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L 20. L 00. Cavityenhanced dipole forces for darkfield seeking atoms and molecules. David McGloin, Kishan Dholakia. Tim Freegarde. Dipartimento di Fisica, Università di Trento 38050 Povo (TN), Italy. J F Allen Physics Research Laboratories, University of St Andrews,
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L00
Cavityenhanced dipole forces for
darkfield seeking atoms and molecules
David McGloin, Kishan Dholakia
Tim Freegarde
Dipartimento di Fisica,
Università di Trento
38050 Povo (TN), Italy
J F Allen Physics Research Laboratories,
University of St Andrews,
Fife KY16 9SS, Scotland
OPTICAL BOTTLE BEAM
Dipole force traps for darkfield seeking states of atoms and molecules require regions of low intensity that are completely surrounded by a bright optical field. Confocal cavities allow the resonant enhancement of these interesting transverse mode superpositions, and put deep offresonant darkfield seeking dipole traps within reach of lowpower diode lasers.
COAXIAL RING ARRAY
OPTICAL DIPOLE FORCE
(
)
Jdipole traps eliminate the magnetic fields needed for MOTs1
æ
ö
w
z
1
1
(
)
ç
÷
2
=

r
z
ln
1
(
)
ç
÷
(
)
(
)
0
2
2
FAR OFF RESONANCE25
Jbroadband interaction and
Jminimal scattering, hence suitable for spectrally complex atoms and molecules
Lintense laser beam needed to compensate for interaction weakness
BLUEDETUNED610
Jdarkfield seeking to minimize residual perturbations
Lneed isolated islands of low intensity for closed trapping region
RESONANT CAVITIES1113
Jcan greatly increase circulating intensity, as optical absorption is low
Loptical field not a single cavity mode
w
z
w
z
w
z
è
ø
2
2
1
COMPOSITION
towards
high intensity
=
+



0
.
691
0
.
332
0
.
165
0
.
332
0
.
525
E
L
L
L
L
L
00
10
20
30
40
towards
low intensity
CONFOCAL CAVITIES
L/R2
1
confocal
Intensity distribution within a perfectly confocal resonator.
Above left: mean intensity shown for central 40% of the cavity. The solid lines show where the forward beam has fallen to e2 of its onaxis intensity.
Above: viewed on a wavelength scale around the cavity centre, the modulation due to interference between the counterpropagating beams is apparent. Here,
l = 100 mm, = 780nm, = 2.
Left: depth of modulation due to interference between forward and return beams. Black=0, white=100%.
0
1
L/R1
Intensity distribution around the centre of a confocal cavity.Dashed and solid lines indicate the nodal and antinodal planes; the dotted line shows where the lowest part of the trap wall is maximum. Logarithmic contours (four per decade) refer to the peak intensity on axis. l = 100 mm, l = 780 nm, a = 0.492.
Intensity distribution when the cavity mirrors are 0.1 mm from their confocal separation (Dl/l = 0.001), for r2 = 0.99,
t2 = 0.01. The nodal surfaces, shown dashed, are now curved, reflecting the increase in Gouy phase with mode number. Central and trapping intensities are reduced by about a third.
RAY OPTICS
Applications:
R2
R1
GAUSSIAN BEAMS
HALF TRIP
ROUND TRIP
even
odd
even
CAVITY MODES
Cartesian
i + j
HermiteGaussian
cylindrical
2p + m
LaguerreGaussian
Amplitudes ap0 of mode components forming the complete fivecomponent optical bottle beam with =2.
LAGUERREGAUSSIAN BEAMS
MECHANICAL AMPLIFIER
col intensity
(
)
(
)
(
)
m
æ
ö

+
+
æ
ö
æ
ö
1
exp
i
2
p
m
1
tan
z
z
2
2
2
4
p
!
2
r
2
r
r
i
kr
(
)
trap centre
intensity
ç
÷
ç
÷
ç
÷
J
=


+
J

R
m
r
,
z
,
L
exp
i
m
i
kz
L
(
)
ç
÷
ç
÷
(
)
(
)
(
)
ç
÷
(
)
(
)
(
)
pm
p
+
d
p
+
2
2
2
1
p
m
!
w
z
2
R
z
w
z
w
z
w
z
è
ø
è
ø
è
ø
0
m
trap centre position
(
)
2
2
p
z
w
0
(
)
(
)
(
)
(
)
(
)
2
where are Laguerre polynomials and , , .
=
+
m
=
+
=
L
x
w
z
w
0
1
z
z
R
R
z
z
z
p
R
R
l
z
Variation of trap col (dotted) and trap centre (dashed) intensities – in units of the well depth at zero mirror displacement – and trap centre position (right hand scale) as mirrors are displaced from their confocal separation.
(
)
(
)
å
e
=
r
,
z
a
L
r
,
z
(
)

+
w
w
w
w
pm
pm
p
s
!
j
=
+
=
j
j
0
1
1
0
sin
s
1
p
pm
a
cos
sin
+
ps
0
w
w
w
w
p
!
s
!
(
1
)
L
0
1
1
0
qm
(
)
[
]
+
p
s
!
(
)
+

=
j
j
j

+
j
s
1
p
1
2
2
a
cos
sin
p
cos
s
1
sin
(
)
ps
1
+
p
!
s
1
!
a
(
)
pmq
[
]
[
]
+
{
}
p
s
!
(
)
(
)
+

=
j
j
j

+
j
j

+
j

j
s
1
p
2
2
2
2
2
2
a
cos
sin
p
cos
s
1
sin
p
cos
s
2
sin
p
cos
(
)
ps
2
+
2
!
p
!
s
2
!
SINGLE TOROID
LARGE PERIOD STANDING WAVE