Technical Note of Apparatus of Spin-dependent
Short-range Forces Experiment
Ping-Han Chua,∗
a
Triangle Universities Nuclear Laboratory and Department of Physics, Duke University,
Durham, North Carolina 27708, USA
1. Measurement
The free induction decay (FID) is applied to measure signals of nuclear
magnetic resonance(NMR) from 3 He precession. The system is controlled by
a pulse generator. It sends triggers to a function generator, a computer DAQ
card, and preamplifiers, sequently. After receiving a trigger, the function
generator generates a pulse with few cycles (usually we use 3 cycles with
voltage 10 volts) to a rf coil. The rf coil generates an oscillating field around
the Larmor frequency and tip the spin of 3 He with a small angle. The trick
is to get signals big enough for NMR measurement but small enough so that
FID signals don’t decay too quickly. Once the spin is away from the holding
field direction, the spin starts to precess and induces an emf in the pickup
coil. The induced current will go through a preamplifier and be recorded
through the DAQ card. The more details of operation are described in [1].
The parameters for the preamplifiers are really empirical. Usually we set
the filter range to cover the Larmor frequency. The gains are set so that
the signals of two pickup coils have similar heights and best signal-to-noise
ratios. Usually we set the gain around 103 to 104 .
2. Electronics
I briefly describe the electronics used in this system. The block diagram
of the electronics is shown in Fig. 1 [2]. The function generator is Tektronix
Corresponding author at : Triangle Universities Nuclear Laboratory (Bldg), Duke
University, Durham, North Carolina 27708, USA. Tel.: +1 9196602950
Email address: pinghan@gmail.com (Ping-Han Chu)
∗
Preprint submitted to Elsevier
October 9, 2014
AFG 3021. The pulse generator is Quantum Composers Model 9614. The
preamplifier is Stanford Research System Model SR560. The DAQ card is
NI PCI-5122.
Figure 1: Block diagram of electronics
3. Magnetic Fields
The magnetic field system is composed of several coils in order to provide a uniform magnetic field, as shown in Fig. 2 [3]. The red Helmholtz
coil with diameter of 60 inches provides the holding field along the ẑ-axis.
Three square Helmholtz coils, called the compensation coils, with length of
84 inches along x̂, ŷ and ẑ-axis, respectively, form a cube [4]. One square
Helmholtz coil can generate a maximum magnetic field more than 600 mG
with current I=3 amp [6]. This assembly of the compensation coils can compensate the background fields, which is dominated by Earth’s fields, so that
the magnitude of the residual background field is less than 10 mG within a
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cubic space of length of 10 cm [5]. Together with magnetic shielding systems with the shielding factor 1000, the magnitude of residual background
fields, in principle, can be reduced to less than 0.01 mG. Once the absolute
magnitude of the field becomes small, the gradient becomes small as well.
Currently, we do not have magnetic shielding systems. Without shielding,
Cx and Cy do not play roles to improve T2 .
Two types of gradient coils are used in this system, Maxwell coil and
Golay coil (in the page 17 of [4]). The Maxwell coil, as shown in Fig. 3, can
provide gradients of dBz /dz. The Golay coil, composed of saddle coils, as
shown in Fig. 4 can provide gradients at transverse direction. This system
includes two sets of Maxwell coils with radius of 7 inches (a = 7′′ ) along
ẑ-axis, and two sets of Golay coils with radius of 7 inches (a = 7′′ ) providing gradients of dBz /dx and dBz /dy, respectively. The detailed studies are
described in [7, 8, 9].
The compensation coils are fixed with respect to the holding field and
the supportive table. The gradient coils and the cell holder are one set and
can be moved together. We can adjust the height and the location of the
assembly of the gradient coils with respect to the supportive table. Then the
height and the location can be fixed using nuts and plastic threaded rods or
screws.
Each gradient coil can be re-connected in different ways to create not only
linear gradients but also quadratic gradients. At each end of coil, there is a
label on it. Here we list the combination of each coil. The dash, “−”, means
the connection between two ends of coils.
