Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qilab.phys.msu.ru/papers/OpticsSpectroscopy-1999-87(3)-ru.pdf Äàòà èçìåíåíèÿ: Mon Feb 4 18:39:30 2008 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 20:04:46 2012 Êîäèðîâêà: koi8-r

CE -
. . , . . , . . . , , 119899 1999




, - . , , -, , , . , , .



(. [1, 2]) , , (). - , (. . 1). L , L R -- ()
12 R

--

= L - L -

12

= 0,

, ("" ), . , , . , . [3, 4], . |1 |2 - -

, -

. , , , , 12 . , , 12 , ,
12

= 0.

[5] |1 |2 , . 1

,


, , . , [6]. , , . , . - . + kv, k -- v -- .
R



,

R + (kL - kL )v -

, . [7] , . , . , . . , , , () . , [8]. 2


, . , , , .

1. -
, , ^ H = - 12 |2 2| + 13 |3 3| + g cos(L t+) |1 3| + g cos(L t+ ) |2 3| +. ., (1) |1 , |1 1| . g g , . . , AL , AL d13 , d23 : 1 1 g = d13 AL , g = d23 AL . , L L
13

23 , . , -

, U0 (t) = exp [-(i/ )( L |3 3| - |2 2|)t] , = ^ H = U ^ H = - |3 3| + R |2 2| + L - L
12

-- , [9] -1 0

(1)

^ (t) H U0 (t), , (2)

g g |1 3| + |2 3| +. . 2 2

= L - 13 , R = L - L - 12 |1 |3 .


- ^ = (i/ ) H , ,

L L
RWA

. - = , =

R = 0 {ek } = {|3 3|, ^ |1 1|, |2 2|, (|1 2| + |2 1|)/ 2, -i(|1 2| - |2 1|)/ 2, (|1 3| + |3 1|)/ 2, -i(|1 3| - |3 1|)/ 2 (|2 3| + |3 2|)/ 2, -i(|2 3| - |3 2|)/ 2}
3


L

RWA

-- |3 |1 |2 ; , |1 |2 .
12

0 0 0 = 0 0 -g /2 0 -g / 2



-2

-
12


12

0 0 0 - 0 0 g /2 0 g /2
12

0 0 0 0 - 0 g /2 0
12

0 0 0 0 g /2 - - 0 0

g/ 2 -g / 2 0 -g /2 0 - 0 0

0 0 0 0 -g /2 0 0 - -

w 0 0 0 g/ 2 0 0

-w 0 0 0 0 0 g/ 2

- g /2

g/ 2 0 -g / 2 -g /2 0 0 0 -

(3)

-- |1 |3 |2 |3 , 12 , 12 , w -- ,

, , .

2.
[10, 11]. , . . t t + , [12]: K( ) = 0 S (0, t) - (t)[S (t, t + ) + (t + )] , ^ ^ ^
t

(4)

± (t) -- / ^ -- , (0, t) (t, t + ), , 0 S (0, t) (t) t. ^ ^ - (4) (. . 2a).
2.1.

|k |3 , k = 1, 2. S (t1 , t2 ) = T exp

2

t

1

L( )d , T

4


0| (3) - L
RWA RWA

. -

(4) :
8

L

, -

K ( ) =

13 23 Ck e(k - iL ) + Ck e(k - iL ) .

(5)

k=0

l Ck3 , l = 1, 2 -- , :

C

13 k

= 0|13 · |k ^-

k | ^

+ 13

,

C

23 k

= 0|23 · |k ^-

k | ^

+ 23

,

(6)

, , -; k , |k k | -- L
RWA

" · " 3â3-

.

:

8

F ( ) = 2 e

k=0

13 23 Ck Ck + i ( - L ) + k i ( - L ) +

.
k

(7)

, , (15), ,
l3 k

l = 1, 2. , [13].
2.2.

