Level crossing spectroscopy rudresh ghosh saurish chakrabarty

Introduction  Well known Doppler-free technique  Pre laser era: atomic spectroscopy  LASERs used for optical pumping which allows molecular spectroscopy

Topics of Discussion Basic principle and exptl setup Hanle effect Quantum mechanical description Advantages – disadvantages Modifications

Basic principle and exptl setup Schematic expterimental setup for level crossing spectroscopy

Basic principle and exptl setup Sample placed in uniform magnetic field Illuminated by polarized light Emits fluorescence Shape of signal I fl (B) gives g 

Important equations E(t)=E(0)exp[-(i  12 +  /2)(t-t o )]  L =g j  o B/ħ I(B, ,t)=I O exp[-  (t-t o )]cos 2 [  L (t-t O )-  ] I(B,  )=R -∞ ∫ t I O exp[-  (t-t o )]cos 2 [  L (t-t O )-  ]dt O = I O R[1/  +(  cos2  +2  L sin2  )/(  2 +4  L 2 )] /2 I(B)=(I 0 R/2  )[1-(1/(1+(2g  0 B/ ħ  ) 2 )]  B 1/2 =ħ  /g  o =ħ/  o g 

Hanle Effect In case of Zeeman subl-evels of a degenewrate J level, the M levels cross each other at B =0,when the field is tuned from +ve to –ve values. This is called Hanle effect or zero-field level crossing.

Quantum mechanical description Level scheme for optical pumping of Zeeman levels by light polarised in y-direction.Each of the two excited Zeeman levels can decay into three final state sub-levels.Superpsition of two different routes (J”,M) ->(J f,M) generates interference effects

Quantum mechanical description I2> x = - 1/2 1/2 [a M+1 IM+1>+a M-1 IM-1> I2> y = - i/2 1/2 [a M+1 IM+1>-a M-1 IM-1>]  2 (t)=e -  t-t 0 )  e -iH  t-t 0 )/ħ  2 (t 0 ) = e -  t-t 0 )  e -i(E 0 +  B gMB)(t-t 0 )/ħ [I  2 > x sin  B g  t-t 0 )  ħ + I  2 > y cos  B g  t-t 0 )  ħ ] I(E x,t)=cexp(-  t’)sin 2 (  B gBt’/ħ) I y (E x )=(c  B gBt/ħ) 2 /{1+  B gBt/ħ) 2 }]

Advantages Compared to other Doppler free techniques needs simple exptl arrangement Sign of dispersion shaped Hanle curve determines the sign of the Lande g factor.

Disadvantages There is change in absorption profile with change in magnetic field.Laser bandwidth must be sufficiently large so that all Zeeman components can absorb the laser radiation independent of the field strength B.Should not be so large so that simultaneous excitations of different closely spaced transitions occur. Large magnetic fields are required for Hanle signals from short lived molecular levels with small g.

Modifications To improve signal to noise ratio a method known as stimulated level crossing spectroscopy is used Use of electric fields instead of magnetic fields Studying molecules with simultaneous electric and magnetic level crossing spectroscopy give the value of g and  simultaneously.

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