Laser Spectroscopy and Potential Modeling Kit Leonard Advised by Dr. Jim Shaffer University of Oklahoma
Main Experiment -Electrons held in free space above a dielectric surface -Motion normal to surface quantized by Coulomb potential -In-plane motion controlled by electrodes, quantized by harmonic oscillator potential -Individual electrons can be excited using an infrared laser -Goal: Create entangled states that can be used to store quantum information Electrons Electrode Potential Dielectric (Quartz) with Rubidium surface layer Positively charged electrodes Grounded conducting surface Insulating layer between electrode and grounded surface
My Projects Laser Spectroscopy Tune the laser to excitation frequencies of electrons Precise enough to excite energies normal to surface, avoid in-plane excitation Potential Modeling Find parameters for electrodes that produce desired potential shape Energy level spacing/number of bound states Check accuracy of harmonic oscillator approximation Electrons Electrode Potential Dielectric (Quartz) with Rubidium surface layer Positively charged electrodes Grounded conducting surface Insulating layer between electrode and grounded surface
Voltage (mv) Spectroscopy Setup Measure absorption frequencies of CO 2 using a tunable laser Hold current at 96mA, change temperature to adjust frequency Drops in output power indicate absorption by CO 2 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 1) laser 2) chopper 3) Vapor cell 4) detector 5) scope Experimental Setup 1) Quantum Cascade Laser*, Wavelength 4300-4350 nm 2) Optical chopper- chops laser signal into pulses 3) CO 2 vapor cell 4) Photodetector- measures incoming laser power, outputs voltage 5) Oscilloscope- displays signal from photodetector Absorption Peaks at 96 ma *Current and Temperature Adjustable 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Temperature (C)
Spectroscopy Objectives Match observed absorption pattern to known spectrum of CO 2 Frequencies of absorption peaks are well known Observe linearity of laser response Linear frequency response needed to match results Linear power response less important, observe general behavior
Absorption Results: Absorption Spectrum Comparison: 1968 Spectroscopy study using spectrographs 1 Results obtained through laser spectroscopy Normalized Absorption 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Temperature (C)
Absorption Temperature (C) Temperature (C) Results: Laser Behavior 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 Combined Absorption Conditions 0 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 Current (ma) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 P41 R22 P52 P40 R24 P39 R26 P38 P50 R28 P37 P36 P48 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Conditions for P48 Absorption Current (ma) R26 Absorption vs Lorentzian y = -0.4917x + 49.576 R² = 0.9995 0 15.36 15.37 15.38 15.39 15.4 15.41 15.42 15.43 15.44 15.45 15.46 Temperature [C]
Conclusions: Laser Spectroscopy Laser frequency varies linearly and can be accurately determined for given input conditions Laser power varies approximately linearly with some fluctuation Some broadening of absorption peaks is present, effects are minimal Broadening independent of power Laser can be tuned precisely to excite normal-to-surface electron energies while avoiding excitation of in-plane energies
Potential Modeling Examine how in-plane motion of electrons is quantized Find best parameter values for electrodes Similar experiments use a liquid Helium surface to vertically confine electrons Electron spacing ~0.5 μm, Laser wavelength ~1 cm Our experiment uses a dielectric surface Electron spacing ~5 μm, Laser wavelength ~4.3 μm Can electrode geometries from liquid He experiments also be used in our experiment? How can the electrode potential function be simplified by approximations?
Potential (V) 5. 10 6 w V 1.26 10 11 Results r 5. 10 7 L 8. 10 6 c 6.24 10 18 a z 31 5. 10 6 5. 10 6 Position (m) max width 50 Red: Sinusoidal multielectrode approximation Blue: Actual potential (1000 electrode array) 0.00001 Green: Actual potential (single electrode) Blue: Harmonic coscillator potential Red: Sinusoidal multielectrode approximation 118.88 +Harmonic Oscillator approximation is valid +Electrons can be localized by electrode potentials with many (100+) bound states +Bound states are spaced by 20 GHz +Sinusoidal approximation* holds when multiplied by a constant *comes from a different electrode geometry
max width 50 Limitations 0.00005 Potential of a 40x40 array of electrodes. Curvature effects are sharper, well depth is unchanged. Zoomed-out view of the actual electrode potential for a 100x100 array. Note that wells have constant depth despite overall curvature. -Sinusoidal approximation not valid over large arrays +actual potential can be flattened out -Large arrays are needed to see agreement between sinusoidal model and actual potential -Adjusting parameters has a limited effect on improving fit
Conclusions: Potential Modeling In-plane position of electrons can be localized using electrodes Electrode potential can be approximated by a harmonic oscillator potential Energy gap between in-plane excited states is ~20 GHz as desired Large electrode arrays are needed to reduce curvature effects Altering electrode dimensions has a limited effect on the shape of the resulting potential
Summary Laser is capable of precisely exciting individual electrons Electrons can be confined by an electrode array with reasonable dimensions Energy gap between in-plane excited states is large enough to avoid unwanted excitations by the laser System could potentially be used for quantum information and quantum computing! Electrons Electrode Potential Dielectric (Quartz) with Rubidium surface layer Positively charged electrodes Grounded conducting surface Insulating layer between electrode and grounded surface
Acknowledgements Dykman, M. I.; Platzman, P.M.; Seddighrad, P.; Qubits with electrons on liquid helium, Physical Review B, Vol 67, 2003. Oberly, Ralph; Rao, K. Narahari; Hahn, Y. H.; McCubbin, T. K.; Bands of Carbon Dioxide in the Region of 4.3 Microns, Journal of Molecular Spectroscopy, Vol 25, Issue 2, p. 138-165, 1968.