The Wonderful World of AJP Zeeman Effect Experiment
The Wonderful World of AJP Zeeman Effect Experiment with High-Resolution Spectroscopy for Advanced Physics Laboratory Dr. Andrew Taylor Physical Sciences, Inc. Andover, MA Dr. Oleg Batishchev and Alex Hyde Department of Physics, Northeastern University, Boston, MA January 9th, 2018 Abstract An experiment studying the physics underlying the Zeeman effect and Paschen-Back effect is developed for an advanced physics laboratory. We have improved upon the standard Zeeman effect experiment by eliminating the Fabry-Perot etalon, so that virtually any emission line in the visible spectrum can be analyzed. Emitted light from a ~1T magnet is analyzed by a Czerny-Turner spectrograph equipped with a small-pixel imaging CCD. The experiment was taught as part of the Principles of Experimental Physics course at Northeastern University to a combination of graduate/undergrad students. Zeemans original sodium experiment is recreated, and the splitting of argon and helium lines is measured as a function of field
strength. The students analyze the proportionality of the splitting magnitude to both the B-field strength and lambda squared. The Bohr magneton is calculated and compared to theory. Student feedback is positive, citing the ability to experimentally witness a quantum mechanical effect. A. Taylor, A. Hyde, and O. Batishchev, Am. J. Phys. Vol. 85, No. 8 (2017). History of the Zeeman Effect In case you missed it in your Modern Physics class 1896: Pieter Zeeman observed a widening of the sodium D line in the presence of a magnetic field (normal Zeeman effect). 1897: Zeeman observed the line through a polarizer; he found two outer circularly-polarized peaks and a central plane-polarized peak; verified Lorentzs theoretical predictions. 1898: Thomas Preston observed quartet pattern of lines in a magnetic field (Anomalous Zeeman effect). 1902: Paschen, Runge, and others fine Anomalous Zeeman effect patterns of six, nine, eleven, etc. in atomic spectra. 1925: Schdinger formulates wave equation 1925: Pauli and Heisenberg formulate nascent quantum mechanics to explain the Anomalous Zeeman effect
1926: Uhlenbeck and Goudsmit, Bichowsky and Urey independently discover the intrinsic spin of the electron, Quantifying the Zeeman Effect An external magnetic field B exerts a torque on an electrons magnetic dipole and shifts the energy of the atomic level from the non-perturbed energy by where is the Land g-factor, is the Bohr magneton, and is the projection of the total angular momentum J = L + S. The change in wavelength from a small change in energy is Substituting and , For practical laboratory settings, pm. Image sourced from: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html Zeeman Effect in Physics Teaching Lab
Example: Zeeman Experiment at MIT Junior Physics Lab Understanding the Zeeman effect is important for historic and current research Experiments introducing the effect are widely used in physics laboratory curricula Common approach utilizes electromagnets and Fabry-Perot etalon Requires Reflectivity to resolve splitting of lines Usually measures only a few spectral lines Electromagnets and/or etalon require liquid cooling to maintain performance Replaced Fabry-Perot with high-resolution spectroscopic system that allows measuring the entire spectrum Replaced electromagnet with permanent magnets with 1T
McPherson M216 Spectrometer Side view of M216 installed in the NEU Plasma Lab Made by McPherson in 1960s Used at Harvard Center for Astrophysics Donated to NEU Plasma Lab in 2014 Asymmetrical Czerny-Turner design = 1 m focal length with 1200 g/mm grating Large 8 collecting and 12 focusing mirrors Originally designed for 35 mm film Was retrofitted to deliver high spectral resolution in UVNIR range with new CMOS camera and collecting optics Initial Viability Test of Spectroscopic System Tested Resolution in measuring Zeeman Effect using a simple proof-ofconcept Initial proof-of-concept setup
Pasco Spectral Tube 50-W discharge tube and 125 V Power Supply Modified a Pasco Spectral Tube power supply to lay flat, and two attached N50 neodymium magnets created a T field at center of tube Optical fiber pointed in center of field Observed Zeeman triplet splitting of the He I 706 nm line MU1403 camera, 5 um slit Side peaks approx. half of center peak Initial spectrum of Zeeman Effect Permanent Magnet Holder for Zeeman Effect Magnet Holder was designed by Prof. Batishchev Holder body and arm
Machined by NEU machine shop Two 8 arms each loaded with a 2 N52 neodymium permanent magnet, remanence T at surface Threaded for 1 mm/rotation travel Handles added and marked Rotation of arms in the body varies separation distance Upper and lower openings through which the light source is placed Side opening notched for mm-measurements Sturdy wooden frame cut, assembled, and installed on optical bread board table 3D-printed tube stop on top and bottom to secure light source Assembled Holder in frame Calibration of B-Field Strength Measurements Measured Field Strength across the magnet face at various Placed the sensor tip of an Alpha Labs gaussmeter on a moveable stage
Made multiple measurements at mm to determine accuracy Magnetic field at as a function of separation distance T For a given , measured every mm, starting at Ran calibration 3x to eliminate possible sensor tip misalignment Achieves 1.19 T in center Approx. uniform across face of magnets Magnetic field as a function of radial distance from the
center for varied Light Source and Collection Optics Continued to use Pasco Spectral tubes Used optical fibers for emission collection from discharge to M216 Cannot bring fiber directly into Magnet Holder, built two-lens collimator Back lens selected to match the NA of the fiber Front lens selected to collect light from smallest possible Retrofitted M216 entrance slit with optical fiber attached Left: Collimator for collected emission Right: end tube into which the collimator
fit UV-VIS Spectroscopic Systems Utilized two spectroscopic systems 1:Ocean Optics USB4000 for broad UVVIS coverage 3648 pixels at 2 nm/pix resolution 2: McPherson spectrometer with Touptek MU1403 14 MP Camera and customized LabVIEW interface 4096 x 3286 ~350-1100 nm spectral range 1.4 m pixelm pixel LabVIEW VI controls integration time, gain, color, etc.
