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2
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(
number of papers
600
500
400
300
200
100
1984
1986
1988
1990
1992
1994
1996
1998
2000
year
: &&
! 0
0 0 '
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¾<
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K
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},
a)
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9p
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}
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>
Recoiling
atoms
Matter wave
grating
b)
@
Probe
beam
“Dressing”
beam
>
PMT
D 6 '0 20
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* ' * F = Æ
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,
=
0
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=
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2 0 0
, =
2 0 * 2 00
0 3 ,- '
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' C
D * ' 0 '
* 0 ' B
0 ' 0
00
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* 20 = ' 0 0 C 0 D ,' ' 2 * ' 0
>)(? E * 7 0
, =
0
* F 2 0 F -
0 * 0
0 ' 0 &G
* 0 00 0
20 : I ,' ' ' 0 :
' 00
0 20 20' 0 # Q ' (
(
>F)&? * 0 " /84 * ' 00 ' E R
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&
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0
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0
2 &&
0 20 SRS
PC
Fiber
S
AOM
AOM
PD
Probe Beam
l/2
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PI
AOM
PD
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q
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BEC
Slit
Telescope
PMT
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9% 0
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0
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00
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0
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0 A 3
A 33
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T ' * &
2 & 2 ' 0 3 00
0 * ) &
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E ' 0 * 0 =' '
&)
frequency in KHz
a)
12 KHz
6 KHz
2.0
12
10
8
6
b)
4
-10
-5
0
5
10
1.5
amplitude
0 KHz
1.0
-6 KHz
0.5
-12 KHz
c)
0.0
0.0
0.1
0.2
0.3
0.4
-10
0.5
: )(
-5
0
5
10
detuning in KHz
time in ms
D 0 7 D = * F ' =
C)&D
* =' D !
0
0 * 6
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P P
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Æ
M C)&D
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0
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: 0 +L 1L
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00
0
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F >)1?
, &(
a)
Relative number of atoms
1.0
0.8
0.6
0.4
0.2
0.0
0
100
200
400
500
time / ms
b)
t=30 ms
: )+
300
600
t=400 ms
9 D * B
0 * F C&
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)/
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b)
a)
0
: )/
1
time [ms]
0
1
time [ms]
D 0 >F ))
D? D ,' 2
P P a)
b)
0
50
100
150
200
250
300
0
50
100
: )1
*
0 150
200
250
300
time [ms]
time [ms]
D 3 >F)/
D?
)0 ' ; &)G ; &)G I ' 0
* 20
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VC D
VCD C/ L)/ D M 7
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&
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&GG 0 ,' 7 0 )
0 0 7 ' I
0 0 C!%*D 0 A >F )1?
,
'
' 0 )1
&/
% 4
(a)
(b)
gain
3
2
1
0
0.0
0.5
0.0
0.5
time [ms]
dressing beam
probe beam
: )5
9
0 ' D 9 0
0 * 0 0 /5 #O &/ #O G& #O 0
/ #O * 0 ' ; G 5 00 0
0 ' 2 ' D
.
0 0 '0
20
0
D
!
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00
7
P P ,' 0 ' * 0 U ,' ' 0 0 0 ' ' ' 0 * 0 ' ' 0
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P
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G
;
G
U
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U
G
;
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G
G
G
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0
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%
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P
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C D
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X =
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P
U
C
D
C)1D
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K =
* 0 00
&
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=
C)1D
&&
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0
2
4
6
0
2
4
6
8
0
10
2
4
8
6
10
12
time in
14
2p/G
: )8 0 =
0 0 =
C)8D
* 0 0
0 ' ' 0 0 ' 0
0 0 =
&
(
&M
'
&
U
C&
0 C)/D
'
D
&
; &M
(C& D
C)5D
2
7 0 0 ' 20
<
< >F)8? * 0 0
' $ 0 ' 0 ' ' 0 0
2 ' 20
0
0 =
0 Æ
C C DM
D
SCDSC D ; SCDSC D M U
.0
=
C)5D
&
U =
(
C
&D
G
% C)8D
6 0 0F 0 0 ' * '
)
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0 ) ;
* +, * +, * +, * +, ;
(
&
(M&U
C)4D
* ' ' ' =
0 0
= * << ' B
0 E ' 0 B
0 * ' >F)4? )G
* )G
2 0 '
&8
delay [ µs]
(a)
-0.2 0.0 0.2 0.4
time [ms]
(b)
20
0
1
2
3
gain
: )4 ! ' 0F
D B
0
*0
!%* 0 0
'
&+G , ,' 0
0 G&& #O
,
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F
=
C)&/D
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7 ! ' 0 2 * 0 ' C)/D
# #
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20
D '
C D
& U
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=
- ; & +. 0' . ' + / C U D ' 0 &4
1.001
1
c) 1
0.999
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5/
0
Im[n(M)]
b)
1/vG [s/m]
Re[n(M)]
a)
0
-5/
-0.0015
5/
5/
-5/
: )&G
2 0 =
C)&GD
D * 0
; / + &G
C
002
D 0
3 # 20
0
U;/ ,
' 0
D *
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C
=
002
D D
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!
