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15 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Observation of universality in
7
Li three
-
body recombination
across a Feshbach resonance

Lev Khaykovich

Physics Department, Bar Ilan University,

52900 Ramat Gan, Israel

ITAMP workshop, Rome, October2009

If it is not

an accidental

coincidence

Observation of universality in
7
Li three
-
body recombination
across a Feshbach resonance

Lev Khaykovich

Physics Department, Bar Ilan University,

52900 Ramat Gan, Israel

ITAMP workshop, Rome, October2009

Efimov scenario

This resonance

This minimum

Experimental system: bosonic lithium

Why lithium?

Compared to other atomic species available for laser cooling,

lithium has the smallest range of van der Waals potential:

0
4
1
2
6
0
31
16
a
mC
r









Thus it is easier to fulfill the requirement:
|
a| >> r
0

Experimental system: bosonic lithium

Bulk metal


light and soft

MOT setup

Magneto
-
optically

trapped atoms

What’s lithium?

Experimental system: bosonic lithium

Hyperfine energy levels of
7
Li atoms in a magnetic field

The primary task: study of 3
-
body physics in a system of identical bosons

Experimental system: bosonic lithium

Hyperfine energy levels of
7
Li atoms in a magnetic field

Absolute ground state

The one but lowest Zeeman state

Experimental realization

with
7
Li atoms:

all
-
optical

way to

a Bose
-
Einstein condensate

Optical dipole trap

N. Gross and L. Khaykovich, PRA
77
,
023604
(
2008
)

Direct loading of an optical dipole trap from a MOT

0
order

(helping beam)

+
1
order

(main trap)

main trap

helping beam

* The helping beam is effective only
when the main beam is attenuated

Ytterbium Fiber Laser

P =
100
W

w
0

=
31
m
m

U =
2
mK

Q

=
19.5
0

w
0

=
40
m
m

N=
2
x
10
6

T=
300
m
K

Feshbach resonances on F=
1
state

0.060
0.065
0.070
0.075
0.080
0.085
0.090
0.095
0.100
-200
-150
-100
-50
0
50
100
150
200


Scattering length [a
0
]
Magnetic field [T]
black: 11;11
red: 10;11
green: 10;10
yellow: 1-1;10
cyan: 1-1;1-1
Atoms are optically pumped to F=
1
state

Theoretical predictions for Feshbach resonances

S. Kokkelmans, unpublished

Search for Feshbach resonances

High temperature scan
: the magnetic field is raised to different values +
1
s of waiting time.

The usual signatures of

Feshbach resonances

(enhanced
inelastic

loss).

Enhanced
elastic

scattering:

spontaneous evaporation.

From the whole bunch of possible resonances only
two

were detected.

Spontaneous spin purification

Spin selective measurements

to identify where the atoms are.

Spin
-
flip collisions:

|F=
1
, m
F
=
0
>

Feshbach resonances on m
F
=
0
state

Compared to Cs or
6
Li the background scattering length is small: a
bg

~
20
a
0


Do we have a broad resonance? What is the extension of the region of universality ?

0
0
*
40
r
a
R


1

res
s
Straightforward approach is:

Feshbach resonances on m
F
=
0
state

A narrow resonance


R
e

is very large

A broad resonance


R
e

crosses zero.

Resonance effective range is extracted from the effective range expansion:

Far from the resonance


R
e

>
r
0

|R
e
| =
2
r
0

40
G

2
1
)
(
cot
2
k
R
a
k
k
e




Experimental results

Low temperature scan for Feshbach resonances (T =
3
m
K),
50
ms waiting time.

Positions of Feshbach resonances from atom loss measurements:

Narrow resonance:
845.8
(
7
) G

Wide resonance:
894.2
(
7
) G

Two
-
body loss

What type of loss do we see (we are not on the absolute ground state)?

Coupled
-
channels calculations of magnetic dipolar relaxation rate.

This rate is ~
3
orders of magnitude smaller than the corresponding measured rate.

Unique property of light atoms!

For heavier atoms the situation can be more complicated
: second order spin
-
orbit

interaction in Cs causes large dipolar relaxation rates.

