Active Magnetic Field Stabilization

Our goal is to generate magnetic fields on the order of 3 Gauss and to stabilize these magnetic fields to within a signal-noise ratio of $10^3$ for longterm drift (over the course of hours to days) and for 60Hz harmonic noise. This magnetic field stabilization scheme will improve stability for experiments that rely on (near) constant magnetic fields.

Table of Contents

• Motivation
  • Zeeman Sublevels and Fine Structure
  • Zeeman Effect
• Components List
• Schematics and Components
  • Experimental Setup
  • Moku Go
  • N Channel MOSFET
  • Helmholtz Coils
  • Magnetometer
• Feedback Control
  • PID Controller
  • Tuning Controller
• Feedforward Control
  • Line Triggering
  • 60Hz Harmonic Cancellation
• Combined Feedback Feedforward Control
• Two Probe Stabilization with Qnimble and LNA
  • Two Probe Setup Guide
  • Two Probe Data
• Future Work
• Repository File Structure
• Contributors

Motivation

Zeeman Sublevels and Fine Structure

In many physics groups investigating the interaction between light and matter use single, or few, atoms confined to a "trapping region." Lasers can drive electronic transitions between energy or angular momentum levels in atoms to investigate their internal structure and to run atomic clock and quantum logic experiments. Pictured above is the level structure of a Strontium 87 ion whose different orbitals experience further splittings for slight changes in the transition frequency which are called "Zeeman Sublevels." Often, exciting transitions between particular Zeeman sublevels is advantageous for certain experiments due to the long lifetimes of the excited state and narrow laser frequencies required to drive the transtion.

The Zeeman Effect

Unfortunately, ambient magnetic fields in the laboratory can shift the Zeeman Sublevels of an atom during the course of an experiment causing a loss in precision and failure of an experiment. Therefore, to run many atomic and molecular optics, or AMO, experiments it is vital to stabilize the magnetic field experienced by the confined atoms or molecules against ambient magnetic field noise. The goal of our project was to generate and stabilize a 3 Guass magnetic field against slow and fast magnetic field drift as well as the 60Hz harmonics from the mains electricity.

Components List

1. MOKU:Go - Microcontroller to act as Oscilloscope, PID loop, and AWG
2. MOSFET N Channel - Transistor with input pin, and sends current from drain to source pins
3. OPAMP LM358AP - Low Noise OP AMP
4. Bartington Magnetometer - reads magnetic field 0-10G, 3kHz bandwidth
5. Oscilloscope DS1064 - with option to AC line trigger

Schematics and Components

Experimental Setup

Our Experimental Setup consists of two coils which produce the Helmholtz Field at the center (in our case, 3G). The magnetometer is placed at the center of the coils, and the voltage reading is sent to the Moku:Go controller. The controller is connected to a laptop on which we use the Moku software to run the PID loop and control its parameters. The PID loop output error signal is sent to the first shunt transistor on the bread board (see Future Work for our plans to optimize the circuit on a pcb), "MG Out1" in the diagram above, that shunts current from the coils to alter the magnetic field. Simulatenously, an oscilloscope is used to line trigger a TTL signal on the 60Hz AC line from the wall outlet which is input to the Moku:Go and is used to trigger the Moku:Go Arbitrary Waveform Generator (AWG). The AWG signal is sent to the second shunt transistor, "MG Out2", which is used for feedforward.

Moku Go

The Moku:Go is a multi-instrument controller that has high sensitivty, sample rate, and output rate which made it ideal to use for this project. The Moku:Go acted as an oscilloscope for the voltage readings from our magnetometer and processed those readings in its PID Controller that was used to generate the feedback error signal. The Moku:Go also had a built in Artbitrary Wave Form generator with which linear combinations of sin waves of different frequencies, amplitudes, and phases could be output and with which feedforward was accomplished. All of our data was also logged using the Moku:Go data logger instrument which has high sample rate and resolution. The Moku:Go power supplies were not used since constant current mode could not be reliably achieved to output .5A to our coil circuit since the impedence of the circuit exceded 5V.