, p , . 1/ , ^ 0 st , ^ st | L ^
RW A

= 0. -

-

. , ""
5


,
11

= n,

22

exp(- 12 /kB Teff )]-1 , Teff . , . Tp (0, Tp ):
T
p

= 1 - n n = exp(- 12 /kB Teff )[1 +

2

F ( ) = N
0 +

+ (t)e ^

i t

dt

,

(8)

(t) - ^ . , T
p

, N -- , · -- 1/ :
8

Fns ( ) = 2 e C
l3 jk

k=0 j =0

13 23 Cj k Cj k 1 + j i ( - L ) + k i ( - L ) +

,
k

(9)

l3 jk

(6): C

, . .
12

= 0 |j j |l- · |k k | ^ ^3 ^

+ l3

, l = 1, 2.

= 0, , -

. T ,

F

av r

( ) = T Fns ( ),

(10)

T = 1/T .

6


3.
- -- [8, 14]:


P ( ) = g A ( ),

2 pr

A ( ) =
-

C ( )e

i

d .

(11)

gpr -- , , C ( ) = [ + (t), - (t + )] = + (t) - (t + ) - - (t + ) + (t) . (2.1) :
8 13 23 Dk Dk + i ( - L ) + k i ( - L ) +

A ( ) = 2g

2 pr

e
k=0

,
k

(12)

l Dk3 , l = 1, 2 : l Dk3 = 0|l- · |k ^3

k | ^

+ l3

- 0|l+ · |k ^3

k | ^

- l3

.

(13)

4.
(3). , g


=

g2 + g

2

, ,

. L
RWA

, -

g , g , ; L . RWA |g =g =0

. [8, 12]

( + )/g . :
12 12

, (3): 3 3 0 = 0, 1 = - , 2 = -, 3 = ig - - , 4 = -ig - -, 2 4 2 4 2 g + g - -g + -g - 5 = i - , 6 = i - , 7 = i - , 8 = i -. 2 2 2 2 2 2 2 2 (14)
7

0, w 0


4.1.

(6) : C
13 0

=C

23 0

=C C C
13 3 23 3

12 12 23 cos4 sin2 , C2 = cos2 sin4 , 12 i(2 - 11 ) 13 13 = cos4 sin2 1 + , C 4 = (C 3 ) , 2 64g i(2 - 11 ) 12 23 23 cos2 sin4 1 + , C 4 = (C 3 ) , = 2 64g
13 1

=C

23 1

= 0,

C

13 2

=

C

13 6 13 8

C

13 23 13 23 C 5 = C 5 = C 7 = C 7 = 0, 12 i(2 - ) - 12 i(2 23 cos4 sin2 1 - , C6 = cos2 sin4 1 - = g 12 i(2 - ) - 12 i(2 23 = cos4 sin2 1 + , C8 = cos2 sin4 1 + g

- ) - g - ) - g (15)

, ,

cos = g /g , sin = g /g . (7), (15), 12 . , 12 / (10 , .
-2

 10-5 ).

( = 0). , -, -- ±g /2 -- . -, , (7) Ck . , , , ( . 3). , () C
k

mk , /g . , - , . ( ), g


. . (15), , , . ±g ,
8

|k|

kB T /m


, , , ±g /2. , , (, , g , ( . 4). |2 |3 , ±g /2, . . - [15]. , , , , , . , , , , -- , ±g /2. . (7), g ), |1 |3

, C k , , , . , eCk > 0 , -

, , , . (15) , /g , . , , 1/ , , , , . . 1/ 2 . , = , . . 1/ 2 , 1/ 2 . (15), : F ( ) = 2e 12 sin2 cos2 1 +O 2 1
4

, -

: F ( ) 1/ 4 .

(16)

e = - -- .

, , 9


[14, 16], [17] , , . F ( ) = g 2 e 1 +O 2 + 2 g 1
4

(17)

e = - /2.
4.2.

