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.
b.
c.
d.
π-pulse model for a two-level system.
Numerical solution of the optical Bloch equations.
Large-detuning BCF tests in He*.
Chirped BCF slowing.
2. Four-color polychromatic forces
a.
b.
Numerical modeling of the excited-state fraction.
Comparison with BCF and pulse trains.
3. Progress on deflection and slowing of molecules
a.
b.
Plans for BCF deflection and slowing of a CaF beam.
Low-cost instrumentation using 32-bit microcontrollers
and an Android tablet interface.
Radiative forces
Laser
Δ𝑝 = ℏ𝑘
|b
DE  
|a
𝑘, 𝜔𝐿
g = 1/t
Scattered
photon
Basis: absorption changes the momentum by ħk but on average,
spontaneous decay yields Dp = 0. In saturation, Nb = N/2 and the
average force on an atom is
kg
F radiative 
.
2
• Typically d v = 1–9 cm/s for each photon scattered.
• Deceleration is large (4.7  105 m/s2 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.
Intuitive explanation
of the bichromatic force
/d
/d
0  d
0  d
v
• 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.
Given two momentum transfers
per stimulated cycle,
FB, ideal 
kd
But the atom spends ¼ time in the
FB 
wrong (accelerating) cycle, so:

DP 2 k 2 kd


.
Dt  d

and thus,
FB
2d

.
FRad  g
BCF velocity range
4(–)
2(+)
1(+)
3(–)
v
0  d
0  d
Successive pulses alternate in sign, so the BCF:
w
 e
• 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: WRabi  W0 2  (kv)2 is
grossly disrupted if kv ~ W0, , predicting a velocity
range of Dv  d /k.
• Range is huge compared to Dv  g /k for FRad!
 g
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 4He, 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,
W  3 2 d vs. W   4 d .
The velocity range is Dv 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
v
0  d + kv
0  d - kv
For He 23S  23P at 1083 nm, if d = 154g  250 MHz × 2,
• Required laser power from each direction = 23.8 W/cm2.
• Beat note period is  /d = 2 ns, much faster than t = 1/g = 98 ns.
• FB  100 FRad. Deceleration is 4.7 million gravities.
• Velocity range is Δv = d /2k= 135 m/s, still much smaller than beam
velocity of ~1000 m/s  Must add Doppler offsets kv.
• Slowing time is Δt = 5.8 μ s, independent of velocity range.
Chirped slowing of He*
Initial tests: Detuning of 74g  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 = FB / 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.
b.
c.
d.
π-pulse model for a two-level system.
Numerical solution of the optical Bloch equations.
Large-detuning BCF tests in He*.
Chirped BCF slowing.
2. Four-color polychromatic forces
a.
b.
Numerical modeling of the excited-state fraction.
Comparison with BCF and pulse trains.
3. Progress on deflection and slowing of molecules
a.
b.
Plans for BCF deflection and slowing of a CaF beam.
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.
b
a
b
• 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 Na2 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.
• Pexcited 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 375g detuning at 2/9 the power!
Comparison with pulse trains
Imbalanced pulse train, identical phases
Imbalanced pulse train, alternating phases
Accumulating atomic phase shift
• 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 Yatsenko1 (Na2), Meschede2 (Cs).
• Stimulated forces from tailored fsec pulse trains may be promising, especially for cooling (A. Derevianko3).
Voitsekhovich, M. V. Danilelko, … , and L. P. Yatsenko, JETP Lett. 59, 408 (1994).
2A. Goepfert, I. Bloch, …, and D. Meschede, Phys. Rev. A 56, R3354 (1997).
3E. Ilinova and A. Derevinko, Phys. Rev. A 86, 023417 (2012).
1V.S.
Topics
1. The optical bichromatic force
a.
b.
c.
d.
π-pulse model for a two-level system.
Numerical solution of the optical Bloch equations.
Large-detuning BCF tests in He*.
Chirped BCF slowing.
2. Four-color polychromatic forces
a.
b.
Numerical modeling of the excited-state fraction.
Comparison with BCF and pulse trains.
3. Progress on deflection and slowing of molecules
a.
b.
Plans for BCF deflection and slowing of a CaF beam.
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 nearcycling transitions, with Franck-Condon
factor of 0.99 for the (0-0) band of AX,
and 0.999 for BX!

