Methods for Manipulating CaF using Optical Polychromatic Forces

forestevanescentElectronics - Devices

Nov 2, 2013 (3 years and 7 months ago)

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Methods for Manipulating CaF using
Optical Polychromatic Forces

Edward E.
Eyler
,

Scott E.
Galica
, and Leland M. Aldridge

Physics Department, University of Connecticut


Supported by the National Science
Foundation

and the University of Connecticut

Topics

1.
The optical bichromatic force

a.

π
-
pulse model for a two
-
level system.

b.
Numerical solution of the optical Bloch equations.

c.
Large
-
detuning BCF tests in He*.

d.
Chirped BCF slowing.

2.
Four
-
color polychromatic forces

a.
Numerical modeling of the excited
-
state fraction.

b.
Comparison with BCF and pulse trains.

3.
Progress on deflection and slowing of molecules

a.
Plans for BCF deflection and slowing of a CaF beam.

b.
Low
-
cost instrumentation using 32
-
bit microcontrollers
and an Android tablet interface.

Radiative forces

Laser

𝑘
,
𝜔
𝐿

Scattered

photon

Δ
𝑝

=

𝑘

Basis
: absorption changes the momentum by
ħk

but on average,
spontaneous decay yields

D
p

=
0. In saturation,
N
b

=
N
/2 and the
average force on an atom is


Typically
d
v

= 1

9 cm/s for each photon scattered.


Deceleration is large (4.7


10
5

m/s
2

for He*), but to stop an atomic
beam from 1000 m/s requires 11,000 photons and

1

m.


Velocity range is limited by resonance width to

g
/
k.

g

= 1/
t

|
a


|
b



Plane

waves

at

±
d

form

beat

notes,

each

with

an

area

of

~

.

Pairs

cycle

the

2
-
level

system

at

a

rate

d
/


>>

radiative

decay

rate

γ
=
1
/
τ
.


If

left
-
right

rf

phase

shift

is

~

/
2
,

after

each

radiative

decay

there

is

a

75
%

chance

of

excitation

from

the

right



Force

is

directional
.


0



d



0



d


v


/
d


/
d

But the atom spends ¼ time in the

wrong (accelerating) cycle, so:

Given two momentum transfers

per stimulated cycle,

Intuitive explanation


of the
bi
chromatic

force

Successive pulses alternate in sign, so the BCF:


Is very tolerant of deviations from

-
pulses, and of
left
-
right beam imbalance (cancels in quartets).


Is not affected by moderate Doppler shifts

kv
,
which do not break the symmetry!


Upper velocity limit: is
grossly disrupted if
kv

~

W
0,

, predicting a velocity
range of
D
v



d
/
k
.


Range is huge
compared to
D
v



g
/
k

for
F
Rad
!

BCF velocity range


g



e



0



d



0



d


v

4(

) 2(+) 1(+) 3(

)

w

v

Direct Numerical solution

Ehrenfests’s

theorem:

Calculated evolution with no damping


Without radiative
damping, atom stays in
the
v
-
w

plane of the
Bloch sphere.



Under optimal
conditions as shown,
an atom spends about
60% of its time in the
ground state (
w
=

1).



Full numerical solution of OBEs

Force profiles are
calculated
for
4
He, using
code based on previous
versions by Metcalf,
Grimm, Solomon groups.

Predicts
a slightly larger
optimum
Rabi frequency
than
π
-
pulse
model. For
each component beam,



The velocity range is
D
v

d
/
k

, as before.

The velocity profile has a sharp edge, making
cooling

possible as atoms
“pile up” against it. Effective if interaction time exceeds “BCF slowing
time” of

/
(2

recoil
), 5.9
m
s for He*.

For
more on cooling,
see H. Metcalf,
Entropy exchange in laser cooling,
Phys. Rev. A
77
, 061401 (2008).

Application to metastable He* atoms

For He
2
3
S


2
3
P

at 1083 nm, if
d
= 154
g 
250 MHz
×

2

,


Required
laser power from each direction = 23.8 W/cm
2
.


Beat
note period is

/
d

= 2 ns, much faster than
t

= 1/
g

= 98 ns.


F
B



100
F
Rad
. Deceleration is
4.7 million gravities.


Velocity range is
Δ
v

=
d
/2
k
= 135 m/s, still much smaller than beam
velocity of ~1000 m/s


Must add Doppler offsets

kv
.