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0
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7 0 * 2 0 00
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<
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; C
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0
C)&&D
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/
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,
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)&
a)
c)
1.001
-5/
0.002
5/
-10/
0.999
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10/
-10/
5/
0
0
b)
-F
d)
-0.002
: )&&
2 0
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3 P ;
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10/
0
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!
=
0
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0
D
M
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0 =
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T '
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"
;
U
T
G
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G
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C)&4D
* ' 7
=
2
0 : '0
0
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!
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$ !
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* 002
))
b)
a)
6
4
2
0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
time / ms
time / ms
: )&)
: 0
D *
2
' 0 / #O : 0 ' )5 (8 1& 4& &+& )&( ()5 +4/ 51 #O D
E
0
,=
C)))D ! P 20
0
D
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>)(?
>F)&)? , ' ' 0 0
* 0
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,=
U
!X ; U! P"
X ;
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! C ; GD ; G
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, C))&D 6
C))GD
0 0 * 0 '0
0
* F
0 0 0 * 00
" " & & &O) D
00
C,
)(
X ;
P
;
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* =
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1
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7 F 0
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!X
"X
X
P
P
;
;
;
U! P"
!
P
CP
C)))D
P (!D
(
0 =' 0 ;
1
L
)
*
F '
(
1 2 2
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=
0 PC D C D "CD 0 F PC D
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X ; G
P
P;P
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X
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;
;
U! CP (!D"
CP
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* 00
=
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F 0
X ; X C
D X ; X C
D *
*
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0 ' ' 0
*
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K * ' ' F ' 0 * =
0
* = 2 : 0 ' " ; &
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* ' ' P ' P ; P
(!
)+
C))+D
! CGD ; G
F
25
W/W0
20
15
10
5
0
10
time/G-1
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=
C))/D * 0 =
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2 00
/ B 0 G (U G 8U G 4U G 44U & G/U
& 5U U ;
& U &&U ( ' 20
0
P;
U
( U(
P
C))/D
( >F)&(? ( $ U 0F
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20
'
U * 20
0 =
0
,
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( 3 " ; & * ' 00
P ' '
U
( U(
;
U
U
(
;&M)
(
U
(
M(
U
M
C))1D
(
* 20
7 I * F * 7 ' 0
U
(
(
3 00
2 ' 0 1 U 1 ' U ' ' 0 0 1 L 0 , ' )/
0 0 U U :
' 0 ' ' * =
2 C 0 0
2 D 0 &M1 L
1U UU 2 ; & M ) 1L)12 ; & M )U(
C))5D
* =
C))1D >)(?
% & 0F
,
7
* ' 0 00 0 20 # 0 0 ' I 0 ' "0 ' ' 0 >F)&(? -' 0 0 0F 9 ' U
0 U 20
' 0 0 0 * 2
0
'0 20 ' * 0 < 0
<
20
"X
; P
!
P P 00
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(
$
G
3 ' 0 0F '
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0
F : 0
2
' >F)&+? ' 0 U
( >F)&(? -2 &GG, 0 ' * ' ) ' * 2 0
0
*
0 ' 0 0' 20
* ' ' 0
)1
Scattered light intensity
(G - L) ms -1
30
20
10
0
-10
0.00
0.10
time / ms
0.0
1.0
Dressing light intensity / ms -1
: )&+ !0 0 00' D ' /H I
7 * : 0 )4#O /5O &(#O D * ' 0 ' ' * ' 0 0 * '
C D M C D =
C))D ' 00 ' 0 0
* 0
0 0
K 0' :
&" *
: 002
Y
&
&
Y
C))8D
* ' >F )&/? ,' 0 20
.0
00 0 20 0 = * ' ' // O 2 )G
&/ : 0 G(1 * F * C))8D =' >)1? * &" 002
* (" >(5? *
20 ='
3
)5
>
=
0
1.0
-1
0.8
-2
-3
0.6
-4
0.4
-5
-6
0.2
x/x0
0.0
x/x0
-7
0.0
0.0
1.0
?