N Channel Mosfet

We used an N Channel Depletion Type MOSFET as our shunt transistor to control the current flow through the coils. The MOSFET is a "Metal Oxide Semiconductor Field Effect Transistor" which changes its resistance been its source and drain pins in response to an applied voltage to its gate pin. The MOSFET(s) were placed in parallel with the coils and the error signal from the Moku:Go was output to their drains to modulate their resistance and consequently the current passing through the coils to do feedback and feedforward control.

Helmholtz Coils

Coils in a Helmholtz Configuration were used for this project due to the stability of the magnetic field in the center of the coils. The coils were placed in series so that the magnetic field pointed in the same direction along the quantization axes parallel to the magnetometer and perpendicular to the plane of the coils with a magnitude $B=(\frac{4}{5})\frac{\mu_{0}NI}{a}$. The resistance of the coils used was on the order of $.3\Omega$ which meant that driving a total current of .25A through our circuit and >.1A through the coils resulted in a 3G magnetic field.

Magnetometer

The magnetometer used in this project was a Bartington Mag-03 fluxgate magnetometer that had a sensor bandwidth of 3kHz and a measuring range of .7 to 10G. The sensor noise floor is <6pTrms per $\sqrt{Hz}$ at 1Hz and offered excellent resolution required for precise PID feedback control. The magnetometer output a voltage signal with a 1:1 ration between volts and gauss to the Moku:Go which applied the PID controller to it. In the future, this magnetometer's ability to sense along three sepperate axes could allow for active magnetic field stabilization along three quantization axes or to sense a magnetic field gradient along one axes.

Feedback Control

Our feedback loop consists of a magnetometer, a PID loop in MOKU:Go, and a MOSFET in parallel to the coils shunting current to ground to modulate the field.

The Bartington Magnetometer is placed at the center of the coils, and sends its reading to the first input pin of the MOKU:Go. The voltage to field ratio of the magnetometer is 1V/G. This is sent to the MOKU's PID loop, where we varied the P and I parameters to reduce the standard deviation as much as possible. The D term was not used as this ended up saturating the PID loop once the external magnetic field became too high. We tuned the parameters to optimize for long term drift cancellation, so Feedforward could handle the faster moving deviations.

The output of the PID loop was a signal that we sent into a Non-Inverting Amplifier, then to the MOSFET in parallel with our coils.

The NonInverting Amplifier circuit consisted of an OpAmp, two resistors, and a capacitor. The circuit is below, and the gain of this circuit is 6. The purpose of this circuit is to set the input of the MOSFET in the middle of its range of 0-60 volts. We would then have more control on how much it attenuates the signal.

The output of this circuit was sent to the MOSFET to shunt current accordingly to ground.

Tuning Controller

When the PID feedback was off, there were significant noises in our magnetic field signal that were mostly composed of 60 Hz harmonics. As the feedback was enabled, the standard deviation decreased from 3.9 mG to 0.8 mG. We observed a distinct attenuation of power in small frequencies range of our FFT plot. However, there still remained 60 Hz harmonics peaks that are slightly reduced by PID feedback. By integrating the power spectral density over frequencies from 0 to 300 Hz, above which the PID feedback ceases to effect, we obtained an area ratio of 163.

Feedforward Control

Feedforward control consists of modifying the input to the system by modulating the source of the disturbance. In this case, the disturbance is the 60Hz from the powerwall that leaks through the DC power supply, as well as 60Hz that enters the magnetic field from laptops and other devices that run at 60Hz.

Our feedforward methology relies on finding the phase of the 60Hz sin wave in the magnetometer and shunting current to decrease the amplitude of this singal.

Line Triggering

We AC line triggered from DS1064 Oscilloscope, and produced a TTL (time-to-live) at this frequency and sent this to the Moku:Go. The Moku's AWG produced a sin wave at this frequency. We set the period of this sin wave to be slightly more than 60Hz (~60.05 Hz), so that any error in the TTL's phase did not affect the AWG's produced sin wave.

