Saturated Absorption SpectroscopyandFrequency Modulation Spectroscopyof Rubidium Atoms铷原子的饱和吸收光谱和频率调变光谱Dan LeeGrade 98, School of Physics, Department of Technical Physics摘要在这个实验中，我们测量了85Rb和87Rb原子的饱和吸收光谱和频率调变光谱．在饱和吸收光谱中，87Rb原子的|F=1〉→|F＇=0,1,2〉和|F=2〉→|F＇=1,2,3〉,85Rb原子的|F=2〉→ |F＇=1,2,3〉和|F=3〉→|F＇=2,3,4〉以及它们的交错信号都被完全的捕捉住.这里,F表示的是5S1/2基态的超精细能级，而F＇则表示的是5P3/2激发态的超精细能级. 87Rb 原子的｜F=2〉→|F＇=1,2,3〉的谱线则被用于调频技术．AbstractWe have measured Dtransitions of 85Rb and 87Rb atoms with saturated2absorption spectroscopy and frequency modulation spectroscopy. These saturated absorption spectra, |F=1〉→ |F’=0,1,2〉and |F=2〉→ |F’=1,2,3〉of 87Rb atoms, |F=2〉→ |F’=1,2,3〉and |F=3〉→ |F’=2,3,4〉of 85Rb atoms, and their crossover lines are completely resolved, where F indicates the hyperfine level of the 5S1/2 ground state and F’ indicates that of the 5P3/2 excited state. The derivatives of the |F=2〉→|F’=1,2,3〉 spectra of 87Rb atoms are obtained with the technique of frequency modulation.As we know, the Rubidium atom is one kind of boson. It obeys the Bose-Einstein statistics. In 1995, Rubidium atom was successfully used to realize the Bose-Einstein condensation.In the nature, there are two types of isotopes of Rubidium: 87Rb and 85Rb. If we consider the hyperfine structure of the isotopes of 87Rb and 85Rb, we can get the figures for their energy levels. The hyperfine structure is resulted from the spin of the nucleus, which is called Zeeman effect that can lead to the separation of the energy levels in magnetic field.Fig. 1 below shows us the hyperfine structure of the 87Rb.Fig. 1. The hyperfine structure of the energy levels of87RbFig. 2 below shows us the hyperfine structure of theRb.Fig. 2. The hyperfine structure of the energy levels of 85RbThe two figures are similar to each other. The small differencebetween them is that the separation of energy levels of 85Rb is less thanthose of 87Rb. Another difference between the two isotopes is that the spin of the nucleus of 87Rb is 3/2 and that of 85Rb is 5/2.I did such a following experiment to study the main energy level and the spectrum at first. The experimental setup is shown schematically in Fig. 3.Fig. 3. Experimental setup for the absorption spectrum of the RubidiumThe diode laser is driven by the current from the laser diode driver and is controlled by the temperature controller.We choose the diode laser as the laser resource here because it has too many advantages: the inexpensive price, the small line width that is less than 100 kHz , the high output power which can reach more than 10 mW, the large tunable range of wavelength which is more than 20 nm , the high stability and the high sensitivity. All above, the most important merit is that it can provide the laser whose frequency is just what we need in such experiments.In this experiment, we also use a function generator to output a triangular wave with appropriate frequency and amplitude. We input this wave into the laser diode driver and then make the laser current changein a proper range. The amplitude of the triangular wave decides the range. So the wavelength (or frequency) of the laser changes with the triangular wave. The Rubidium atom will absorb some photons from the laser when their frequency is proper. The spectrum is shown in Fig. 4, where the amplitude of the triangular wave is 200 mV and its frequency is 80 MHz.Fig. 4. The absorption spectrum of the RubidiumOne thing that we must emphasize is why we do not choose the square wave or serrated wave but triangular wave. The current from the laser diode driver that drive the laser cannot be changed too drastically. Otherwise the diode laser would be damaged. From the Fig. 4, we can see the four apparent spectra lines. From right to left, we mark them as a, b, c, d.In fact, each line of a, b, c, d contains fine spectra. The a-line contains the spectra lines from 87Rb |5S 1/2,F=2> to |5P 3/2,F’=1,2,3>. Theb-line contains the spectra lines from 85Rb |5S 1/2,F=3> to |5P 3/2,F’=2,3,4>. The c-line contains the spectra lines from 85Rb |5S 1/2,F=2> to |5P 3/2,F’=1,2,3>. The d -line contains the spectra lines from 87Rb |5S 1/2,F=1> to |5P 3/2,F’=0,1,2>.But because of the Doppler broadening effect, we cannot distinguish the fine spectra lines. The reason is interesting. We know that only theatoms can absorb a certain kind of photons whose energy (or frequency) exactly matches the separation of the energy level of the static atom. In fact, all the atoms