Slowing time is
Δ
t

= 5.8
μ
s, independent of velocity range
.


Chirped slowing of He*

Initial tests: Detuning of 74
g



velocity range of just 1.57
d
/
k = 200 m/s, but the
lasers are linearly chirped during 20
-
40
m
s to follow the changing Doppler shift.

Results for chirped slowing of He*

Measured

Simulated using
F

=
F
B

/ 2.

Maximum usable chirp was limited by
rf

phase noise and other technical issues, At 300
MHz, measured slowing is by 2.84
d
/
k = 370 m/s

Simulations match well, and clearly show that efficient slowing to rest is feasible if
rf

phasing is improved and detuning
d

is slightly increased.

M. A.
Chieda

and E. E.
Eyler
, to be published (2012),

Topics

1.
The optical bichromatic force

a.

π
-
pulse model for a two
-
level system.

b.
Numerical solution of the optical Bloch equations.

c.
Large
-
detuning BCF tests in He*.

d.
Chirped BCF slowing.

2.
Four
-
color polychromatic forces

a.
Numerical modeling of the excited
-
state fraction.

b.
Comparison with BCF and pulse trains.

3.
Progress on deflection and slowing of molecules

a.
Plans for BCF deflection and slowing of a CaF beam.

b.
Low
-
cost instrumentation using 32
-
bit microcontrollers
and an Android tablet interface.



In the pulse
-
pair limit, time in the excited state can be arbitrarily short.










With four frequencies, pulse duration and phase evolution can be sculpted.



A chopped
cw

laser is also a possibility


sharper envelope, but much less
phase control.



Early results on Na
2

by the
Yatsenko

group (1994) showed a BCF
-
like force
with retro
-
reflected 488 nm mode
-
locked laser pulses, but lacked
tunability
.
Momentum change was limited to ~ 20
ħk

by optical pumping.

Calculated PCF vs. BCF with no damping


Based on equal amplitudes with
d
=

rf

and 3

rf
, and a 30


phase shift.



P
excited


for a 2
-
level atom is 41% for BCF and 24% for PCF


very
favorable for molecules!

Calculated force profiles


Provides most of the width of a 375
g

detuning at 2/9 the power!

Comparison with pulse trains


Pulse train is very sensitive to l
-
r beam imbalance, unless phase
-
modulated.


Easier to produce a 4
-
color beam (with an AOM) than to chop a
cw

laser at
200
MHz.


Still, some success in early experiments by Yatsenko
1

(Na
2
), Meschede
2

(Cs).


Stimulated forces from tailored
fsec

pulse trains may be promising, especial
-
ly

for cooling (A. Derevianko
3
).

1
V.S.
Voitsekhovich
, M. V.
Danilelko
, … , and L. P.
Yatsenko
,
JETP
Lett
.
59
, 408 (1994).

2
A.
Goepfert
, I. Bloch, …, and D.
Meschede
,
Phys. Rev. A
56
, R3354 (1997).

3
E.
Ilinova

and A.
Derevinko
, Phys. Rev. A
86
, 023417 (2012).

Accumulating atomic phase shift

Imbalanced pulse train, identical phases

Imbalanced pulse train, alternating phases

Topics

1.
The optical bichromatic force

a.

π
-
pulse model for a two
-
level system.

b.
Numerical solution of the optical Bloch equations.

c.
Large
-
detuning BCF tests in He*.

d.
Chirped BCF slowing.

2.
Four
-
color polychromatic forces

a.
Numerical modeling of the excited
-
state fraction.

b.
Comparison with BCF and pulse trains.

3.
Progress on deflection and slowing of molecules

a.
Plans for BCF deflection and slowing of a CaF beam.

b.
Low
-
cost instrumentation using 32
-
bit microcontrollers
and an Android tablet interface.

Direct laser slowing and
cooling of molecules

A quasi
-
cycling transition is needed.
OH, CH, etc. are candidates.
Easiest
are CaF and
SrF
: visible
-
light transitions; nuclear spin
I

of just ½.

The
DeMille

group at Yale recently achieved
both transverse cooling and longitudinal
slowing
of
SrF
,
using
radiative forces with numerous multiple
vibrational and hyperfine
repumping

lasers.