0.0
1.0
@
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.4
t/ms
t~0.32 ms
t~0.32 ms
: )&/
0.5
t/ms
. *
: C))8D D
* 0 *
: ' 0 0
0
2
D * D 20
D * 0
' >F)&+
D? ' 0
2
2 !
;
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4
4 , 3
3
C))4D
* 0 W 6
0 2 C)&GD * : 6
20
0 * 20 C))4D ' 0
2 * 0
$
$ >(8?
1C-C DD ; & M
-C D ; C D
)
&C-C DD
C)(GD
>F)&1? 6
( 0 C))4D ' 00 0
0 20 &
)8
1
0.5
a)
b)
-3/
3/
0
: )&1 D 6
U ; ( D =
C))4D * &G S ; 4GÆ ; /84
F >F)&/? ' &GH
' (
! )
3 002
' ' 0
, =
' '
, 0'
' 0'
7 0
F : F 7 0
: 0 0 F K 00
00 0
F ' 00
0
0
* F
' ) 20
GL )L F
F 3 >F)&5? # ' ' 0
*
0
0 0
,
Æ * F ,
0 # F ' 0
>)1? * 7 ' 2 OD 7 * ' C
OD
' I C
W0 /GH ' 0 K ' 0 9 ' ,
C
D 0I * 0 0
2
0 2
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: )&5
%
F D
0 ' D :
2 )L
F ' D * 0
K I
* ' 00
00 0
<'<
a)
c)
b)
: )&8 6 7 C % D 0
D E
7 0
2
002
* D
3
20
0 * 2 D 0 ' ' 0 ' =
0
0 C 0D 9 ' ' 0
:
' ' 0
2 . 0
2 & : 2
0 2 '0
) &GG &G/ &5 B * >F)&8
D? * 2 (G
9p
Single atom
Collective
Fig. 2.12
Fig. 2.14
Fig.2.7
Rabi
oscillations
9d
Steady state gain
and slow light
: )&4
Superradiance
3
7 "
0 0 7 0'
' & * ' *
: 00
&
C
D * 2 2 ' >:)&8D?
2 0 ' *
! 0 00
0 0 * 7 (G
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* * 7 00 >F)&4? * ' * 7 >F)5? >F)&)? >F)&+?
* 0 ' 7 ' 2 : 2
0 20 >(4? 0 0 0 ' &5 O : 2
0 2 0 ' >+G +& +)?
' 0F 0 * 0 ' ' 0F
00 0 ' 20 (&
* 0 '
0
* ' K ' I 0 , >F)&G? 0 0 0 0
0
F ' 0F * ' ='
0 ' 0F
2 ' ' 0
2 3 0 0 0
0 0 9 0 ' 0
* 0F
0 ' F
' >F)5? &GH & : &G '0
) & 0 & 0 0 * )G
' & 0
&G 0 0 ' ' 0
C.6D * >F)&4?
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2
0 00 ' K D 9 ' : ' F ,- * ' = 0 ' 3 ' 0F
' >+(?
()
& $' 1% " ! 0 & ' & - & 2
34 ' 34 34 & 5 ) / 34 '6 34'6 ' 0 &
F 0
0 0
0 0 0 * 0 ' 0 * B
0
F 00
0 0 * ' 0
00 ' ' 00 * 0
' 0 ' * 0
' 00
0
,-. ' 0
0 0 ' * 0 ' ' 20 0
0 0
0
# 0
& * 00 &
' )G +GH 0' 20 ,' 0 ((
z
y
x
: (&
00 0
0 0
* F ' 2
' ' '
0
20 0
0 0 C9"*D
0 ' '0F # =' 0
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)
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:
' 00' & G ) G ' * 00 00
# 0 =' 0 '
* 20 7
:;& :;) + 90
0 0
' .3
0 0 0 A 0 * 0
0
' .3
'
5 CD L P CD
;
+T
L U
& CD
8T&
C(&D
P 0 0 =' # &G1+ * ") /84 0
T ; )
) ( &G
* 0
20 ' * ' 1 #O &
&
0 U;&G % 0 9 0
0 0 0' ' &G ' 00 =' L (+
=
C(5D * 0 0
' 00 = 0
# 0
B
= 0
' 00 = * 0 0
B
0 00 =' 2 = 0
* 0
00
0 '
0
2 0
: 0
B
' '
& C D ;
20
" C
D" C
D
) " C
D
)
0 #
' '
Æ
" C
D ; "
Æ
"
2
&M
C
&O
20
" C
D
Æ
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" C
D
)
C()D
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C((D
'D &G1+ 3 0 0
' 002
3 0
0 0
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'
"Æ
& C D "
) Æ
&
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&M
&
"Æ "Æ )
)
; "Æ "Æ
C(+D
* 0
WC2'D =
C(+D =
C(&D *
F2 0
0 T U '
& 9 00 =
;
;
;
!Æ
!Æ
& M !Æ
0
0
(/
) ) &G
) ) &G
) ) &G
6 ?