We then obtained the signal from the magnetometer, and sent this into the MOKU:Go in multi instrument mode. We then phase shifted the sin wave produced by the Moku to be in phase with the 60Hz wave in the magnetometer reading. We then sent the in phase sin wave from the AWG to the second MOSFET in our circuit to shunt away current at this frequency to attenuate 60Hz in the magnetic field.

As a result, the 60Hz in the magnetic field was attenuated.

60Hz Harmonic Cancellation

The power spectral densities over frequency corresponding to cases of feedforward on and feedforward off are nearly identical, as what we have expected. This is because we were outputing a 60 Hz sinusoidal wave that is in phase with the magnetometer signals, the rest of the spectrum should, therefore, be highly similar. As we zoomed into the region of interest (f = 60 Hz), we observed an approximaely 8 dB attenuation at 60 Hz by subtracting the peaks to their respective noise floors, which are about the same in this case.

Feedback and Feedforward

After the individual implmentation of PID feedback and mains electricity feedforward, we combined both methods to further attenuate the noises in our signal. The standard deviation was reduced to 0.4 mG, as contrast to 0.8 mG for PID feedback alone. There was about 35 dB attenuation of power spectral density at 60 Hz, from which we obtained by subtracting the peak value at 60 Hz from their respective noise floors. Through integrating the power spectral density to the bandwidths of PID feedback alone (f = 300 Hz) and of Feedback and Feedforward (f = 850 Hz), we calculated area ratios of 705 and 65, respectively.

Two Probe Stabilization with Qnimble and LNA

Two Probe Stabilization Setup Guide

1. The moku:go will be used for live measurements so you can tune things more quickly, the Qnimble is what’s actually used as the PID controller.

2. Two BNC connectors go from the two magnetometer output ports that are being used to the LNA setup with the breadboard. Each BNC coming from the magnetometer should have a BNC to banana adapter on the end. The grounds of the banana adapters should be connected. The positive side of the banana adapters should go into the breadboard’s banana connector slots, one into the breadboard’s ground (green female end banana connector on the breadboard) and one into the breadboard’s Vb (black female end banana connector on the breadboard).

3. Current then travels through those two ports and then each through its own 10k resistor. After current passes through each respective 10k resistor, there is a junction that then goes to the breadboard’s Va (red female end banana connector on the breadboard).

4. The LNA’s input port should have a BNC to banana adapter on it, and you should put a banana cable (preferably red) from the breadboard’s Va connector to the positive terminal of the LNA. There should be another banana cable (preferably black) going from the ground of the magnetometer signals (it doesn’t matter which you connect it to since they should be connected to each other already)

5. The output of the LNA is split with one end into the moku’s input and one into the Qnimble’s input.

6. The LNA is a current amplifier, but we want to amplify a voltage, so we put resistors out front. It should be such that the resistors are quite high because we don’t the magnetometers to have to output much current at all. V=IR tells us that the current read will be I=V/R, so with 10k resistors like I’ve used, the current read by the LNA will be 1e-4 in amps of the voltage going in. For example if I supplied one volt, I would have 100uA being read by the LNA. Because I have two ~1V signals (for a 1 gauss field read by each probe) coming in from each magnetometer output, they will each turn into 100uA of current, and by the junction rule that current adds to 200uA when it goes into the LNA input, so it will read 200uA. There should be no concern about back flow of current because the LNA has very nearly zero resistance and the back flow path requires the current to flow through an extra 10k ohm of resistance, so the backflow current should be pretty much zero.

