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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

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Level crossing spectroscopy

Level crossing spectroscopy

rudresh ghosh

saurish chakrabarty


Introduction
Introduction

  • Well known Doppler-free technique

  • Pre laser era: atomic spectroscopy

  • LASERs used for optical pumping which allows molecular spectroscopy


Topics of discussion
Topics of Discussion

  • Basic principle and exptl setup

  • Hanle effect

  • Quantum mechanical description

  • Advantages – disadvantages

  • Modifications


Basic principle and exptl setup
Basic principle and exptl setup

Schematic expterimental setup for level crossing spectroscopy


Basic principle and exptl setup1
Basic principle and exptl setup

  • Sample placed in uniform magnetic field

  • Illuminated by polarized light

  • Emits fluorescence

  • Shape of signal Ifl(B) gives gt


Important equations
Important equations

  • E(t)=E(0)exp[-(iw12+g/2)(t-to)]

  • wL=gjmoB/ħ

  • I(B,a,t)=IOexp[-g(t-to)]cos2[wL(t-tO)-a]

  • I(B,a)=R-∞∫t IOexp[-g(t-to)]cos2[wL(t-tO)-a]dtO

    =IOR[1/g+(gcos2a+2wLsin2a)/(g2+4wL2)] /2

    I(B)=(I0R/2g)[1-(1/(1+(2gm0B/ħg)2)]

    DB1/2=ħg/gmo

    =ħ/mogt


Hanle effect
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
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) ->(Jf,M) generates interference effects


Quantum mechanical description1
Quantum mechanical description

  • I2>x=-1/21/2[aM+1IM+1>+aM-1IM-1>

  • I2>y=-i/21/2[aM+1IM+1>-aM-1IM-1>]

  • y2(t)=e-g(t-t0)/2 e-iH(t-t0)/ħ y2(t0)

    = e-g(t-t0)/2 e-i(E0+mBgMB)(t-t0)/ħ[Iy2>xsinmBgB(t-t0)/ħ + Iy2>ycosmBgB(t-t0)/ħ ]

  • I(Ex,t)=cexp(-gt’)sin2(mBgBt’/ħ)

  • Iy(Ex)=(ct/2)[(2mBgBt/ħ)2/{1+(2mBgBt/ħ)2}]


Advantages
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
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
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 t simultaneously.



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