Peter SchmidtNielsen
Adam Marblestone
Physics of Information Technology (Spring 2010)
Nuclear quadrupole resonance excitation of pdichlorobenzene
Introduction: NQR spin resonance phenomena can be conceptualized in much the same way as NMR spin resonances, but they occur with zero external field. This vastly simplifies the experimental constraints on a proof of principle, lowbudget experiment. In NMR, an external B field is used to create a net magnitization vector which then rotates as spins are flipped, creating a macroscopically observable signal. In NQR in a solid, the macroscopically visible spin dynamics, in response to rf pulses, comes from the interaction of nuclear spins with electric field gradients in the material, rather than macroscopic polarization by an ambient B field. However, there is a subtlety in that this interaction does not create a net spin polarization in the absence of rf exciation, because the nuclearspin/electricfieldgradient interaction is insensitive to nuclear spin direction. The result is a set of equations analogous to the Bloch equations for spin dynamics in NMR. This result follows from a full quantum treatment of the interaction of the nuclear quadrupole moment with the electric field gradients in the crystal [1]. Our goal for the project is simply to observe evidence of this effect using a device of our construction.
System Design:
Block Diagram:
Design considerations:
The sample: pdichlorobenzene, Cl35, no need for external B field
Tuned probe: tunable capacitors, analog and digital, conditions for real and imaginary parts of the impedance
Isolation for the receiver chain: crossed diodes vs. purely switch based, digital noise, distortion from diodes
TTL switch control: switching timescales, pulse sequence complexity, insertion loss, isolation
Pulse sequence: spin echo, FID vs. ringdown
Signal generation: class E amplifier vs. the power amplifier we are using vs. what we can do with cheap circuit components
Amplifier noise figures and initial signal detectability: choice of two amplifiers, noise floor of spectrum analyzer, Friis formula for cascaded amplifiers, RF design vs what can be done on a simple PCB, correct "order of operations" when searching for a signal
Filtering: active vs. passive, amplifier gain bandwidth product, oscillations, impedance matching, microstrip design, small inductors
Homodyne detection: mixing, nonlinearity in mixer, lowpass and bandpass filtering, spectrum analyzer as homodyne detector
Electromagnetic shielding: copper boxes, low conductivity of the adhesive, need to solder together joints
Future versions: Yael's mininmr board, fabable microstrip circuit using fast opamps, impedance matching "onchip"
Software:
screenshot
Estimated System Parameters:

Relation between applied voltage and field strength, current divider model of probe
Sample properties
Relation between field strength and pulse sequence parameters
Materials:
"Moth Ice" (from any hardware store)
Sprague Goodman GKG series ceramic trimming capacitors (4.5  65 pF) [4X]
Miniature ceramic flathead screwdriver (for tuning probe without capacitive coupling)
Copper boxes and vinyl cut copper sheets (for shielding)
Atmega ATtiny45 microcontroller
PCB to SMA connectors
Minicircuits ASW250DR SPDT switches [3X]
Minicircuits ZFL 500LN amplifiers [2X] (can be replaced with high speed op amps, GBP > 500 MHz)
Experimental Progress:
implemented RF switching from logic board
implemented matched passive 34 MHz bandpass filter
implemented matched, tuned coil at 34 MHz, characterized with network analyzer and LCR meter
constructed full experimental setup
estimated device parameters (such as probe field strength) in order to estimate initial pulse lengths
tell the story of our problems and solutions so far...
References:
[1] Bloom, Hahn, Herzog.
Free magnetic induction in nuclear quadrupole resonance. Physical Review 97:6 (1955) [the best for basic NQR theory]
[2] Maguire.
Towards a Table Top Quantum Computer. MS Thesis, 1999 [RF and NMR wisdom]
[3] Maguire.
Microslots: Scalable electromagnetic instrumentation. PhD thesis, 2004 [contains some NQR work]
[4] Robinson.
A sensitive nuclear quadrupole resonance spectrometer for 260 MHz. 1982 J. Phys. E: Sci. Instrum. 15 814 [good SNR formulas]
[5]
Pulsed NMR: Spin Echoes. MIT Junior Lab Manual.
http://web.mit.edu/8.13/www/12.shtml; see also related here
www.physics.nyu.edu/~physlab/Experimental_Phys/PulsedNMR.pdf [references to the basic designs for observing spin echoes]
Acknowlegements: We would be nowhere on this without huge help from Yael and Rehmi on both design and practical implementation details. Thanks also to Clarissa Zimmerman for walking us through her NMR apparatus in the Bioinstrumentation Lab.
Appendix: raw lab notebook and initial musings
More thoughts on measuring/estimating probe field: we realized there is a current divider inside the probe so it is not quite as simple as current = V/50. Still, knowing coil inductance and the capacitance of our tuning capacitors, we could calculate it from current divider relationship.
Also observed resonance with Smith chart view. Need to learn how to interpret this.
Resonance does seem tunable: need to tune series cap to get a decent signal size, and both caps affect the resonance frequency
TNT resonance frequency for NQR is < 1 MHz, hence the parameters we chose
For future probes, it might be good to order some SMA to PCB mounting connectors