Orientational dependence of optically detected magnetic resonance signals in laser-driven atomic magnetometers

Appl. Phys. B (2017) 123:35 DOI 10.1007/s00340-016-6604-8 Orientational dependence of optically detected magnetic resonance signals in laser‑driven atomic magnetometers Simone Colombo1 · Vladimir Dolgovskiy1 · Theo Scholtes1 · Zoran D. Grujić1 · Victor Lebedev1 · Antoine Weis1 Received: 2 September 2016 / Accepted: 28 November 2016 / Published online: 29 December 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract We have investigated the dependence of lock-indemodulated Mx-magnetometer signals on the orientation of the static magnetic field B0 of interest. Magnetic resonance spectra for 2400 discrete orientations of B0 covering a 4π solid angle have been recorded by a PC-controlled steering and data acquisition system. Off-line fits by previously derived lineshape functions allow us to extract the relevant resonance parameters (shape, amplitude, width, and phase) and to represent their dependence on the orientation of B0 with respect to the laser beam propagation direction. We have performed this study for two distinct Mx -magnetometer configurations, in which the rf-field is either parallel or perpendicular to the light propagation direction. The results confirm well the algebraic theoretical model functions. We suggest that small discrepancies are related to hitherto uninvestigated atomic alignment contributions. 1 Introduction Optically pumped atomic magnetometers, also known as optical magnetometers (OM), are based on resonant magneto-optical effects in atomic (usually alkali-metal) vapors [1]. We refer the reader to the comprehensive overview of various OM methods and their applications in Ref. [2]. Magnetometers based on optically detected magnetic This article is part of the topical collection “Enlightening the World with the Laser” - Honoring T. W. Hänsch guest edited by Tilman Esslinger, Nathalie Picqué, and Thomas Udem. * Simone Colombo 1 Physics Department, University of Fribourg, Chemin du Musée 3, CH‑1700 Fribourg, Switzerland resonance (ODMR) have the longest history in the field of atomic magnetometry, and the so-called Mx-magnetometer using a single light beam has proven to be a highly sensitive and robust device. The theoretical modeling of the signals generated by ODMR-based magnetometers is addressed in great detail in a recently published textbook (Chapter 13 in Ref. [3]). ODMR magnetometers infer the modulus B0 =ω0 /γF of the magnetic field vector B0 from the (driven) Larmor precession frequency ω0 of an atomic vapor’s magnetization, where γF is the gyromagnetic ratio of the used atom (γF /2π ≈ 3.5Hz/nT for 133Cs). The precession is driven by a much weaker additionally applied oscillating field B1 (t), called the ‘rf-field’. In the standard Mx-magnetometer, a single circularly polarized light beam whose frequency is resonant with an atomic transition is used both to create the medium’s spin polarization by optical pumping [4] and to read out the spin precession signal. The magnetometric sensitivity of an OM, i.e., the smallest magnetic field change that the device can detect (in a given bandwidth), depends on many parameters, such as the light intensity, the atomic number density, the size of the atomic sample, the spin coherence time, and the amplitude of the rf-field. Moreover, the sensitivity critically depends on the relative orientations of the light propagation direction k̂, the rf-field B̂1, and the field of interest B̂0. The latter dependencies imply that there are, on the one hand, orientation(s) that optimize the device’s sensitivity, and, on the other hand, orientations (so-called dead-zones) for which the sensitivity vanishes. The quantitative understanding of these dependencies is crucial when designing a magnetometer, be it for a laboratory application in which the orientation B̂0 of B0 is mostly known a priori, or for field applications where the knowledge of the dead-zones is of great importance. 13 35 Page 2 of 11 The problem of the OM sensitivity’s orientation dependence is closely related to the so-called ‘heading error’ that has already been addressed in the very early accounts on optically pumped atomic magnetometers [5]. Several attempts have been made to overcome those fundamental effects and realize dead-zone-free OM [6–10]. The object of the present paper is an experimental verification of the theoretically predicted [3] orientation dependencies of lock-in-detected signals in different Mx -magnetometers of two distinct geometrical configurations, viz., rf-field either parallel or perpendicular to the light’s k -vector. For this, we have developed a computer-controlled experimental setup allowing the rotation of a static magnetic field vector of constant modulus over the full 4π solid angle. We record magnetic resonance spectra at 2400 discrete (θB , φB) orientations of the field, and off-line analysis permits then three-dimensional representations of the results. 2 Experimental setup The experimental setup (Fig. 1) is mounted inside of a cubic five-layer µ-metal shield (produced by Sekels GmbH) with inner dimensions of ∼503 cm3. The central part of the magnetometer is a spherical (30 mm diameter) Pyrex cell with paraffin-coated inner surface which is connected by a capillary to a reservoir stem containing a droplet of solid cesium producing a S. Colombo et al. room-temperature saturated atomic vapor [11]. Laser light is guided to the setup by a multimode fiber which effectively scrambles the light polarization. The out-coupled (≈2 mm diameter) light beam’s polarization is made circular using a linear polarizer and a quarter-wave plate. We use a polarimeter (Thorlabs, model PAX5710IR1-T) for the precision control of the light’s polarization (cf. Sect. 7.1). The frequency of the extended cavity diode laser (Toptica, model DL100 pro) is actively stabilized to the center of the F=4 → F ′ =3 hyperfine transition of the Cs D1 line (=894.6 nm) by means of a separate saturation-absorption spectroscopy unit. The power of the laser beam is kept constant by an active stabilization circuit using an intensity modulator (Jenoptik, model AM894) driven by a slow PI controller with a 10 Hz cutoff frequency. The power of the transmitted light beam is detected by a photodiode whose photocurrent is amplified by a current-to-voltage converter (Femto, model DLPCA-200, 106 V/A gain, 200 kHz bandwidth) and fed to a lock-in detector (Zurich Instruments, model HF2LI). Magnetic resonance spectra are recorded by automated frequency sweeps of the rf-coil current produced by the built-in oscillator of the lock-in amplifier. The frequency dependence of both the in-phase and quadrature signals obtained by phase-sensitive demodulation of the photodiode signal is stored for off-line processing. The amplifier’s bandwidth and the finite inductivity of the rf-coil imply that the photocurrent’s Fourier component of interest (oscillating at ∼35 kHz) is phase-shifted by a (frequency dependent) val (...truncated)