7. Because we have 10k resistors out front, set preamp to -200uA input offset. Be careful to make sure that you have the negative mode selected. Input offset depends on the resistors used, and -200uA is corresponds to zeroing the current of 2 signals each of 1V (for 1 gauss as read by each magnetometer probe) coming in. Have the preamp gain set to 100mA/V for tuning (this LATER gets increased to 200nA/V once you zero the center the fluctuating B field reading about 1G for each probe)

8. Turn on the op amp and circuit power supplies, OP Amp gets 20-30V, circuit pwr gets ~0.2A to start (you will vary this to get an LNA reading centered about zero).

9. With the circuit pwr, the power supply needs to have its current limit set to output at a fixed current as opposed to a fixed voltage, so set that limit to 0.2A and that in the later steps to control the current.

10. Turn on the LNA and view the LNA’s output in the moku:go desktop app with the Qnimble’s DAC offset set to ~0.4V.

11. Vary the circuit pwr current until the moku:go shows the signal as closely centered about zero as you can get, this means the field read by each magnetometer probe is 1G

12. Now increase the gain on the LNA to 10uA/V, repeat step 11 if the center of the signal changes from zero.

13. Now increase the gain once again to 1uA/V, again repeat step 11 if needed (best to get the signal as near as possible to centered about zero). You may also need to vary the DAC offset in the Qnimble applet for more fine tuning to get the LNA output centered about zero.

14. Now increase the gain on the LNA to the final level of 200nA/V and again tune the DAC offset to get it as nearly centered about zero as possible.

15. Now it’s ready for testing the stabilization performance.

16. Note that this is very finely tuned for whatever setup you have it set to, so if you move a magnet within the vicinity or move a current carrying wire within the vicinity, you likely will have to re-calibrate by adjusting the DAC output offset in the Qnimble applet again.

17. Here are some parameters have performed well in tests: P=0.0005, I=0.05, D=0, SP=0, DAC=0.414 The optimal DAC (DAC offset) value will probably differ, see the above setup guide for proper DAC tuning.

Two Probe Stabilization Data

Note that this plot did not use feedforward or a direct attenuation of the 60Hz noise, this plot is only to showcase the ability to attenuate low frequency noise with the Qnimble Quarto as a controller, an SRS LNA to amplify the signal, and B field probes whose measurements are fed into a passive averager circuit to allow for two probe stabilization. This data was recorded for the PID parameters suggested in the setup guide. Many sets of parameters were tested, but this plot represents the most significant reduction in low frequency noise without significant overcorrection noise at higher frequencies. There is a small overcorrection hump that peaks at ~1kHz, but it is at roughly 1/1000 the noise levels of the low frequency noise that has been attenuated.

Future Work

For our future work we hope to implement the stabilization setup developed above on a linear paul trap. We hope to first move optimize our circuits with voltage regulators to protect the operation amplifiers and coils from DC current spikes that could damage the circuitry and potentially the magnetometer. We would then like to implement feedforward for further 60Hz harmonics to attenuate up to 240Hz which would likely increase our PID bandwidth as well. Finally, we would then aim to implement our setup on a linear paul trap by designing new coils to it the ion trap geometry and then use the ion itself to quantify the magnetic field stability in addition to, or perhaps instead of, the magnetometer.

Repository File Structure

All of the analysis and plotting of our data was done in python and the code used along with the plots included in this README are in the AMFS/Analysis_code subdirectory. The raw data is saved in CSV file format in the AFMS/Data subdirectory and can be used to reproduce or customize the included plots. The PCB schematics for the circuit board we want to use in the future have been included in the AMFS/PCB Schematics folder, however these were not used for this project and have not been tested. We have also included a pdf of our final presentation for this work in the AFMS/Presentation subdirectory. All schematics, photographs, and figures appearing in this README are stored in the AMFS/Figures folder. Finally, we included test scripts made public by liquid instruments to help with trouble shooting the Moku python API in the AMFS/Controller folder. This code was not used for this work but may be useful in the future should we want to switch to the Moku python API instead of the Moku Desktop App.

Contributors

This work was primarily done by Luka Sever-Walter, Xuanwei Liang, and Samyuktha Ramanan for 15CL at UCSB.