• Compensation coil Cx : Cx 1 − Cx 2 − Cx 3 − Cx 4, quadratic gradient
• Compensation coil Cy : Cy 1 − Cy 2 − Cy 3 − Cy 4, quadratic gradient
• Compensation coil Cz : Cz 1 − Cz 2 − Cz 3 − Cz 4, quadratic gradient
• Gradient coil dBz /dx : x1 − x2 − x3 − x4, linear gradient
• Gradient coil dBz /dy : y1 − x2 − x3 − x4, linear gradient
• Gradient coil dBz /dz 1: z1 − z2 − z4 − z3, linear gradient
• Gradient coil dBz /dz 2: z1 − z2 − z3 − z4, quadratic gradient
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Figure 2: Magnetic field assembly, including the holding field, the compensation fields and
gradient fields.
4. Optimization
The goal is to improve the sensitivity of the precession frequency. The
sensitivity depends on two factors, the signal-to-noise ratio and the transverse
relaxation time, T2 . The signal-to-noise ratio depends on the particle density,
the polarization, the geometry of the pickup coil, and the resonance RLC box.
The particle density is a default input when constructing cells. Larger
particle density should have stronger signals; however, larger particle density
as well as larger pressure gives shorter transverse relaxation time, decreasing the sensitivity. There is a trade-off between larger particle density and
longer transverse relaxation time. Currently, we don’t have a good method
to optimize particle density. People (T. Chupp’s group at Michigan and
Walsworth’s group at Harvard) using SEOP for precision measurements use
the particle density of 1 amg. Duke group used a cell with the particle density of 7 amg for the phase II and made new cells with the particle density
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Figure 3: Maxwell Coil
of 3 amg for the phase III.
The polarization depends on the laser frequency and power, the oven
temperature and the longitudinal relaxation time. Both needs to be optimized before experiments. In order to tune the laser frequency, a spectrum
meter (SM240/SM440 Compact CCD Spectrometer) is put behind the cell
and the oven. The absorption spectrum shows double peaks with a dip at
the center if the laser is absorbed by rubidium atoms at a right frequency.
The laser power is limited by the laser itself. The oven temperature should
be optimized by checking the amplitude of FID signals versus temperature.
For a rubidium only cell, the temperature is about 160-180 ◦ C. For a hybrid
cell (rubidium-potassium mixture), the temperature is usually higher than
200 ◦ C. The longitudinal relaxation time depends on the property of the cell,
especially the surface properties. It is beyond the discussion of this note.
Several factors can affect the performance of pickup coils: the number
of turns, the size of the coil and the inductance which depends on the first
two factors. Duke group uses commercial pickup coils with diameter about
1 inch with inductance of 2 mH and resistance of 7 Ω (made by Ablecoil
http://www.ablecoil.com/).
The resonance RLC box is to change the natural frequency of the circuit.
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Figure 4: Golay Coil
Once the inductance of the pickup coil is known, it is straightforward to add
a capacitor in the circuit to change the natural frequency close to the Larmor
frequency. It needs an empirical test to determine the capacitor in series or
in parallel in the circuit.
Another critical noise is the rf noise. We observed strange rf noise in the
frequency spectrum; the signal became very noisy with many spikes. After
surrounding every electronics, including preamplifiers, function generator,
pulse generator, etc., with aluminum foil, the problem has been reduced.
The optimization of the transverse relaxation time is tricky. We have done
field mapping using a fluxgate magnetometer with stepping motors [6, 10].
We can scan the background field, the holding field, the compensation fields
and the gradient fields, respectively. With a careful tuning, in principle, the
location of the cell should have quite uniform magnetic fields at the level
of less than 0.1mG/cm [11]. However, the T2 is usually quite short without
further tuning. There are three possible reasons. First is the background
fields changing with time because of the activities around. It is not easy
to avoid the background changing without magnetic field shields. Second is
the power supply stability. We have observed the time-dependent drift of
magnetic fields. Each coil is controlled by a power supply (E3646A 60W
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Dual Output Power Supply). Many power supplies increase the instability
of the magnetic fields. Third is the field generated by polarized atoms [12].
In the page 8 of [12], we estimated a spherical cell with radius of 1 cm with
pressure 3 atm and polarization 40% can generate a gradient of 2.66 mG/cm.
It can destroy any optimization of fields based on the result of field mapping.
Therefore, the optimization of the transverse relaxation is quite empirical.
We found out that the configuration of the magnetic field and spin directions
can be quite important for the transverse relaxation time in [13] and phase
II. The reason is not clear. It seems that it is easier to cancel out gradient
fields for a certain configuration, especially when the magnetic field direction
is inverse of the polarization direction. Polarized atoms can play a role
to compensate gradient fields. We strongly suggest that people should try
different configurations for the optimization of transverse relaxation.
