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

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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. R. Narkowicz, D. Suter, and I. Niemeyer, Rev. Sci. Instrum. 79, 84702, 2008. 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