>
6 ?
>
6 ?
>
C(/D
5
;
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0
'
L 8 L ;
7
8
L
&/
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C(5D
* 00 =' F '
L ; C D
;
C(8D
L L : (8 &G
; )5
L >+1? C:;&D
! 0
20 ; L )8/ &G
7 ?
>
C(4D
F
' 00 *
: >(G?
9 ;
)
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20
F 2
* 0 ;(GG 0
;1G '
2
2 0 (5/ * 0
F 0
0 C
D /G 0 >F((?
# 0 ' ' &/ 0 9"* * F 0 ' F 0 ' *
0 0 1GG 2 F & ' 7 F :
' 20 0 ' 0 &G 9"*
* 00 = F 0
0
* 7 (1
x)
Displacement
t/ms
50
100
150
200
y)
t/ms
100
200
1000
2000
300
400
500
z)
: ()
3000
4000
5000
t/ms
*
00 = 0
0 0 * ' C&D F 3 0 0 (G I * 00
= ; ++( ; &/1 ; &G/G ' 20
* >F()? * 00 002
' 0 0
* 0 &G/GO++(;)(5 20 (5/
*
0
' ' 0 0
0 ' 7 * 8 0 7
00
' 0 0
' * )) 0 E;GG1 * 20 '
/
"Æ ; 2 W =
C(/D 00 = &&
* =
0 ; G +/
#
0 ' -=
$ /5+ * 0
=
$ /) &G C(1D 0
0 +(
C(4D &G G+
0 0 * 0
' =
C(5D &G ))
&G
* 00 =
C(&GD (+G
&)G /) ! * 0 0 00 0
0 0 K 0
E 0
' K # 0 (5
,d1
,x
f3
f2
f1
r
d1
: ((
x
d2
30 0
0
,' F 0
0 * / &/ ) / ( & ) * * 0 0
9 C(D F2 >F((? E
F C&D * 0 ' * +G 2 0 &) O 0
' &
: 00 CE RBD +# 0 0
* 0 ' >+5? * F
0 0
9 = 0 *
F ' 0 C);)M(D W ,."
2 00 0
' &
G
&
&
G
&
&
)
G
&
&
G
&
&
&
G
&
&
G
&
9 G
G
2
C(&&D
* 0
0 C
D * 0
0 & & 0
C);(D # 0 F C&D
-=
C(&&D 0 C
/
D; ) M
/
C(&)D
# F ' & ' & * ' 0 * 0
(8
/ / D 00
C * 0 ' / / * 0
' 00 00 0
00 = * = ' 0
' 0 * 0
0
: *
: =
C(&GD
0
9 ; )
9
&/1
9
;&5G * &1 O * )G 3 0
0
0
F &G &G # # GG() O C
/GD / .0
>F(+? ' +GH 4 * ' = X #
20
0
X &1G O ' /G GG() O
9
&G * C & >F((?D ' * 0 ' @3@ '0 0 0'
0
* 0
0 0
' 20 2 : '
# +)5 0 0 : &GO 20 0
0 ,' 0 K' ' ' ' 0 * 2 /G O 0
)G +
(# ,-
& ' * &
' (G I *
(4
14
number of atoms / million
12
10
8
6
4
2
0
10
0
20
30
40
50
60
70
time / s
: (+
6 :;&;& 0
0 0 * F ' ' 0
0
0 0 0 *
20 >F(+?