2 +

A 21/2, N =1 or B  , N =0
J =1/2, F =0,1, (+) parity
606.3 nm or 530.96 nm
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/cm2, velocity range
is150 m/s.
Remaining Problem: Hyperfine structure
and unresolved m sublevels.
J =3/2
X 2 , N =1
+
J =1/2
F =2
F  =1
48.9
24.2
F =0
-22.6
F =1
-98.3 MHz
Finding an effective two-level system
The N   1  N   0 transition is rotationally
closed, but has several non-participating (F, mF)
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 Q11(0.5)/RQ21(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.
2 +
A 21/2 or B 

F =1
J =1/2(–), N =1
F =0
F =1
m = -1
0
1
30.5 MHz
X 2 , N =0, J =1/2
+
F =0
0
-91.5 MHz
Detailed evaluation of option (3) with d / 2 =250 MHz predicts Dv ≈ 150 m/s with a single
vibrational repump for A↔X, Dv ≈ 100 m/s with only rotational repumping for B↔X.
For details, see M. A. Chieda and E. E. Eyler, Phys. Rev. A 84, 063401 (2011).
CaF supersonic beam
Beam source: Similar to Field,
Hinds groups, a laser-ablated Ca
plume is entrained in a supersonic
jet of He/SF6 or Ar/SF6.
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 DL100 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 singlemode 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.
DL100
TA (1.5W)
PPLN
B 2 +
v=1
v=0
531
A 2
585
605
X 2 +
X 2 +
BCF
Detection
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.
2nd daughter
board (DAC,
ADC, phasesensitive
detector, etc.)
DDS/arbitrary
waveform generator
(up to 180 MHz clock)
PIC32MX250F128D
200 MHz differential
amplifier
For more, see http://www.phys.uconn.edu/~eyler/microcontrollers/ , also E. E. Eyler, to be published.
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.
Tablet
SPI
Microcontroller
SPI
35-4000
MHz
frequency
synthesizer
35-4000
MHz
frequency
synthesizer
Loop filter
rf switch,
HMC284
Loop filter
7th-order
low-pass
filter, LFCNxxx
15 dB amp,
GVA-62+
SPI
7th-order
low-pass
filter
Digital step
attenuator,
DAT-xx-SP+
Secondary output
Main output
Summary
• The bichromatic 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 Dv > 150 m/s with BCF.
• Homemade instrumentation is well-suited to general laser lab
use.
Estimated BCF parameters for CaF
Bichromatic detuning
Deceleration
d / 2
a
250 MHz
1.4 × 106 m/s2
Bichromatic velocity range
Dvb
150 m/s
BCF slowing time
Tb
108 m s
Loss time
Tloss
14 m s
Loss-limited velocity range
Dvloss
19.4 m/s
Optimal irradiance
Ib
60 W/cm2
Ratio of BCF to rad. force
Fb : Frad 12.4
These values are for Q11(0.5) of AX without vibrational
repumping.With one repump laser, Dvloss exceeds Dvb.
For BX , Dvloss is larger by at least a factor of five.
Experimental tests
now underway!
For more details on AX, see M. A. Chieda and E. E. Eyler, Phys. Rev. A 84, 063401 (2011).
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 grad) is 2.3×107 m/s2,
yielding Dv = 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 = 154g (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).
A typical radiative-force beam slower
• This “Zeeman slower” at the University of Manchester loads a
magneto-optical trap (MOT).
• Limited velocity range is compensated by a z-dependent Zeeman shift
in a tapered solenoid coil.
• Long path necessitates laser collimation and/or magnetic focusing.
From http://es1.ph.man.ac.uk/AJM2/AJM.htm
UConn bichromatic force decelerator for He*
Bichromatic detuning δ = 2π fAOM
Doppler shifts ±2Δ
Typical results from the UConn
He* decelerator
Without BCF
With BCF
Difference
• In these tests, at most 20% of the atoms within range Dv can be slowed.
• Caused by small size of laser beam, needed for tests at very large
detunings d.
M. A. Chieda and E. E. Eyler, to be published (2012),
Upper limits of static BCF slowing
Non-directional!
• 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!
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 104 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.
Tablet, with
scrolling
parameter list
and pop-up
keypad
5-byte packets,
command+data
USB
USB
Text strings for display
PIC32MX250
microcontroller
Non-volatile
parameter storage
(EPROM emulation
in program memory)
Parallel I/O, timers,
10-bit ADCs
SPI
Touchscreen
entry?
Slider
changed?
Toggle selection
or display pop-up
keypad
Modify current
parameter
Programmable I/O:
ADCs, DACs, PLLs,
DDS chips, etc.
Optional rotary encoder
knob, serial LCD
display
Serial I/O and
external
interrupts
Apparatus for chirped helium deceleration
Toptica DL100 lasers produce about 40 mW in each bichromatic beam pair without
amplification, adequate for a BCF detuning of 74g or 120 MHz.
AOMs
To He*
beam
apparatus
Lasers
Homemade rf frequency
synthesizers
Frequency locking and
beam conditioning
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).