Report of Doppler-Free Saturation

8/16/2019 Report of Doppler-Free Saturation

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Doppler-Free Saturation

Spectroscopy

Group: 66

Karakoc, Deniz (03657305)

Wang, Bo (03662383)

Luchko, Ivan (03663869)


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1. Introduction

We learn the theory and experiment of Doppler-free saturated

absorption spectroscopy, using it to observe and measure the

hyperfine structure of 7 and .

2. Hyperfine Structure of Rubidium

The level scheme for the 5/ → 5/ transition in 7 and could be shown in Figure 6 form manual like below.


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Hyperfine Coupling constant

We can calculate the hyperfine structure shift by using the

equation 24 in manual.

∆ v = A 2 + [3( + 1) 4(+1)(+1)8(21)(21) ] Where C = F(F + 1) J(J + 1) I (I + 1). A and B are thehyperfine coupling constant that descript the magnetic dipole

and electric quadrupole interaction between electron and

Nucleus.

Hyperfine Shift

By using the equation above, we could calculate the energy

shift of 5/ in 7 and . For convenience, we write thisenergy shift as a function of A and B.∆ v = a ∗ A + b ∗ B The result is listed below.

7 5/

F C a b F C a b3 4.5 2.25 0.25 4 7.5 3.75 0.25

2 -1.5 -0.75 -0.75 3 -0.5 -0.25 -0.55

1 -5.5 -2.75 0.25 2 -6.5 -3.25 -0.1

Cross-Over Line

Three additional cross-over lines will also be observed in

experiment. The frequency of these cross-over line is in the

middle of the lines above. For convenience, we add them into

the table.

7

5/

F a b F a b

3 2.25 0.25 4 3.75 0.252,3 0.75 -0.25 3,4 1.75 -0.151,3 -0.25 0.25 2,4 0.25 0.075

2 -0.75 -0.75 3 -0.25 -0.551,2 -1.75 -0.25 2,3 -1.75 -0.3251 -2.75 0.25 2 -3.25 -0.1


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3. Analysis of Data

The shot form Oscilloscope is listed below. The left part

come form 7 and the right part come form .

a. Energy Calibration

The first thing is to determine the relation

between Energy and time in Oscilloscope.


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We use the signal form the Fabry-Perot

interferometer, the green one, to calibrate.

The frequency difference between two

adjacent peaks is the free spectral range,500 MHz.

After finding the Peaks, we fit it linearly like

below.


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Then we could plot the D2 line based on

Frequency.

b. Cross-over Line

As the rubidium atoms are under roomtemperature, they follow the Maxwell –

Boltzmann distribution. The cross-over line

comes from the atoms with speed of−


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on z direction. Base on Maxwell –Boltzmann

distribution, like below, their population are

much high than the ones with 0 speed on z

direction. Therefore their amplitude is larger.

For short, we will note the transition line

7 : 5/, = 2 → 5 /, = 3 as (3), andthe cross over line between 7 : 5/, =

2 →5/, = 2 and

7 : 5/, = 2 →5/, = 3 as (2,3).c. Rb87

The shot of Rb87 D2 line is listed below.


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From left to right, these peaks are (1), (1,2),

(2), (1,3), (2,3), (3). After fit the peaks with

Lorentz, we got relative frequency of these

peaks.


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Then by using the table we got before, we

could fit these six peaks with a 2D plane to

find out the Hyperfine Coupling constant A

and B of 7 5/.


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Compare the official values from “Rubidium 87 DLine Data, Daniel A. Steck” the error is smaller than5%.


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d. Rb85

The analysis is similar. From left to right,

these peaks are (2), (2, 3), (3), (2, 4), (3, 4),

(4). After fit the peaks with Lorentz, we got

relative frequency of these peaks. Here the

peak (2) are too small to fit, so we dropped

it.


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Then by using the table we got before, we could fit

these six peaks with a 2D plane to find out the

Hyperfine Coupling constant A and B of 5/.


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Compare the official values from “Rubidium 85 DLine Data, Daniel A. Steck” the error is smaller than5% too.

Documents

Report of Doppler-Free Saturation