Investigation On The Measurement Of Magnetic Field Based On Coherent Population Trapping

Measurement of magnetic fields with picotesla sensitivity is critical to many applications, such as, the detection of the weak magnetic field produced by human brain, heart in the area of biomagnetism, and the detection of weak magnetic field in the area of condensed-matter experiments and palaeomagnetism. Because of its high sensitivity, small size and low power disspation, CPT magnetometer has been paid more and more attentions from the scientists all over the world. In this thesis, we systematically studied the measurement of magnetic field based on coherent population trapping, and our work which includes two parts has been concluded below.Ⅰ.Experimental SetupA vertical-cavity surface-emitting laser (VCSEL) was used as the light source, because it allows efficient phase modulation at high microwave frequency by directly modulating its driving current. Collimating lens was installed here to produce collimatec beam; and temperature circuit control system, current circuit control system, and frequency stabilization circuit control systems were constructed here to stable laser output.A signal generator was applied here to trigger the microwave oscillator to produce a scanning signal. Its central frequency isωm(3.417GHz); its range is tunable, which is between 1Hz to 1MHz; and its modulated power is 7dBm.We used a standard cylindrical glass cell (1.5mm diameter, 3mm length) containing isotopically pure 87 Rb and 5 Torr of Ne buffer gas. We control the temperature of the cell by changing the voltage added to the crystal which was placed under the cell. And a pair of Helmholtz coil was installed here to change the longitudinal magnetic field.Ⅱ.Results and analyses of the measurement of the magnetic fieldTo study CPT resonance response to different direction and magnitude of magnetic field, we add an additional magnetic field to compensate the background magnetic field.(We conduct it by a phenomenon , that is when there is no magnetic field , there will be only one transimission peak when the modulating frequency is swept by this frequency range.)There will be different CPT resonance to different magnetic field direction. When the magnetic field is applied along the light propagation direction, or the component in this direction is dominant, there will be three peaks.When the magnetic field is applied perpendicular to the light propagation direction, or the component in this direction is dominant, there will be four peaks. When the component in the longitude direction is comparable to its latitude counterpart, there will be seven peaks. In order to facilitate measurement, we used the CPT resonance corresponding to the longitude magnetic field. In the presence of a longitude magnetic field, the magnetic sublevels with different magnetic quantum mF of the D1 line (52S1/2→52P1/2) of 87 Rb shifts by different amounts, as shown in Fig.2.The CPT resonance at 12Δhfs are observed only for non-shifted m F=0 pair, while for m F=±1 the CPT resonance occurs at 12 (Δhfs±2g FB).So when the oscillator frequency is swept around these values, three CPT peaks will be observed, as shown in Fig.3.In this case, it is easy for us to calculate B field from the frequency difference between one of the side peak and the middle peak. We chose the left side peak for it is relatively higher. (Because optical pumping preferentially populates the negtive-m magnetic sublevels.)In the experiment, the whole operation is shown as follow. First, to adjust the middle peak to the middle line of the oscilloscope, when scanning the modulation frequency in a wide range. Second, to adjust its accurate position step by step when gradually lessen its scan range, until the peak is too wide to makesure its precise position. Then the middle frequency of the scan range which we can read from the oscillator is just the frequency of the middle peak, we name it asν0; and we can get the frequency of the left peak in the same way, we name it asν1. Then,So we can measure the absolute magnitude of B field with this method. Table.1 shows 10 sets of experiment data recorded in our experiment. Here, I represents the current value of Helmholtz coils. The method of calculating the variation of the magnetic field is similar. The only difference is that, in this case, we just need to measure the frequency difference between the left peaks before and after the change of the magnetic field, instead of measuring the frequency difference between the left peak and the middle peak corresponding to every magnetic field. The frequency of the left peak before and after the change of the magnetic field were named respectively asν1 andν1', so the variation of the magnetic fieldΔB can be calculated by the following equation,Then we measure the variation of the magnetic field in this method. Table.2 shows 9 sets experimental data of the variation of magnetic field recorded in our experiment. Here, we used two pair of Hemholtz coils to apply the magnetic field, the data before"+"represents the bigger current (with A as unit), the data after"+"represents the smaller current (with mA as unit). And I represents the current value before the change of the magnetic field, I 'represents the current value after the change of the magnetic field.The resolution of the magnetometer is the smallest change of the frequency or the B field that can be identify by the magnetometer.We can get the resolution of our system by judging the smallest frequency change of the middle peak. In experiment, every time we changed the middle frequency by 10 Hz, we recorded the position of the peak corresponding to it. Then we got 10 sets experimental data in this way. After that we read the position of the highest point of every peak by origin, and then draw the points with the middle frequency as x-axis, and the position of the peak as y-axis, as shown in Fig.4.As shown in Fig.4, the relationship between the change of the peak's position and the change of the middle frequency is linear, and the fitting line equation is,This relationship shows that our system can identify the frequency change of 10Hz, or can even identify the change less than it (which can be calculated from the above equation ). So we can conclude that the resolution of our system is below 10Hz, corresponding to 1. 4×10?9T. And we can also expect a better resolution after adopting a new approach to read the position of the peak (A method similar to the method we use to lock the position of the laser's frequency).