move in all directions. Due to Doppler effect, the atom can be excited by those photons whose frequency is slightly away from the exact ones; meanwhile the separation among the energy levels of the hyperfine structure of Rubidium is tiny, too. All of above lead to the result that we are not able to distinguish the fine spectra.If we want to distinguish these fine spectra, we can use the method to get the saturated absorption spectrum. The experimental setup is also displayed as a brief outline in Fig. 5.Fig. 5. Experimental setup for the saturated absorption spectrumWhen the laser comes to the BK7, most of it will penetrate the BK7, which is called saturation beam, and only a small part of it will be reflected, which is called probe beam.The saturation beam and the probe beam nearly overlap each other in the opposite directions. As the chopper rotates, it will chop the saturation beam at a certain frequency. If it always covers the saturation beam, we will get the same spectra as the Fig. 4 shows. But that thesaturation beam works or not at a certain frequency will provide a reference signal (one kind of TTL signal) and the lock-in amplifier will deal with the TTL signal and the signal from the probe beam that has passed the Rubidium vapor cell.The detailed spectrum will be shown as following:Fig. 6. The spectrum of a-line in the saturated absorption spectrum experimentThe parameters of this experiment are listed below:Lock-in amplifier: Time Constant: 10 msSensitivity: 1 mVTriangular wave: Amplitude: 25 mVFrequency: 100 MHzFig. 6 shows us 6 spectrum lines obviously. From right to left,we mark them as a1, a2, a3, a4, a5 and a6. The a1-line, a3-line, a6-line representthe spectrum lines from 87Rb |5S1/2,F=2> to |5P3/2,F’=1>, from 87Rb |5S1/2,F=2>to |5P3/2,F’=2> and from 87Rb |5S1/2,F=2> to |5P3/2,F’=3>, respectively. Thethree other lines stand for crossover lines, which appear due to the Doppler effect. So there is a crossover line between each two lines of a1, a3 and a6.The parameters of this experiment are listed below:Lock-in amplifier: Time Constant: 10 msSensitivity: 1 mVTriangular wave: Amplitude: 20 mVFrequency: 80 MHzFig. 7 also shows us 6 spectrum lines obviously. We mark them as b1, b2, b3, b4, b5 and b6 in the same way. The b1-line, b3-line, b6-linerepresent the spectrum lines from 85Rb |5S1/2,F=3> to |5P3/2,F’=2>, from 85Rb|5S1/2,F=3> to |5P3/2,F’=3> and from 85Rb |5S1/2,F=3> to |5P3/2,F’=4>,respectively. The three other lines stand for crossover lines.Fig.8. The spectrum of d-line in the saturated absorption spectrum experimentThe parameters of this experiment are listed below:Lock-in amplifier: Time Constant: 10 msSensitivity: 1 mVTriangular wave: Amplitude: 20 mVFrequency: 50 MHzFig.8 shows us 5 spectrum lines but not obviously. D1, d2, d3, d4 and d5 are marked in the same way. The d1-line, d2-line, d5-line representthe spectrum lines from 87Rb |5S1/2,F=1> to |5P3/2,F’=0>, from 87Rb |5S1/2,F=1>to |5P3/2,F’=1> and from 87Rb |5S1/2,F=0> to |5P3/2,F’=2>, respectively. Thetwo other lines stand for crossover lines. In my opinion, another crossover line exists but we are just not able to measure it.It is the most difficult to get the saturated absorption spectrum for c-line. Fig.9 shows the experimental result and its appearance is far below that for a-line or b-line.The parameters of this experiment are listed below:Lock-in amplifier: Time Constant: 10 msSensitivity: 1 mVTriangular wave: Amplitude: 20 mVFrequency: 20 MHzSuch a figure is frustrating. I have tried to find the reason leading to such a bad result. There is no problem with the experimental setup because we can get good spectrum lines for a-line etc. Maybe the reason is that the instruments are not stable as the time goes on. But we can get as the same wonderful figure for a-line as before. Strictly speaking, I do not get success in the saturated absorption spectrum experiment for c-line. But I have to do the further experiment and I am told that only spectrum lines we need to apply to the further experiment are those for a-lines. So I give up making it clear before the fifth week.To make the figure more clearly, we design the experiment below. The experimental setup is given briefly in Fig.10. The left function generator produces sin-wave with high frequency and small amplitude as a referencesignal. The right function generator outputs a triangular wave with relatively low frequency and high amplitude. The