* =
0
;
' ' '
C(&(D
' =
* 8 )& 0
I =
' ' & 0 I0 . ' &
:;& ' * :;) 0
' &5 B
0 ' 0
, 0' & * 0
& &
2
: 2
0 &
& G >+8 +4? * ' 0 0 ;& ;G >F(1? C
&G
D F C,
%
/G B
D ' 0
' >+8? ' 0 0 ' 2 '
0
3 ' E
0
=
C(5D 7
=
K 20
E F ' ' +G
CD ;
M
M
/D
20C+
L
)& 1+ ( )G/( &G
C(&+D
C D
* 00 = 0 0
&/ 1 '
8 &/
;
; &G/G & D
C(&/D
; ++( ;
)5 >+1? C
&
F 0
0
;GGG5 ;
; &(8 C& /1
G )&D &G
0 0 & &( &G
>+/? * F 0 ( &G
>/G? ( &G
>/&?
)
* 7
=
C(&(D ' C* 0 D
CD ;
M
M
/D
20C)
C(&1D
'
;
+ &/
L
5 1+ & 1/5/ &G
C D
C(&5D
: ' >F(+? GGG5 ' C1 1 ) (D &G
0 '
&G
O 7 F (+ B
>+8? * ' 7
;& ;G )+ % (+ B
0
0 /G ;G&G : & / &G
' 0
&+ ;GG+ 3 0 20 >+/?
' 00 ' ) &G
+&
number of atoms / million
14
12
10
8
6
4
2
2
4
6
8
10
time / s
: (/
6 :;) ;) 0
0 0 * F ' ' ./ 9 0
0 0 0
' 00 '
'0F 0 ' 0 F * :;) 0
' &55 B :;& # & ) ) = &
: =' ! 811) * K
0 ) * / 6
0 >/)? =' &551+()G B +G (+ B
7 F
0 :;& >F(/?
9 =
C(&+(&5D 7 ) 0 0 :;)
)
;(+ >/(? =
C(&/ (&5D ;
8 &/
)& 1+ L
+)
) 11// &G C D
C(&8D
E/h in GHz
1
+2
+1
0
F=2
0.5
-1
0
-0.5
-1
0
200
400
600
-2
1000
800
1.77GHz
E/h in GHz
0
-0.2
-1
-0.4
-0.6
0
-0.8
F=1
-1
0
200
400
600
+1
1000
800
B in Gauss
: (1 - '0F F 3
0 :;) 0 F :;& *
=
;
3
+ &/
5 1+ ; G GG5 L
& +1&) &G
C D
C(&4D
0 ' F =
C(&+D ; C& 8
G (D &G
' F =
C(&1D ; C( /
& GD &G
.0
=
C(5D
;+8 ;(( 3 20
' )
) 00 $ 0 ;G 3 ' =
>F(1? ' '
F =' +(
a)
atom count
atom count
c)
25.5
26.0
26.5
27.0
27.5
26.20
26.25
26.30
26.35
26.40
26.15
26.20
26.25
26.30
26.35
26.40
atom count
atom count
25.5
26.0
26.5
27.0
27.5
frequency / kHz
(1.7716 GHz offset)
: (5
26.15
d)
b)
frequency / kHz
(1.7716 GHz offset)
) G 00' & G
D D 0
00 9"* "0 D D * : 00 0 * 0 D D ) D D &/ *
0
D D / &/ I * D D )&/ D D )/1 D
D )4 * = >F(8? 0
' F I
' =
0 F 00 D+/G D)/G D)G
D)G
# 0 20 ' & G ) G F :
F 0 )+( % )++ % & & & G 7 F (+ B
' & G & & F ' )58 B 7 * =
))& OB 7 &5G8 * 0 &5
B =' C(+D # 0 '
00' C D F =' 0 &GH 0 :;) I
# 00' 7 ' >F(5? : 00 ) 0 00 9"* *
>F(5
D? 9"* C(&D : >F(5D?
++
frequency / kHz
26.5
26.4
26.3
26.2
26.1
0
20
40
60
80
100
120
12
density / 10 cm-3
: (8 3 =' 0 ' * =
' = F >F(5? * 20
*' ' &/ &G >F(5D? * F )1G45M+G5+ &G
O * 0 20 >/+?
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* :
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0 00 F ' 0 * : =
0 '
C3 3 D
3 3
C()GD
* ' F C
D ' "00 ,
0 0 * ' F *
0 00 0 ' ) G
* 0 0 20 I 9"* 7 >F(5D D?
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: ' 0 7
=
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= C ; ++ ( >F(8?
0 ) &/ ' 00 ' 7 : 0 2 0 F 0
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T
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