E.S
. Shuman, J.F. Barry, and D.
DeMille
,

Nature
467
, 820 (2010
),

J.F. Barry, E.S. Shuman, and D.
DeMille
, PRL
108
, 103002 (2012).


Level scheme for
cw

slowing of CaF

Both
A

X

and
B

X

in
CaF are
near
-
cycling
transitions,
with Franck
-
Condon
factor of 0.99 for the (0
-
0)
band of
A

X
,
and
0.999 for
B

X!


The BCF avoids excessive radiative
cycling: system is
in
the upper state
~1/7
of
the time, and there are many BCF cycles
per radiative cycle.


If
d

= 250 MHz
×

2


(30
×
natural
width
),
BCF needs ~60 W/cm
2
,
velocity range
is150
m/s.


Remaining
Problem: Hyperfine structure
and unresolved
m

sublevels.

Finding an effective two
-
level system

The transition is rotationally
closed, but has several
non
-
participating (
F
,
m
F
)
sublevels.
Three approaches are possible:

(1)
Live
with it. The
BCF is zero
or positive for
every level. If
levels are rapidly mixed
, the
average
force is still large.

(2)
Alternate BCF pulses (
s
-

polarization) with
optical pumping (
s
+
) for state selection.

(3)
Use
the
Q
11
(0.5
)/
R
Q
21
(0.5)
branch (shown). A
rotational
repump

laser
is
needed, but the four
transitions
all
have the same line
strength.
Tests using He* as a model are encouraging.

For details, see M. A.
Chieda

and E. E.
Eyler
, Phys. Rev. A
84
, 063401 (2011).

Detailed evaluation of option (3) with
d
/
2


=
250 MHz predicts
D
v


150 m/s with a single
vibrational
repump

for
A

X
,
D
v


100 m/s with only rotational
repumping

for
B

X
.

CaF supersonic beam

Beam

source
:

Similar

to

Field,

Hinds

groups,

a

laser
-
ablated

Ca

plume

is

entrained

in

a

supersonic

jet

of

He/SF
6

or

Ar
/SF
6
.


Pulsed

valve
:

Homemade

using

a

Noliac

multi
-
layer

PZT

disk

bender

(~
150

V)
.

Presently

in

testing
.

Deflection

experiments
:

Can

be

done

without

vibrational

repumping

or

Doppler

offsets
.

With

pulses,

don’t

even

need

a

cycling

transition!


Longitudinal

slowing
:

After

testing

with

a

supersonic

beam,

will

switch

to

a

cryogenic

beam

for

stopping
.

Low
-
cost 531 nm BCF lasers

Main

BCF

laser
:

Toptica

DL
100

external

cavity

diode

laser

at

1062

nm,

amplified

to

~
1
.
5

W,

then

doubled

in

a

homemade

resonant

cavity
.



Under construction.


100
-
250
mW

expected at 531 nm.


Repump

laser
:

Photodigm

DBR

at

1062

nm

(a

one
-
piece

100

mW

tunable

single
-
mode

laser!)

with

a

PPKTP

waveguide

doubler
.



Doubler

is under construction.


5
-
15
mW

expected at 531 nm.


Detection laser
: Existing 585 nm
cw

dye
laser.

531

B

2

+

X

2

+

BCF

585

A

2


X

2

+

Detection

v

= 1

v

= 0

605

DL100

TA (1.5W)

PPLN

Microcontroller
-
based
lab instruments

We use 32
-
bit Microchip PIC processors with a USB interface to an Android tablet for
graphics and user input. A single Android app works with nearly all of the instrument
designs, by loading parameter lists upon connection.

New designs include a temperature controller (pictured), general lab interface, laser
current driver interface, and
rf

frequency synthesizer.

USB interface

Dual 16
-
bit DAC

Touch
-
screen tablet controls

22
-
bit ADC

For more, see http://www.phys.uconn.edu/~eyler/microcontrollers/ , also E. E.
Eyler
, RSI
82
, 013105 (2011).

General lab interface


Nine uncommitted I/O or timing lines, plus power supplies and one or two daughter
boards. Timing resolution is 25 ns.
Reassignable

I/O pins add flexibility.


Waveform generation daughter board (shown) uses the new AD9102 /9106
combination DDS/arbitrary waveform generator chips.