former and the later are input into the adder at the scale of 1/10:1. How do they modulate the laser diode driver? We know that the frequency of the laser will oscillate as the current from the driver oscillates and the current is controlled by the input-signal. t f f f t I I I m L L m ωωcos cos 00+=⇒+= Because m f is far less than L f 0, the signal S (m f )that the photo detector receives can be in the form of Tailor expansion as the following:......!2)())((cos ))(()()cos ()(222_+++−−−−−→−+=t Cos f f S df d t f f S df df S t f f S f S m oL L m oL LoL ExpansionTaylor m oL L ωωω Generally speaking, Hz f oL 14108.3⨯≈Hz f m 610≈Hz 4102⨯≈πω1<<oL m f fFig.10. Experimental setup of the differential saturated absorption spectrum of RubidiumSo we can ignore the third item and later ones. The)(oL Lf S df din the second item is just the differential signal that we need. After the lock-in amplifier deal with the S(f L ) signal and the reference signal, we can get the differential signal.Fig. 10 does not show us where the neutral-density filters are. In my opinion, their quantities and their locations are not important because they are just used to adjust the power of the saturation beam and the probe beam in order to get an ideal result revealed in Fig. 11.To summarize, we have demonstrated three kinds of experiments to get the spectrum of Rubidium. All above these help us study the energy level and the structure of the Rubidium better. A5, the most distinguished spectrum line in all, is what we just need to use to lock in the frequency in the experiment of low-temperature-atom spectrum, which is another interesting experiment.AcknowledgementsIn the past four weeks, I spent an ordered and instructive time on such a special subject. It is the first time for me to come to the department of physics, NTHU. Such an experience will be remembered forever.I am grateful to Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment (CURE), the Peking University, Beijing and the National Tsing Hua University, Hsinchu, which provide me such an opportunity to have a so precious experience.I am grateful to my instructor, Prof. Yu, an erudite and vigorous man. He is always not only enthusiastic to me but also strict with me. Under his wise guidance, I have such a chance to shoot a glance at the research field of the laser cooling.I also appreciate my elder school-sister Hsin-Ying Chiu and my elder school-brothers: Ying-Cheng Chen, Yean-An Liao, Hsih-Kuang Tung, Yun-Fan Chen, Guan-Qi Pan, Hong-Wen Zhuo, Jun-Jie Liao. They are warm-hearted to help me. They give me many good suggestions on study. I hope they would not mind that my bothering them during the last month.De-Hong Chen is another lab-mate that I must thank to. He provides me with much facility. It is he who makes my life here more convenient.I always hold the view that I can finish my report without a hitch due to the help of all others.Thanks all.References[1] Li-fu Mao, “Development and Study of Dark Magneto-Optical Trap”, the master’s thesis of Tsing Hua University, Hsinchu, Taiwan ,1998.[2] 施宙聪，陈皙墩，《稳频半导体雷射》，科技新知14卷5期, 第30页.[3] M. J. Snadden, R. B. M. Clarke, and E. Riis, “Injection-locking technique for heterodyne optical phase locking of a diode laser”, Opt. Lett. 22, 892 (1997).The Introduction to My Advisor:Ite Albert. Yu(余饴德)Name: Ite Albert, YuResearch Interests: Optics, Atomic & Molecular Physics, Laser (Exp.) E-mail addressAddress: 101 Section 2 Kuang Fu Road, Hsinchu, TaiwanDepartment of Physics, National Tsing Hua University, Hsinchu, Taiwan Telephone: (03)5742539 Fax: (03)5723052Education:1987-1993 Ph.D..1980-1984 B.S. in Physics, National Tsing Hua University,Hsinchu, Taiwan.Employment:1995-present, Associate Professor of Physics, Tsing Hua University, Hsinchu, Taiwan1993-1995, Postdoctral Researcher of Harvard-Smithsonian Center for Astrophysics,Research Interests:Experimental Atomic and Molecular PhysicsLaser Trapping and CoolingBose-Einstein CondensationNonlinear SpectroscopyQuantum OpticsSelected Publications:Selected Papers:Y. C. Chen, C. W. Lin, and I. A. Yu, "Role of degenerate Zeeman levels in electromagnetically induced transparency", Phys. Rev. A 61, 053805 (2000).Y. C. Chen, Y. W. Chen, J. J. Su, C. Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold 87Rb atoms for various laser-polarization configurations", Phys. Rev. A 63, 043808 (2001).Other Publications:雷射冷却与低温原子的非线形光谱物理双月刊廿二卷五期 2000年10月 443页443-451 (2000).。
