Chapter 8Doppler-free laser spe

ctroscopy

Contents

8.1 Doppler broadening of spectral lines 8.2 The crossed-beam method 8.3 Saturated absorption spectroscopy8.4 Two-photon spectroscopy 8.5 Cablibration in laser spectroscopy

8.1 Doppler broadening of spectral lines

The Doppler effect on the observed frequency of radiation. Radiation that has an angular frequency of ω in the laboratory frame of reference has the frequencies indicated in a reference frame moving with a speedν e.g.the rest frame of an atom. Only the component of the velocity along the wavevector k contributes to the first-order Doppler shift.

8.2 The crossed-beam method

Oven

Laser

Slit

Atomic

beam

Laser beam

Detector

α

Atoms

Laser beam

Slit

Over

is the Doppler width of a gas at the same temperature as the beam.

Df

beamD

vf f

8.3 Saturated absorption spectroscopy

dvkv

vfNAc

g

g

dvkvgvNAc

g

g

dvkvvN

H

4/)(

)2/()(

)()(

)()()(

220

212

22

2

1

212

22

2

1

Integration of the contributions from all the velocity classes gives the absorption coefficient as

8.3.1 Principle of saturated absorption spectroscopy

dvkvvNvN abs )()()(( 21

For all intensities, the integral of the number densities in each velocity class equals the total number density in that level, i.e.

11 )( NdvvN

and similarly for． The total number density

2N

21 NNN

2/1)1(sat

hole I

I

The hole burnt into the lower-level population by a beam of intensity I has a width

ω )(1 vN

)(2 vN

ω

)(2 vN

)(1 vN

hole

D

A saturated absorption spectroscopy experiment

Laser

BS

Pump

beamProbe

beam

M1

sample Detector

A plot of the probe intensity transmitted through the sample as a function of the laser frequency. With the pump beam blocked the experiment gives a simple Doppler-broadened absorption, but in the presence of the pump beam a narrow peak appears at the atomic resonance frequency.

ω

ω

ω0

Sig

nal

wit

ho

ut

Pu

mp

bea

m

Sig

nal

wit

h

pu

mp

bea

m

)(2 vN The population densities of the two levels and as a function of velocity for three different laser frequencies: below, equal to, and above the atomic resonance, showing the effect of the pump and probe beams.

)(1 vN

)(1 vN

)(2 vN

)(1 vN

)(2 vN

)(1 vN

)(2 vN

8.3.2 Cross-over resonances in saturation spectroscopy

E3

E2

E1

ħω12ħω12 ħω13

)(2 vN

)(1 vN

3( )N

)(2 vN

)(1 vN

3( )N

)(2 vN

)(1 vN

3( )N

)(2 vN

)(1 vN

3( )N

ω12 ω13

Inte

nsi

ty

of

pro

be

bea

m a

t d

etec

tor

ω

Cross-over

8.4 Two-photon spectroscopy

LaserLaser

Beam splittter

sends light

to calibration

Filter

Detector

Sample Lens

Mirror

If the atom absorbs one photon from each of the counter-propagating beams then the Doppler shifts cancel in the rest frame of the atom

)1()1(c

v

c

v

1

2

2i

i1

i

Laboratoey

frame

ω ω

(1 )c

(1 )c

Atom frame

When twice the laser frequency equals the atomic resonance frequency all the atoms can absorb two photons; whereas in saturation spectroscopy the Doppler-free signal comes only from those atoms with zero velocity.

122

F'=1

F=0

F'=0

F=1

Inte

nsi

ty o

f L

yman

-a r

ad

iaio

n

Relative frequency of ultraviolet radiation(MHZ)

0 200 800

21 21s S

Lyman-a

21 22s S

collisions2p

• Transit time

• Collision broadening

• Laser bandwith

• Secood-order Doppler effect

• Light shift

.1.0~ 02

2

2MHzf

c

ufD

8.5 Cablibration in laser spectroscopy

Laser spectroscopy experiments use tunable lasers , i.e. laser systems whose frequency can be tuned over a wide range to find the atomic, or molecular, resonances.For example,dye lasers(early experiments ), solid lasers (nowdays ),semiconductor diode lasers and so on .But the method of calibrating the laser frequency depends on whether the experiment requires absolute or relative measurements.

8.5.1 Calibration of the relative frequency

Detector

Etalon

2I Molecules

Laser Beam splitter Na vapour 1

2

3

1.Spectrum to be calibrated

2.Molecular

3.Etalon transmission

8.5.2 Absolute calibration

19106

(a) A two-photon spectrum of the 1s-2s transition in atomic hydrogen as in Fig.8.11 but on a different scale.

(b) (b) The saturated absorption spectrum of molecular tellurium used for calibration. The absolute frequency of the line labeled i was determined with an uncertainty of (by auxiliary measurements). Adapted from Mclntyre et al.(1989). Copyright 1989 by the American physical Society.

A frequency chain

6fHelium-neon laser

=260THZ (1.15μm )

5fcolour centre laser

=260THZ (2.3μm )

Molecalar iodine

=520THZ (0.576μm )

=48020

7f

0f

22

2

5

4fCarbon dioxide laser

=26THZ 11.5μm )

7

7

7

7

Methanol laser

=3.72THZ3f

Methanol laser =525GHZ2f

Microwave source

=75.1GHZ1f

Microwave source

=10.7GHZ0f

Co

un

ter C

s frequ

ency

stand

ard

8.5.3 Optical frequency combs

Recently, a new method of measuring optical frequencies has been invented that has revolutionized optical metrology. The new method relies on the ability to generate frequency combs using laser techniques, i.e. laser radiation that contains a set of regularly-spaced frequencies.

The experimental arrangement for the measurement of an optical frequency using a frequency comb from a femtosecond laser.

The signal from this detector contains the frequencies

0 02( ' ) ( ) (2 ' )rep rep repf n f f nf f n n f f

The light from the calibrated frequency comb is mixed with some of the output of the continuous-wave laser whose frequency is to be measured , whilst the remaining light from this second laser is used for experiments , e . g .

Lf

0''beat rep Lf n f f f

Further reading • This chapter has focused on just a few examples of Doppler-free

lase : spectroscopy and calibration to illustrate the important principles . Such measurements of the transition frequencies in atomic hydrogen give a precise value for the Rdberg constant and the QED shift . Nowadays , laser spectroscopy is very widely used more complex situations , e . g . liquids and solids .

• The monogragh by Series ( 1988 ) on the spectrum of atomic hydrogen gives a comprehensive description that includes Lamb and Retherford’s historic experiment and later refinements of the radio-frequency techniques , as well as laser spectroscopy . The measurement of the absolute frequency of light using optical frequency combs is a relatively new technique but already it has had an important impact on optical frequency metrology ( Udem et al. 2002 ) .