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
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)
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
(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
WI al 04,,