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mtERWT ION OF RESONANT RADIATION FIELD WITH Two Lsva .TOMs

by

SUN

IL EIJIILR

Thesis submitted to

Indian Institute of Technology, D or the award of De ree of

DOCTOR OF PHILO PRY

Department of Physics

Indian Institute of Technology, Delhi

June, 1979

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ACKNOWLEDGMENTS

It is a great pleasure to express in deep gratitude to Professor C.L.Mehta for giving me an opportunity to

work with him. I am grateful for his valuable guidance and encouragement to increase and widen my fields of interest.

The excellent atmosphere of his group inspired me to learn more and more. In particular, the academic discussions with Dr. Dilip Ranganathan and Dr. G.P0Agreoal were very stimulating.

I am highly indebted to all my friends for their help, cooperation and affection extended to me to make my stay in pleasant and memorable. In particular, I wish to

thank Dr. G.Bose, Dr. J.P.Dudeja, Mr. Maithili Sharan, Dr. Sa ish Kumar, Mr. R. N. Baghel, Dr. L.R,Gupta, Mr. J.K.Sharma and

Dr. B.S.Daryall for their timely help and advice.

Finally, I thank the Director, Indian Institute of Technology, Delhi for providing the financial assistance.

,c'V'erNA"‘zr- ( STEIL OAR)

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CONTENTS

CHAPTER

INTRODUCTION

THE TIAMILTONIki DESCRIBING TEE SYSTEM

III. THE HEISENBERG EclUATIONS OF MOTION

THE DYNAMICS AND STATISTZS OF THE

SYSTEM

• When mode 1 is strong

PAGE

7 18 25

25

CO Determination of the mode population N1 (t )

(B) Dynamics and Statistics of the modes 27 2 and 3

(1) When initial states of both the 37 modes 2 and 3 are mixtures of

chaotic and coherent states

(ii) When both the modes 2 and 3 are 1+0 initially in coherent states

(iii) When both the modes 2 and 3 are 1+2 initially in pure chaotic states

(iv) When initially the mode 2 is in a 1+3 number state and the mode 3 fs in

a pure chaotic state (C) Statistics of the mode 1 When mode 2 is strong

(A) Determination of the mode-population N2 (t (B) Dynamics and statistics of the modes

1 and 3

(1) When initial states of both the 56 modes 1 and 3 are mixtures of

chaotic and coherent states

1+

5

1+6

1+7 1+9

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(ii) When initially the mode 1 is in a

number state and the mode 3 is in 59 a pure chaotic state

(iii) When the modes 1 and 3 are 61 Initially in number states

(C) Statistics of the mode 2 64

When mode 3 is strong 65

4, When any two modes are separately strong in 69 two complementary time-domains

TWO SPECIFIC EXkMPLES 72

Pumping of an atomic system initially in 72 ground state ( Nio - 0 ) by a coherent field

(A) When A > B$ AB)2

B >>1 73 ( mode 2 strong )

(B) When B > 44.) B-A )2 > B .?*1 7?

( mode 3 strong )

2, Coherent spontaneous emission 81 (A) When A-B ( mode 2 strong ) 82 (B) When AB ( mode 1 strong for 85

t<to

Vi. TAYLOR SERIES EXPOS= OF THE PHOTON NUMBER 89 OPERATOR N

3(t)

1, Atomic system in ground state and field in 90 coherent state

2. Atomic system in Dicke state and field in 90 ground state

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WI al 04,,

3. 4tomic system in Dicke state and field in 91 number state

4. Atomic system in Dicke state and field in 91 0.01.:..

,re,nt state

VII, COMPARISON WITH PREVIOUS RESULTS 92 1 • Computer results of Walls and Barakat 92 2. Results obtained in parametric approximation 93

3. Results of Persico and Vetri 94 Li-, Results of Bonifacio and Preparta. 97

5.

Results of Senitzky

99

VIII. TIME EVOLUTION OPETIATOR FOR N INTERIXTING QU.40ETUM 100 H1:RM0NIC OSCILLATORS

1'. laimination of linear terms in the Hamiltonian 103

2.

Close-form explicit expression for U 107

3

The case for N = 2 and concluding remarks 109

APPENDDC 113

REFEREITCES AND FOOTNOTES 118

References

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