(9), (10), C :
i3 k

=

T j =0

i Cj3 /j , (15), k

C

13 3 23 3

C

23 13 23 13 C 0 = C 0 = C 1 = C 1 = 0, T 13 C2 = cos2 (n cos2 + (1 - n) sin2 ), T 23 sin2 (n cos2 + (1 - n) sin2 ), C2 = T i(2 - 11 ) = cos2 (n cos2 + (1 - n) sin2 ) 1 + , 2 64g T i(2 - 11 ) = sin2 (n cos2 + (1 - n) sin2 ) 1 + , 2 64g

C C

13 4

13 = C 3 , 23 = C 3 ,

23 4

C C T T 23 C6 = T 13 C8 = T 23 C8 =
13 6

13 5

=C

23 5

=C

13 7

=C

23 7

= 0, - - - - , , ,

(18)

=

cos2 (n cos2 + (1 - n) sin2 ) 1 -

i(2 - ) g i(2 - ) sin2 (n cos2 + (1 - n) sin2 ) 1 - g i(2 - ) cos2 (n cos2 + (1 - n) sin2 ) 1 + g i(2 - ) sin2 (n cos2 + (1 - n) sin2 ) 1 + g

(15), (18), . , , n, 0 . ^ , . ,
10


0, w 0 :
12

(6) , (15) , (18). , .
4.3.

T , (1 - n)T , w nT , -

(13) , , : D D
13 5

13 7

12 i + sin 1 + 2 g 12 i + = sin 1 - 2 g =

, ,

D D

23 5 23 7

i + 1 cos2 1 + 2 g 1 i + = cos2 1 - 2 g =

, (19) .

, . , , |1 |3 , (13), (19) , . , |2 |3 , -- . |1 , |2 |3 . . |1 |3 , ±g /2 A
13

2 sin2 = g 2 /g , g = 0 -

, /2. ,

. : , . = - L ,

= 0 ( . 2b),
11


. = 0, .


, , g 5 , -. , - , . , , -. , , . "" F ( ) 1/ 2 -

F ( ) 1/ 4 , , .

12 , , . . .. . p Volkswagen Stiftung No. 1/72944.

12



[1] . . , . . , . . , . . , 163(9), 1 (1993). [2] E. Arimondo, Progress in Optics (North Holland, Amsterdam, 1996), Vol. 35, p. 257. [3] J. H. Xu, Ph. D. thesis, Scuola Normale Superiore, Pisa, Italy (1994). [4] S. Brandt, A. Nagel, R. Wynands, D. Meschede, Phys. Rev. A 56, R1063 (1997). ¨ [5] O. Schmidt, Ph. D. thesis, Universitat Hannover, Hannover, Germany (1995); O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, Phys. Rev. A 53, R27 (1996). [6] H. R. Gray, R. M. Whitley, C. R. Stroud Jr., Opt. Lett. 3, 218 (1978) [7] P. L. Kelley, P. J. Harshman, O. Blum and T. K. Gustafson, J. Opt. Soc. Am. B 11, 2298(1994) [8] A. S. Manka, H. M. Doss, L. M. Narducci, R. Pu, and J. L. Oppo, Phys. Rev. A 43, 3749 (1991). [9] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge Univ. Press, 1995. [10] . , : , - : , 1966. [11] . . , , - . -: , 1981. [12] . . , . . , , 113, 144 (1998) [13] Y. Stalgies, I. Siemers, B. Appasamy, T. Altevogt and P. E. Toschek, Europhys. Lett., 35(4), p. 259 (1996) [14] B. R. Mollow, Phys. Rev. A 5, 2217 (1972). [15] S. H. Autler and C. H. Towns, Phys. Rev. 100, 703 (1969) [16] B. R. Mollow, Phys. Rev. 188, 1969 (1969). [17] Martin B. Plenio, J. Mod. Opt. 43, 2171(1996)
13




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12

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12

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12

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Þ ú ÷

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