S. Kokkelmans, unpublished

Tree
-
body recombination rate

Analytical results from the effective field theory:

























4
2
0
2
2
1
8
.
16
sinh
ln
cos
1
.
67
e
a
a
s
e
a
C


m
a
a
C
K
4
3
3



Theory:

















2
0
2
sinh
ln
sin
2
sinh
4590
a
a
s
a
C
0

a
0

a
Tree
-
body recombination rate

Experiment:

This simplified model neglects the following effects:


-

saturation of K
3

to K
max

due to finite temperature


-

recombination heating (collisional products remain in the trap)


-

“anti
-
evaporation” (recombination removes cold atoms)


N
N
n
K
N



2
3

The first two are neglected by measuring K
3
as far as a factor of
10
below K
max


For the latter, we treat the evolution of the data to no more than ~
30
% decrease

in atom number for which “anti
-
evaporation” causes to underestimate K
3

by ~
23
%.

Tree
-
body recombination rate

a
>
0
: T=
2


3
m
K; K
3

is expected to saturate @
a

=
2800
a
0

a <

0
: T=
1


2
m
K; K
3

is expected to saturate @
a

=
-
1500
a
0

N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL
103
,
163202
(
2009
).

4
.
0

res
s
Summary of the results

Fitting parameters to the universal theory:

a
+

=
244
(
34
)
a
0

a
-

=
-
264
(
10
)
a
0

a
+
/|
a
-
| =
0.92
(
0.14
)

Experiment:

UT prediction:

a
+
/|
a
-
| =
0.96
(
0.3
)

Minimum is found @
a

=
1150
a
0

=
37
x
r
0

Both features are deep into the universal region:

Efimov resonance is found @ |
a|

=
264
a
0

=
8.5
x
r
0


-

=
0.223
(
0.036
)


+

=
0.232
(
0.036
)

Randy Hulet’s talk: minima are found @
a

=
119
a
0

and
a

=
2700
a
0
(BEC


0
temperature limit!)


Efimov resonance is found @ |
a|

=
298
a
0
(similar temperatures)

Summary of the results

Fitting parameters to the universal theory:

a
+

=
244
(
34
)
a
0

a
-

=
-
264
(
10
)
a
0

a
+
/|
a
-
| =
0.92
(
0.14
)

Experiment:

UT prediction:

a
+
/|
a
-
| =
0.96
(
0.3
)

Minimum is found @
a

=
1150
a
0

=
37
x
r
0

Both features are deep into the universal region:

Efimov resonance is found @ |
a|

=
264
a
0

=
8.5
x
r
0


-

=
0.223
(
0.036
)


+

=
0.232
(
0.036
)

The position of features may shift for lower temperature.

How much do they shift?

Summary of the results

H.
-
C. Nagerl et.al, At. Phys.
20
AIP Conf. Proc.
869
,
269
-
277
(
2006
).

K. O’Hara (
6
Li excited Efimov state):

180
nK
-
>
30
nK

the resonance position is shifted by ~
10
%

(and coincides with the universal theory)

J. D’Incao, C.H. Greene, B.D. Esry

J. Phys. B,
42 044016
(
2009
).

Summary of the results

Fitting of the Feshbach resonance position:

a >

0
B
0

=
894.65
(
11
)

a <

0
B
0

=
893.85
(
37
)

The resonance position according to the atom loss measurement:
894.2
(
7
) G

Detection of the Feshbach resonance position by molecule association

The resonance position according to

The molecule association:
894.63
(
24
) G

Summary of the results

Fitting of the Feshbach resonance position:

a >

0
B
0

=
894.65
(
11
)

a <

0
B
0

=
893.85
(
37
)

The resonance position according to the atom loss measurement:
894.2
(
7
) G

The resonance position according to the molecule association:
894.63
(
24
) G

If K
3

were

to increase by
25
% (overestimation of atom number by ~
12
%),

the position of the Feshbach resonance from the fit would perfectly agree:

a >

0
B
0

=
894.54
(
11
)

a <

0
B
0

=
894.57
(
25
)

Minimum would be @
a

=
1235
a
0


Efimov resonance would be @ |
a|

=
276.4
a
0

a
+
/|
a
-
| =
0.938

Feshbach resonance on the
absolute ground state

|R
e
| =
2
r
0

40
G

Preliminary results for the absolute
ground state

Conclusions


We show that the
3
-
body parameter is the same across
the Feshbach resonance on |F=
1
, m
F
=
0
> spin state.



The absolute ground state possesses a similar Feshbach
resonance


possibility to test Efimov physics in different
channels (spin states) of the same atomic system.



Mixture of atoms in different spin states


a system of
bosons with large but unequal scattering length.

Who was in the lab and beyond?

Bar
-
Ilan University, Israel

Eindhoven University of

Technology, The Netherlands

Servaas Kokkelmans

Noam Gross

Zav Shotan

L. Kh.