Once the proper configuration is determined, the following procedure is
applied. The cell is moved around until the best T2 is approached. In principle, we should scan every points in the space step by step. However, it is not
practical to scan the lattice of space; we usually optimize the vertical direction first because it is not easy to move the cell along this direction. Once the
height of the cell is optimized, we can move the cell at the horizontal plane,
forward and backward, rightward and leftward until the T2 is optimized. It
is easier if there are three people working on this process together. The next
step is to tune the gradient coils. In this system there are seven coils we
can tune. So far we have only used four of them, dBz /dx, dBz /dy, dBz /dz 2
and Cz because of the limitation of the number of power supply. However,
without magnetic shielding systems, Cx and Cy do not play roles to improve
T2 . We try four gradient coils independently and fix the one which can provide the best T2 . Then we try other three coils and repeat this process. The
optimization process may go back and forth between several coils.
Usually a T2 of two seconds is quite common for our current setup. However, it is possible to get T2 longer than ten seconds for two pickup coils with
careful tuning(like the page 7 in [19]). A very special case that T2 ∼ 80
seconds for one pickup coil has been obtained(in the page 8 of [13]).
5. Comments
In order to succeed the experiment, a cell with strong signals and a long
longitudinal relaxation time is necessary. We require the signal to noise ratio
close to 10. As mentioned before, this can be done by reducing noise and
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increasing polarization, etc.. Besides, a long longitudinal relaxation allows
that the signal amplitude won’t decay quickly while applying FID. Another
thing is the transverse relaxation time. The transverse relaxation does not
depend on the cell itself. We have tried several cells including TINY, Pablum,
KellyK #1, KellyK #2, and Test Cell #5(in the page 25 of [14], [15], [16])
and all of them give similar T2 result. The only trick to improve T2 is to
carefully tune the gradient fields and the cell location. A T2 of at least 10
seconds for both pickup coils is possible and necessary.
In a long run, a system like the one in Walsworth’s group at Harvard is
necessary; more details are described in D. Bear’s thesis [17, 4, 18]. Magnetic
field shields and a solenoid are needed to provide more uniform magnetic
field and improve T2 . The holding fields and oven temperature need to be
stabilized.
In this note, we focus on the improvement of the frequency sensitivity.
We can see the success of this experiment is possible. However, a cell with
good polarization and a long T1 is necessary for reliable signals. Currently, a
new cell being constructed with a short length (5 cm) and thinner windows
(100 µm) gives us a good chance to improve sensitivity.
Recently, we observed signals with a very long T2 (longer than 50 sec)
using the cell Pablum [20]. Pablum is a cell with T1 longer than 10 hours and
high density of 9 amg, and has stable polarization. This test demonstrates
the possibility to push T2 longer than 10 seconds using gradient coils if the
cell has long T1 and stable polarization. However, current magnetic field is
not extremely stable so that the NMR signal may change between cycles.
Sometimes the signal increases and then decreases (like the page 8 in [20]).
In fact, it is similar with the node point we observed before in a shorter time
scale because of non-uniform gradient fields. If the measurement time can
be extended up to 100 seconds, we should be able to observe decaying NMR
signals with node points. However, the DAQ card limits the measurement
time because its maximum record length is 2 × 106 points. It is possible
to lower the holding field as well as the precession frequency so that the
measurement time can be extended. It requires the construction of new RLC
boxes and the retuning of gradient fields.
References
[1] Y. Chang, http://www.phy.duke.edu/~ pc102/MeasurementProcedure.docx
[2] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20120904.pdf
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[3] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20131108.pdf
[4] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20130828.pdf
[5] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20140207.pdf
[6] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20140124.pdf
[7] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20140227.pdf
[8] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20140307.pdf
[9] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20140321.pdf
[10] P.-H. Chu, http://mep.phy.duke.edu/index.php/Field_Mapping
[11] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140402.pdf
[12] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20130824.pdf
[13] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140620.pdf
[14] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140326.pdf
[15] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140411.pdf
[16] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140523.pdf
[17] D. Bear, Ph.D. thesis (2000)
http://walsworth.physics.harvard.edu/publications/2000_Bear_HUPhDThesis.pdf
[18] P.-H. Chu, http://www.tunl.duke.edu/~ pc102/20131122.pdf
[19] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20140628.pdf
[20] P.-H. Chu, http://www.phy.duke.edu/~ pc102/20141006.pdf
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