered. The spectra of magnetooptical rotation and of magnetic circular dichroism have been obtained for the first time for the nontrivial initial population of magnetic sublevels of excited electronic states of an alkali atom, as well as under conditions of two-photon resonance. The decrease in the amplitude of resonances of initially populated fine-structure levels is explained by population transfer, taking place in strong fields. This transfer affects the rotation of the plane of polarization. The lower the initial population, the more pronounced the population transfer. Numerical experiments have shown that analysis of the resonance shapes in the spectra of magnetooptical rotation can yield information on the initial population of magnetic sublevels of excited electronic states of atoms.

Nonlinear magneto-optical rotation with modulated light in tilted magnetic fields

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.

Nonlinear magneto-optical rotation and Zeeman and hyperfine relaxation of potassium atoms in a paraffin-coated cell

Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{\ensuremath{-}}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\ensuremath{\gamma}}^{NMOR}∕2\ensuremath{\pi}=2.0(6)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of $^{39}\mathrm{K}$ atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\ensuremath{\gamma}}_{\mathit{expt}}^{\mathit{hf}}∕2\ensuremath{\pi}=10.6(7)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ and a shift of $\ensuremath{-}9.1(2)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.

Robust, high-speed, all-optical atomic magnetometer

A self-oscillating magnetometer based on the nonlinear magneto-optical rotation effect with separate modulated pump and unmodulated probe beams is demonstrated. This device possesses a bandwidth exceeding 1kHz. Pump and probe are delivered by optical fiber, facilitating miniaturization and modularization. The magnetometer has been operated both with vertical-cavity surface-emitting lasers, which are well suited to portable applications, and with conventional edge-emitting diode lasers. A sensitivity of around 3nG is achieved for a measurement time of 1s.

Nonlinear Forward Scattering in Cesium Vapor: Experiment with Simultaneous Scanning of Laser Frequency and B-Field

We present the results of an experimental study of nonlinear magneto-optical rotation in a buffer-gas-free uncoated Cs cell on hyperfine transitions F(g) = 3 --> F(e) = 2, 3, 4 of the D(2) line at high laser irradiance (up to 40 mW/cm(2)). The measurements were done in a forward scattering configuration, with simultaneous linear scanning of laser frequency and magnetic field at different temporal rates. The latter revealed, in a single measurement, the dependences of maximum nonlinear Faraday signal and the corresponding B-field on the laser frequency within the Doppler profile.

Construction and applications of an atomic magnetic gradiometer based on nonlinear magneto-optical rotation

We report on the design, characterization, and applications of a sensitive atomic magnetic gradiometer. The device is based on nonlinear magneto-optical rotation in alkali-metal (Rb87) vapor and uses frequency-modulated laser light. The magnetic field produced by a sample is detected by measuring the frequency of a resonance in optical rotation that arises when the modulation frequency equals twice the Larmor precession frequency of the Rb atoms. The gradiometer consists of two atomic magnetometers. The rotation of light polarization in each magnetometer is detected with a balanced polarimeter. The sensitivity of the gradiometer is 0.8nG∕Hz1∕2 for near-dc (0.1Hz) magnetic fields, with a base line of 2.5cm. For applications in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), a long solenoid that pierces the magnetic shields provides an ∼0.5G leading field for the nuclear spins in the sample. Our apparatus is particularly suited for remote detection of NMR and MRI. We demonstrate a point-by-point free induction decay measurement and a spin echo reconstructed with a pulse sequence similar to the Carr-Purcell-Meiboom-Gill pulse. Additional applications and future improvements are also discussed.

Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range

Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived $({\ensuremath{\tau}}_{\mathrm{rel}}\ensuremath{\sim}1\mathrm{s})$ ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding ${10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}\mathrm{G}∕\sqrt{\mathrm{Hz}}$ for small $(\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{G}$) 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$(\ensuremath{\sim}500\mathrm{mG})$, 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.

Nonlinear magneto-optical rotation with amplitude modulated light

The technique of nonlinear magneto-optical rotation with amplitude modulated light is developed. The technique is an alternative to its counterpart with frequency modulated light and can be applied to sensitive measurements of magnetic fields ranging from microgauss to the Earth-field level. The rotation signals exhibit nontrivial features such as narrowed non-Lorentzian line shapes and multicomponent resonances.

Pump-probe nonlinear magneto-optical rotation with frequency-modulated light

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 $\mathrm{\ensuremath{\Delta}}m=2$ and $\mathrm{\ensuremath{\Delta}}m=4$ in $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ atoms, and additionally $\mathrm{\ensuremath{\Delta}}m=6$ in $^{85}\mathrm{Rb}$. 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.

Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation

The detection of nonlinear magneto-optical rotation (NMOR) of polarized light through alkali atomic vapor is a highly sensitive technique for measuring magnetic fields. We demonstrate that when using frequency modulated light to excite the NMOR resonance, it is possible to cause the system to self-oscillate. The NMOR signal is not a simple replica of the sine wave modulation of the light, but rather contains many higher harmonics of the modulation frequency, and we implement two ways of processing the signal to recover the fundamental modulation frequency in the feedback loop and induce self-oscillation. Self-oscillation simplifies and reduces the power consumption of the electronics required to operate a magnetometer, making the NMOR technique attractive for commercialized magnetic sensors.

Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells

Using laser optical pumping, widths and frequency shifts are determined for microwave transitions between ground-state hyperfine components of $^{85}$Rb and $^{87}$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.

Influence of a buffer gas on nonlinear magneto-optical polarization rotation

We show experimentally that the presence of a buffer gas in a rubidium vapor cell modifies significantly the nonlinear magneto-optical rotation of polarization of near-resonant light propagating through the cell. We observe not only the well-known narrowing of the nonlinear magneto-optical resonances, but also changes in their shape and visibility. We explain these effects in terms of coherence-preserving, velocity-changing collisions between rubidium and buffer gas atoms.

Hyperpolarized Xenon Nuclear Spins Detected by Optical Atomic Magnetometry

We report the use of an atomic magnetometer based on nonlinear magneto-optical rotation with frequency-modulated light to detect nuclear magnetization of xenon gas. The magnetization of a spin-exchange-polarized xenon sample (1.7 c m(3) at a pressure of 5 bars, natural isotopic abundance, polarization 1% ), prepared remotely to the detection apparatus, is measured with an atomic sensor. An average magnetic field of approximately 10 nG induced by the xenon sample on the 10 cm diameter atomic sensor is detected with signal-to-noise ratio approximately 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.

Nonlinear magneto-optical rotation produced by atoms near aJ=1→J=0transition

The nonlinear magneto-optical rotation in a medium consisting of $J=1\ensuremath{\rightarrow}J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.

Nonlinear magneto-optical rotation of frequency-modulated light resonant with a low-Jtransition

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.

Selective addressing of high-rank atomic polarization moments.

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 87Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultranarrow (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 supported by a given system has important applications in quantum and nonlinear optics and in magnetometry.

Superluminal optical pulse propagation in nonlinear coherent media

The propagation of light-pulse with negative group-velocity in a nonlinear medium is studied theoretically. We show that the necessary conditions for these effects to be observable are realized in a three-level $\Lambda$-system interacting with a linearly polarized laser beam in the presence of a static magnetic field. In low power regime, when all other nonlinear processes are negligible, the light-induced Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves the dispersion anomalous and very high. As a result, a superluminal light pulse propagation can be observed in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. There is no violation of causality and energy conservation. Moreover, the superluminal effects are prominently manifested in the reshaping of pulse, which is caused by the intensity-dependent pulse velocity. Unlike the shock wave formation in a nonlinear medium with normal dispersion, here, the self-steepening of the pulse trailing edge takes place due to the fact that the more intense parts of the pulse travel slower. The predicted effect can be easily observed in the well known schemes employed for studying of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.

Nonlinear magneto-optical kerr rotation of an oxide superlattice with artificially broken symmetry.

Simultaneously broken time-reversal and spatial-inversion symmetries can be realized in the epitaxially grown oxide "tricolor" superlattices composed of three sequential kinds of perovskite layers including a ferromagnetic one (manganese oxide). As a generic feature of such a system, the magnetic-field-induced second-harmonic generation and the resultant Kerr rotation of second-harmonic light were demonstrated. The signal intensity probes the interface magnetization of the superlattice, where temperature variation is shown to be distinct from the bulk feature.

Nonlinear magneto-optical rotation of elliptically polarized light

We predict theoretically and demonstrate experimentally an ellipticity-dependent nonlinear magneto-optic rotation of elliptically-polarized light propagating in a coherent atomic medium. We show that this effect results from a hexadecapole and higher order momenta of atomic coherence, and is associated with an enhancement of Kerr and higher orders nonlinearities accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. These nonlinearities might be useful for quantum signal processing. In particular, we report an observation of an enhancement the polarization rotation of elliptically polarized light resonant with the 5S_{1/2} F=2 -> 5P_{1/2} F=1 transition of Rb87.

Nonlinear magneto-optical rotation with frequency-modulated light

A magnetometric technique is demonstrated that may be suitable for precision measurements of fields ranging from the sub-microgauss level to above the Earth field. It is based on resonant nonlinear magneto-optical rotation caused by atoms contained in a vapor cell with anti-relaxation wall coating. Linearly polarized, frequency-modulated laser light is used for optical pumping and probing. If the time-dependent optical rotation is measured at the first harmonic of the modulation frequency, ultra-narrow (~a few Hz) resonances are observed at near-zero magnetic fields, and at fields where the Larmor frequency coincides with half the light modulation frequency. Upon optimization, the sensitivity of the technique is expected to exceed 10^{-11} G/sqrt{Hz}.