To install surface
-
mount chips, I use a low
-
cost hot
-
air soldering station,
Aoyue

968A.

For more, see http://www.phys.uconn.edu/~eyler/microcontrollers/ , also E. E.
Eyler
, to be published.

2
nd

daughter
board (DAC,
ADC, phase
-
sensitive
detector, etc.)

DDS/arbitrary
waveform generator
(up to 180 MHz clock)

200 MHz differential
amplifier

PIC32MX250F128D

Broadband frequency synthesizer


Can be used for AOMs, EOMs, direct
rf

transitions, etc.


PLL
-
based ADF4351 chips can cover 35
-
4000 GHz with 1
-
2
ppm

accuracy for $14,
using a $4 Fox 924B crystal oscillator for reference.


Circuit board has been constructed, but software still in development.


Very fast
rf

switch allows 4
-
ns frequency shifting. Amplifier/filter/attenuator
combination allows flexible output levels and harmonic rejection.

15 dB amp,

GVA
-
62+

35
-
4000
MHz
frequency
synthesizer


Tablet

SPI

Main output

SPI

Digital step
attenuator,
DAT
-
xx
-
SP+

Micro
-
controller


35
-
4000
MHz
frequency
synthesizer


SPI

Loop filter

Loop filter

r
f

switch,

HMC284

7
th
-
order
low
-
pass
filter, LFCN
-
xxx

7
th
-
order
low
-
pass
filter

Secondary output

Summary


The
bi
chromatic

force can be up to 300 times
larger than the
radiative
force, with a much wider velocity range. With
chirped beams, can slow a He* beam to rest in 1
-
2 cm.


For molecules, limitations due to “dark state” decay can be
reduced greatly. A four
-
color

version shows
great promise.


CaF has two near
-
cycling systems;
B

X

will be used for tests.
Expecting
D
v

> 150 m/s with BCF.


Homemade instrumentation is well
-
suited to general laser lab
use.

For more details on
A

X
, see M. A.
Chieda

and E. E.
Eyler
, Phys. Rev. A
84
, 063401 (2011).

Estimated BCF parameters for CaF

These values are for
Q
11
(0.5) of
A

X

without vibrational
repumping.With

one
repump

laser,
D
v
loss

exceeds
D
v
b
.


For
B

X
,
D
v
loss

is larger by at least a factor of

five.

Bichromatic detuning

d
/
2


250 MHz

Deceleration

a

1.4
×

10
6

m/s
2

Bichromatic velocity range

D
v
b

150 m/s

BCF slowing time

T
b

108
m
s

Loss time

T
loss

14
m
s

Loss
-
limited velocity range

D
v
loss

19.4
m/s

Optimal irradiance

I
b

60 W/cm
2

Ratio of BCF to rad. force

F
b

:
F
rad

12.4

Experimental tests
now underway!

Single
-
pulse BCF deflection or slowing



Use large
detunings

with long
-
pulsed lasers (
Nd:YAG

or
flashlamp
-
pumped)?



No
repumping
: just use the force available from a single pulse, comparable to
a single radiative period
(~19
ns
×

14/3

for
CaF
A
-
X
).



Could deflect a selected quantum state in nearly
any molecular beam.



Acceleration of CaF with a detuning of

2.1
GHz
(250
g
rad
) is
2.3
×
10
7

m/s
2
,
yielding
D
v

=
4
m/s for one radiative period
. Beam imbalance may constrain
use of larger
detunings
.


Short interaction length reduces
rf

phase problems.

Force profiles vs. Rabi frequency

Calculated for
d
=
154
g

(250 MHz). For He*,
g
/
k

= 1.76 m/s.

Cooling is limited by variations in the force profile across the laser beam
intensity distribution.

The narrow spikes are
multiphoton


Doppleron
” resonances.

For
more on cooling,
see H. Metcalf,
Entropy exchange in laser cooling,
Phys. Rev. A
77
, 061401 (2008).


This “Zeeman slower” at the
Uni
-
versity

of Manchester loads a
magneto
-
optical trap (MOT).


Limited velocity range is
compen
-
sated by a
z
-
dependent Zeeman shift
in a tapered solenoid coil.


Long path necessitates laser
colli
-
mation

and/or magnetic focusing.

