Optical Pumping of Rubidium

Transcription

1 Optical Pumping of Rubidium Practical Course M I. Physikalisches Institut Universiät zu Köln February 3, 2014 Abstract The hyperfine levels of Rubidium atoms in a sample cell are split up into their Zeeman components using the magnetic field of Helmholtz coils. A Rubidium high-frequency lamp serves as the pumping light source to excite the Rubidium sample. The pumping light is filtered to transmit the D 1 Rb line and polarizers are used to produce circular polarization. The circular polarization pumping mechanism selectively repopulates the Rb sample s ground state Zeeman hyperfine levels away from thermal equilibrium population according to whether the pumping light is left or right circularly polarized. The sample cell is then irradiated using RF coils with the frequency of the hyperfine levels, changing the transparency of the sample cell Rb vapor. The change in sample transparency is measured as a function of RF frequency with a Silicon photodiode detector. This technique is used to determine the transition frequencies between hyperfine levels of the 87 Rb (I=3/2) and 85 Rb (I=5/2) isotopes as well as the strength of the magnetic field causing the Zeeman splitting of the hyperfine levels.

2 1 Preparation The experiment is explained in detail in the article by J. Recht and W. Klein in contact, 1/1991. A copy of this article is available at the webside for this experiment or can be handed out by the assistant. The following topics should be prepared in advance before participating in the experiment. Make sure you also cover these topics in your written report. Energy level scheme of 85 Rb and 87 Rb Origin of fine structure, hyperfine structure, and Zeeman splitting Breit-Rabi formula Relative population of energy levels Principle of optical pumping Polarization (especially circular polarization) Experimental setup, function and operation of the individual components Especially: Interference filter Polarization filter λ/4-plate Helmholtz coils 2 Measurement Tasks Record the hyperfine transitions of 87 Rb for 5 different Helmholtz coil currents (for both directions of the magnetic field of the Helmholtz coils) Record the hyperfine transitions of 85 Rb for one specific Helmholtz coil current (for both directions of the magnetic field of the Helmholtz coils) 2.1 Procedure Set-up Switch on the Rb-lamp (Warning: It becomes very hot!) Make yourself familiar with the experimental setup; Check the necessary connections between the individual components of the experiment (see Section 2.2) Adjust the setup to the best possible signal; You should reach an amplitude of about 5 mv at the output of the amplifier. Note: The best way is to remove the interference filter and to follow the beam from the Rb lamp to the detector using a sheet of paper. Make sure the beam passes through the middle of the optical components. Warning: Do not directly touch the optics (windows, lenses, detector)! All optical components are embedded in a mounting, which can be touched without any problems. Log all sources of error and the accuracy of the components

3 Measurements Locate the position of the hyperfine transitions for a given coil voltage. To do so, increase the sensitivity of the oscilloscope and slowly sweep the start or stop frequency of the function generator manually using the control dial. At the location of the transition frequencies there is a significant change in intensity of the signal at the oscilloscope. Note: After changing the frequency, you have to push "Manual" at the function generator. Otherwise the function generator does not react to the trigger signal of the computer (i.e. the functions "adjust()" and "measure()" of the measurement program (see Section 2.3) are not operational). Use the program function "adjust()" to automatically sweep the range between start and stop frequency. Adjust Start/Stop at the function generator to obtain the ideal range for measuring the hyperfine lines (remember to push "Manual" again) Use the program function "measure()" to scan and save the selected frequency range. Note: The system is extremely sensitive to any perturbances. Hence, try to avoid running around etc., while recording the spectrum. Inverse the direction of the magnetic field of the Helmholtz coils by using the switch on the little black box Re-adjust the frequency range ("adjust()") Record the hyperfine transitions with inverted magnetic field ("measure()") 2.2 Apparatus Settings Checklist Rb Lamp: 100 C at stable operation (about 45 min after switch-on) Circulation Thermostat: 70 C Helmholtz Coils: ma Photodiode detector: connected to current-to-voltage converter Current-to-voltage converter: connected to amplifier (located in the blue metal box) Amplifier: connected to the oscilloscope input and the computer (ADC 0 input) Function Generator: connected to the HF coils and to the computer (monitor output at the back of the FG ADC 1 input of the PC) Mode: Sweep (push "Mode" and choose setting " C up" with the control dial) Sweep velocity: 2 sec (push "Sweep" and choose setting with the control dial) Set Start/Stop frequency: push Start/Stop and choose setting with the control dial Enable trigger by computer: push "Manual" the function generator supplies a voltage proportional to the frequency

