Coexistence of Josephson Oscillations and Self Trapping in Optical Waveguide Arrays Ramaz Khomeriki...
-
Upload
katherine-evans -
Category
Documents
-
view
213 -
download
1
Transcript of Coexistence of Josephson Oscillations and Self Trapping in Optical Waveguide Arrays Ramaz Khomeriki...
Coexistence of Josephson Oscillations and Coexistence of Josephson Oscillations and Self Trapping in Optical Waveguide ArraysSelf Trapping in Optical Waveguide Arrays
Ramaz Khomeriki
Dipartimento di Energetica ‘‘S. Stecco’’ and CSDC, Università di Firenze, and INFN, Via S. Marta, 3, 50139 Firenze, ITALY
Physics Department, Tbilisi State University, 0128 Tbilisi, GEORGIA
In collaboration with
Jerome Leon (Montpellier, FRANCE)
Stefano Ruffo (Firenze, ITALY)
Sandro Wimberger (Pisa, ITALY)
S.M. Jensen, IEEE J. Quantum Electron. v. 18, 1580, (1982).
M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, M. K. Oberthaler, PRL, v. 95, 010402 (2005)
02 2
2
212
dz
di
02 1
2
121
dz
di
constP 2
2
2
1
P2
2
2
1
2,1
2,12,1 ie
12
cos12
22 P
H
1-P 0; state ground 1PP If 2c Pa
2P1EEnergy state ground Asymmetric 2a
1EEnergy 0 0, state Symmetric s
A. Smerzi, S. Fantoni, S. Giovanazzi, S. R. Shenoy, PRL, 79, 4950, (1997)
Q Q
Q
N
Z
0
-N
Bose-Einstein Condensates in Optical Lattice
-5 0 5x [2/k
L]
vcos2(kLx/2)
|(x)|2
V0+v
02 0
2
0011000
Kc
n
dz
di
022
11 jjjjjjj K
c
n
dz
di
0 ;0 0;j 11 NN Continuous Approximation - Gross-Pitaevskii equation
0)()()()()()( 2
2
2
jjjjVj
jK
z
ji
0V
1 ;
V 00
lNL
cnn j)(V l2
2L
-N
0
N
100
200
300
0
0.2
0.4
zz
Waveguide Number [j]z
0 100 200 3000
5
10
z
|j|2
V0
)(j),( :Solutions Stationary jez zi
LxlkkLxAj AA for ),()(cn)( A K
lxLkkLxBj BB -for ),()(cn)( B K
lxlebeaj xx -for )(
VA
kA AA ;2
A ;
2
222
;2
B ;
2
222
BkB BB
conditions continuityfour and b, a, B, A, : Parameters Five
)()()()(),( 2211 jzjzjz
-N 0 N-0.4
-0.2
0
0.2
0.4
0.6
Symmetric +
Asymmetric a
Antisymmetric _
j
Waveguide Number [j]
2=0.066
2
)()()( ;
2
)()()( 21
jjj
jjj
01
2
121
Drdz
di
02
2
212
Drdz
di
j)(
jV(j)jj
21
2121
d
dQ
r
;j)(j)( and 0j :overlap zeroAlmost 22
2121 ddd
j)(
j)(
j)(
j)(2
2
42
21
41
d
d
d
dD
rrD
rD
42K T
4for 1|(0)| and 1|(0)| If 21
0 0.5 1 1.5 2 2.5-0.2
-0.15
-0.1
-0.05
0
0.05
P/Pc
(Ea-E
+)/
(Ea+
E+)
Harmonic double well
Square double well
-6-4
-20
24 6
0
0.005
0.01
x [2/kL]
|(x)|2
0 100000
0.25
Time [1/ER
]
V0/E
R
10E/ER
5000
10000Time [1/E
R]