Modified it to integrate image into 1D spectrum and to crop & integrate a small ROI Determination of Spectral Lines He I and Ar I spectra from USB4000 Helium and Argon ultimately chosen as the sources for Zeeman effect experiment Single-isotope elements with >99.6% purity Large number of bright lines across entire UVNIR spectrum Utilized closely-spaced peaks at 587, 706, 751, and 811 nm to calibrate the per-pixel resolution pm/pix Extrapolated resolution for other wavelengths from linear curve
Calibration using closely-spaced peaks Zeeman Effect in Singlets Measured Zeeman splitting of a line as -field varied from 0.51.07 T in 0.1 T increments Schematic of Zeeman splitting in He I 667 nm singlet transition Distance values of , respectively Measured in He I 501 and 667 nm, and Ar I 811 nm singlets Image taken from PHYS5318 lab manual. He I 667 nm at 1.07 T Zeeman Effect in Triplets In the strong field limit, and decouple and interact
independently with the field Schematic of Zeeman splitting in He I 706 nm triplet transition at Paschen-Back Limit All transitions converge to exhibit normal Zeeman triplet with Effect appears when In helium this occurs around B ~ 0.4 T The limit observed in He I 388, 447, 587, and 706 nm triplet lines H. Odenthal et al. Physica,113C 203-216 (1982). Image taken from PHYS5318 lab manual. He I 587 nm at 1.07 T
Study of B-field Dependence Observed Zeeman splitting of a line as field varied in 0.1 T increments from T vs. for He I 587 nm vs. for Ar I 811 nm Collected 5x images for each to gather experimental uncertainty in Analyzed pixel spacing for left and right peak via LabVIEW cursor, averaged for Converted into via measured Graphed vs. for six He I VIS lines and one Ar I line From lines, calculated Bohr magneton value with average accuracy of 10% Bohr Magneton calculation accuracy Study of 2 Dependence
Unique Ability of System Spectroscopic System has unique ability to measure the dependence of Zeeman splitting Analysis is available for virtually any line in the VIS spectrum Used six He I lines from 388706 nm at T Bohr magneton calculation is more accurate and precise using this new method vs. for He I discharge at 1.07 T Anomalous Zeeman Effect in Argon Most argon lines exhibit the Anomalous Zeeman effect (not Paschen-Back) Ar I 696 nm at 1.07 T
Ar I 810 nm at 1.07 T Triplet patterns of with , e.g. Ar I 696 nm Quartet patterns of , e.g. Ar I 810 nm Sextet patterns of , e.g. Ar I 912 nm Excellent candidate to teach the Anomalous Zeeman splitting, either in conjunction with helium or as a separate experiment Ar I 912 nm at 1.07 T Improvements and NIR Extension Increasing groove density will increase per-pixel resolution but decreases the longest viewable wavelength Princeton Instruments IsoPlane 320 with 1200-g/mm grating
and 20 m pixels Maximum Zeeman split magnitude decreased from current magnitude by where is the ratio between 1200g and new grating McPherson M216 + MU1803-FL camera with 1.85 m pixels The bright He I 1083 nm triplet represents ~135% increasing in Zeeman split over He I 706 nm Two systems used to measure lines A. Taylor and O. Batishchev, Can. J. Phys. 95: 993-998 (2017). Designing the APL Experiment Experiment created using the Magnet Holder, USB4000 & M216 + MU1403 spectrometers, and
helium & sodium tubes Designed it around calculating from both - and dependencies of the normal Zeeman and PaschenBack effects Re-create Zeemans original sodium lamp experiment, showing widening of Sodium D line Study -dependence using three helium lines (He I 587, 667, 706 nm) Study -dependence using four helium lines at T (He I 587, 667, 706, and 1083 nm) Designed lab manual and lab report grade guide Sodium lamp used to re-create Zeemans original findings Teaching the APL Experiment Taught experiment for PHYS5318 Introduction to Experimental Physics at Northeastern University in Spring 2017 Total of 14 students, both grad and undergrad, across 14-week semester
Two 3-hour lab sessions Generally 1 to take broad He I and Na I spectra, high-res Sodium D broadening, and some high-res He I Zeeman effect spectra 2nd to take the rest of the He I spectra and analyze the pixel spacing between peaks Graphing, calculation of , and report done outside of class time st Overall positive student outcome with the experiment High comprehension of what to do, mixed comprehension of why it was done Best comment: Ive never done an experiment that explained Quantum Mechanics so well! I think I finally get it! Improvements: start the lab manual with the detailed theory; cut out one or two
He I parts; provide more motivation for finding two ways
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