From http://es1.ph.man.ac.uk/AJM2/AJM.htm

A typical radiative
-
force beam slower

UConn bichromatic force decelerator for He*

Bichromatic detuning
δ
= 2
π

f
AOM

Doppler shifts
±
2
Δ

Typical results from the UConn

He*
decelerator


In these tests, at most 20% of the atoms within range
D
v

can be slowed.


Caused by small size of laser beam, needed for tests at very large
detunings

d
.

With BCF

Without BCF

Difference

M. A.
Chieda

and E. E.
Eyler
, to be published (2012),

Upper limits of static BCF slowing


Results at 450 MHz are consistent with a 1
-
D random walk.


Mechanism 1
: Cumulative
dephasing

due to red
-
blue beam imbalance. Causes
reversals in the force direction by ruining the time
-
reversal symmetry.


Mechanism 2
: Phase shifts in the left
-
vs.
-
right
rf

beat notes weaken the force. At large
d
, cannot avoid phase differences along beam path due to beat note length of 10
-
20 cm.


Both effects are predicted to be large when
d

> 250
g
!

Non
-
directional!

Longitudinal slowing results from Yale


Initial
beam: cryogenic
SrF

beam
source with
v
~
140
m/s
, using He
buffer gas.


Velocity is reduced by 40
-
60 m/s
for red detuning of 260 MHz


At
least 10
4

photons are scattered by
the radiative force.


Some molecules are slowed to 50
m/s.


Estimated velocity profile of the
radiative force is shown as gray
hatched area.


Figure from
J.F
. Barry,

E.S. Shuman, and
D.
DeMille
,
Phys. Rev.
Lett
.
108
, 103002
(
2012).

Basic control flow


A single Android app works with nearly all of the instrument designs, by loading
parameter lists upon connection.


Parameters are stored on the microcontroller, and boards are fully operational without
the tablet. USB control from a PC is possible by switching from host to device mode.


Reassignable

I/O pins make these microcontrollers highly flexible.

PIC32MX250
micro
-
controller


5
-
byte packets,
command+data

Tablet, with
scrolling
parameter list
and pop
-
up
keypad

SPI

USB

Text strings for display

USB

Touch
-

screen
entry?

Toggle selection
or display pop
-
up
keypad


Slider

c
hanged?

Modify current
parameter


Programmable I/O:
ADCs, DACs, PLLs,

DDS chips, etc.


Non
-
volatile
parameter storage
(EPROM emulation
in program memory)


Optional rotary encoder
knob, serial LCD
display


Serial I/O and
external
interrupts

Parallel I/O, timers,
10
-
bit ADCs


Apparatus for
chirped
helium deceleration

AOMs

Lasers

Homemade
rf

frequency
synthesizers

Frequency locking and
beam conditioning

To He*
beam
apparatus

Toptica

DL100 lasers produce about 40
mW

in each bichromatic beam pair without
amplification, adequate for a BCF detuning of 74
g

or 120
MHz.

References

[1] M.
Partlow
,
Bichromatic Collimation to Make an Intense Helium
Beam

(2002).

[2] Cohen
-
Tannoudji

et al.,
Atom
-
Photon Interactions

(Wiley
Interscience
, 1992).

[3] P.
Straten

and H. Metcalf,
Laser Cooling and Trapping

(Springer 1999).

[4] R. Grimm, J.
Soding
, Y.
Ovshinnikov
, Opt.
Lett
.
19
, 658 (1994).

[5] L.
Yatsenko

and H. Metcalf, Phys. Rev. A
70
, 063402 (2004).

[6] M.
Cashen

and H. Metcalf, J. Opt. Soc. Am. B
20
, 915 (2002).

[7] J.
Supplee
, Am. J. Phys.
68
, 180 (2000).

[8] H. Kim, J. Park, H. Lee, J. Phys. B
33
, 1703 (2000).

[9] J. Shirley, Phys. Rev.
138
, B979 (1965).

[10] S. Guerin, F.
Monti
, J
-
M.
Dupont
, and H
-
R.
Jauslin
, J. Phys. A
30
, 7193 (1999).

[11] S. Guerin and H. R.
Jauslin
, Adv. Chem. Phys.
125
, 1 (2003
).

[12] M
.
Cashen
,
Optical Forces on Atoms in Polychromatic Light (2002).