K.Serniak , M.Martens , S. Bertaina , and I. Chiorescu

On-Chip Cavities for Magnetic Resonance Studies
1
K.Serniak ,
1
M.Martens ,
S.
2
Bertaina ,
and I.
1
Chiorescu
1Department
of Physics and The National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
2Faculte des Sciences et Techniques, IM2NP-CNRS (UMR 7334) and Universite Aix-Marseille, Marseille Cedex, France
Introduction
Coplanar Waveguide Design
The control of dynamics of spins in solid-state materials has direct
implications at both fundamental and applied levels. Research topics, in
particular quantum computing, rely heavily on both complex control
techniques and long spin coherence times to achieve intricate and robust
information control.[1] A natural way of driving spin orientation is by using
electromagnetic fields (photons) and it can be done either as a classical
rotation or by entanglement with the field itself. We are focusing on
implementing such techniques in solid-state systems containing diluted,
highly coherent spins.
Electron spin resonance spectroscopy (ESR) is a useful technique for
identifying and characterizing materials with unpaired electrons, and onchip resonators show promising results.[2,3,4] We seek to design and
implement on-chip resonant cavities for ESR studying small, diluted spin
samples. Coplanar waveguide cavities were designed and optimized using
Sonnet EM Analysis software. The cavities were tested at low temperature
to determine their transmission properties and their effectiveness in an
ESR setup.
This type of cavity supports a quasi
TEM mode, as the E and B fields
have small longitudinal components.
Coupling gap dimensions must be
optimized to maximize Q-factor
and minimize reflections from the
input port. This is done by
matching the input impedance z
to the line impedance, which is
traditionally 50 ohms.
is the impedance
normalized to the 50 ohm line.
[6] This quantity gives us the
general reflection coefficient:
Ti thickness
Cavity width
At resonance hν=∆Ez , where ν is the resonant frequency of the cavity,
there will be a drop in the S12 transmission spectrum corresponding to
absorption of energy by the sample.
Heterodyne Detection with a Magic-T Bridge
We detect ESR signals using a
heterodyne system. The ESR
signal (Anritsu 1) is amplified and
mixed with the reference signal
coming from Anritsu2 which is 70
MHz lower in frequency. The
resulting “down-mixed” signal is
70 Mhz and carries with it the
Amplitude
and
phase
information of the original ESR
signal which is analyzed by a
digital acquisition card. The
higher frequency component is
eliminated by band-pass filters.
50 μm
Reflection Measurements of an Aluminum Cavity
Reflection vs Frequency
Reflection vs Frequency
-25
-40
-41
-30
.
In our studies, gamma becomes
the S11 scattering parameter
given by simulation of network
analysis. The Smith Chart shows
graphically both S11 and z.
-42
-43
-44
-45
Smith Chart explained [7]
Optimization by Simulation
Output Power
0 dBm
-2 dBm
-4 dBm
-6 dBm
-8 dBm
-10 dBm
-12 dBm
-35
-40
-46
-45
-47
18370
The energy difference between two Zeeman split spin states is well
defined and proportional to the applied field. For the l=0 and spin ½ case:
10 nm
Input gap, output gap 60 , 300 μm
Amplitude (dBm)
The Zeeman effect refers to the splitting of energy levels corresponding
to degenerate spin states by application of an external magnetic field.
The energy gap produced by Zeeman splitting is determined by the
expectation value of the perturbative Hamiltonian below. [5]
Cavities were fabricated at NHMFL
using positive photolithography and
electron beam evaporation. The data
presented is from one cavity made of
Aluminum with a Titanium adhesion
layer on a silicon substrate(εr=11.9).
Al thickness
80 nm
Amplitude (dBm)
Principles of ESR
[6]
Fabrication
18375
18380
18385
18390
18395
18400
Frequency (MHz)
18370
18375
18380
18385
18390
18395
18400
Frequency (MHz)
Reflection measurements of an superconducting Aluminum cavity (~25
mK in a dilution refrigerator) show a clear resonance at 18387 MHz.
Various input powers were tested, and there was some variability in Qfactor with respect to power. The maximum Q factor measured was
~3000 (featured in left image).
Conclusions
Coplanar waveguide geometry as designed in Sonnet
The input gap (coupling gap 1) was optimized via reflection simulations of a
cavity with no output port. The optimized value was 50 +/- 5 microns. With
the output port added, it was determined that 52 microns was the optimum
value, and a value of 300 microns was chosen for the output gap in order to
minimize perturbation of the cavity by the output line. Simulations assumed
a lossless metal.
•Using Sonnet EM analysis software, we
were able to optimize the cavity
geometry for impedance matching
•Developed a reliable method for
fabricating on-chip cavities
•Coplanar waveguides show promise for
ESR: at 25 mK, Q ≈ 3000
Future Studies
•Improve simulations
•Fabrication of more cavities: Nb, Ag, Al,
with different geometries
•ESR experiments with DPPH and others
References
With Bridge
1.
2.
When the resonant frequency coincides
The simulated S11 parameter shows the with a point in the center of the Smith
resonant frequency of the cavity, and aids chart, the input impedance is matched to
the 50 ohm line.
in maximizing the S11 dip and S12 peak.
3.
4.
5.
6.
7.
QSD 3-D vector magnet
A. Blais, R. S. Huang, A.Wallraff, S. M. Girvin, and R. J. Schoelkopf, Physical Review A, vol. 69, 062320, 2004.
Henderson, C. Ramsey, E. del Barco, T. Stamatatos, and G. Christou, Physical Review B 78, 214413-214415
2008.
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H. Malissa, D. I. Schuster, A. M. Tyryshkin, A. A. Houck, S. A. Lyon, Rev. Sci. Instrum. 84, 025116, 2013.
Griffiths, David J., Introduction to Quantum Mechanics, 2nd Edition, p. 249-283, Addison-Wesley, Chicago, IL,
2004.
Liao, Samuel Y. , Microwave Devices and Circuits, 2nd Edition, p. 62-98, Prentice-Hall, Englewood Cliffs, NJ,
1985.
http://en.wikipedia.org/wiki/File:Smith_chart_explanation.svg