The precession of M around the total (dc and ac) magnetic field (Btot = zB0 + xBrfcos (wrft)) is given by the Bloch equations [10]:(M�BxM�ByM�Bz)=(MxMyMz)��(��Brfcos??wrft0��B0)?(��2Mx��2My��1Mz),(1)where ��1 and ��2 are the longitudinal selleck inhibitor and the transverse relaxation time, respectively. The calculated in-phase and quadrature amplitudes and the phase shift of light power with respect to the driving rf magnetic field, Brf, are given byPip(��)=?P0sin(2��)��rf�Ħ�rf2��2/��1+��22+��2;(2)Pqu(��)=?P0sin(2��)��rf��2��rf2��2/��1+��22+��2;(3)?=arctan?��2��,(4)where ��rf = �� ? wrf is the Rabi frequency, �� = wrf ? wL is the frequency detuning from the Larmor frequency, and �� is the angle between the laser beam and B0.
Several important parameters can affect the magnetometer sensitivity, namely, the laser power; the laser beam profile, the rf field power, the cell size, the buffer-gas pressure, and the density of Cs atoms (which depends on the temperature). Typically, the magnetometer spatial resolution depends on the cell dimensions. In this paper, we focus the investigation on the effects of optical power intensity and vapor cell temperature variations on the sensitivity and bandwidth of the optical Mx magnetometer.3. Experimental SetupThe Mx magnetometer used in the experiment is shown in Figures 3(a) and 3(b). The core of the instrument is a quartz-made cylindrical cell containing Cesium vapor. Also, Neon at 34Torr and Argon at 6Torr are added to the Cs vapor in order to reduce atom collisions. The cell diameter and length are 21mm and 75mm, respectively, yielding a spatial resolution of about 53mm.
In the experiments, the gas pressure inside the cell was increased by increasing the temperature using hot water flowing into a silicon pipe wrapped around the cell. The vapor cell was placed in the center of an electromagnet that generates a dc magnetic field in order to cancel the geomagnetic field and supply a uniform magnetization along the appropriate direction inside the vapor cell. The used electromagnet consists of two parts: (i) a 3D DC coils of dimension 580mm �� 530mm �� 640mm providing a magnetic field with a uniformity better than 1% in the central region and (ii) an additional pair of coils that generate a small-magnitude rf magnetic field along the x-axis.
Each coil pair of the electromagnet was independently driven by a digital power supply to cancel the geomagnetic field along the x- and y-directions and generate a uniform magnetic field along the z axis. The intensity of the magnetic field at the center of the electromagnet was 13��T, as measured by a three-axis smart digital magnetometer Honeywell HMR2300. The AC coils were driven by a waveform generator (Agilent, model 33250A) to produce an rf magnetic field of intensity 200nT, oscillating at 45.5kHz along Anacetrapib the x-axis.