4 2.3 Measurement Program The computer runs under a Linux operating system. Open the terminal: You are automatically in the directory "fp@fp-optisches-pumpen". Create a new sub-directory for your group ("mkdir directory"). Change to the new directory ("cd directory") and start the pdada measurement program by typing "optisches-pumpen". The measurement program provides two functions: adjust() displays the spectrum on the monitor helpful for searching the optimal frequency range. Press "Strg C" to leave this function. measure() starts the recording. 10 individual scans are taken and added up by the computer. If needed, stop the function with "Strg C" (e.g. when a faulty scan was taken) and start again. After the 10 th scan was taken, you have to enter the file name (filename.dat), start/stop frequency, and coil current. The data is saved in ASCII format with the first column containing the frequency, and the second column indicating the intensity. 3 Analysis Determine the hyperfine transition frequencies and assign their quantum numbers for all measurements. What is the best method to obtain precise line center frequencies? What is the accuracy of the transition frequencies? Plot at least two different spectra and label the transitions (F =?, m F =?). Calculate the strength of the magnetic field (for the individual transitions) using the Breit-Rabi formula (see Section 4.2. Hint: The equation cannot easily be solved for B. Either you make an expansion for the square root (after appropriate estimation of x) or you solve the equation numerically. Summarize your results for the transition frequencies, their F and m F quantum numbers and the calculated B-fields in individual tables for each measurement. Calculate the mean value for the magnetic field for a given coil voltage by averaging. Calculate the magnetic fields directly using the parameters for the Helmholtz coils (see Section 4.1). Discuss these results and uncertainties for the magnetic field compared to the results using the Breit-Rabi formula. How large are the uncertainties? What is their origin (systematic errors, statistical errors)? How can these errors be reduced? What is the relation between the uncertainties of the measured magnetic fields (Breit-Rabi) to the uncertainties of the transition frequencies? What is the main parameter limiting the accuracy? Calculate the external magnetic fields affecting the experiment by comparing the measurements with "normal" and with inverted magnetic field of the Helmholz coils. What is the origin of the external magnetic fields? Estimate the influence of the earth s magnetic field on the hyperfine splitting.

5 4 Constants and Formulae 4.1 Constants The uncertainties of the values given here are negligible. number of windings N = 210 distance of the coils R = 11.6 cm nuclear magneton µ N = J/T Bohr s magneton µ B = J/T Landé g-factor g J = Rb nucleus g-factor g I ( 85 Rb) = Rb nucleus g-factor g I ( 87 Rb) = Rb hyperfine splitting W/h ( 85 Rb) = MHz 87 Rb hyperfine splitting W/h ( 87 Rb) = MHz 4.2 Formulae The energy of the Zeeman levels and the frequencies for hyperfine transition between neighbouring levels with m F m F 1 are given by the Breit-Rabi formula as follows W(F ±,m F ) = W 2(2I + 1) + g Iµ B Bm F ± W m F 2I + 1 x + x2 1 ν = h W(F ±,m F ) W(F ±,m F 1) = ± g Iµ B B + W h 2h 1 + 4m F 2I + 1 x + x (m F 1) 2I + 1 x + x2 with x = (g J g I )µ B W B sign ± for F ± = I ± 1 2 Note: For the energies ± applies to the square root whereas for the frequencies it is located at the first term. This is due to the different order of the m F levels for F = 1 and F = 2: F + = I : hν = E(m F) E(m F 1) F = I 1 2 : hν = E(m F 1) E(m F ) Value is taken from CODADA: Internationally recommended values of the Fundamental Physical Constants, Value is taken from D.A. Steck, Rubidium 87 D Line Data and Rubidium 85 D Line Data available online at Value is taken from Arimondo et al., Experimental determinations of the hyperfine structure in the alkali atoms, Rev. Mod. Phys. 49, 31 (1977) In the article by J. Recht and W. Klein, contact 1/1991, the g I -factor is defined as positive. For this reason, the signs in the equation are different. In the old (German) tutorial, the g I -factors were given in units of µ N µ B. That s why the Breit-Rabi formula looked slightly different and the g I -factors given there had different values.