Slowing and cooling of He* and CaF
with optical bichromatic forces
M. A. Chieda and E. E. Eyler
Physics Department, University of Connecticut
Supported by the National Science Foundation
BCF π-pulse model
/
/
w0  
w0  
v
• In each direction, two beams shifted by rf frequencies ± form
a traveling train of beat notes with carrier w0.
• Choose the optical power so that each beat note has an area of
approximately  , inverting a 2-level system.
• Synchronized  -pulses lead to coherent momentum transfer at
rate  / >> radiative decay rate γ=1/τ.
• If relative phase =  / 2, after each radiative decay the chance
of excitation from the right is 0.75  Force is directional.
BCF magnitude and velocity range
Given two momentum transfers
per stimulated cycle,
FB, ideal 
But the atom spends ¼ time in the
wrong (accelerating) cycle, so:
FB 
DP 2 k 2 k


.
Dt  

k

and thus,
The left-hand and right-hand beat notes are timereversed images of one another, so the BCF:
FB
2

.
FRad  g
 e
• Is very tolerant of deviations from -pulses.
• Is not affected by moderate Doppler shifts kv,
which do not break this symmetry!
• Upper velocity limit: WRabi  W0 2  (kv)2 is
grossly disrupted if kv ~ W0, , leading to a velocity
range of Dv   /k.
• Has a huge range compared to Dv  g /k for FRad!
 g
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  vs. W   4  .
The velocity range is Dv  /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 wrecoil), 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
w0   + kv
w0   - kv
For He 23S  23P at 1083 nm, if  = 154g  250 MHz × 2,
• Required laser power from each direction = 23.8 W/cm2.
• Beat note period is  / = 2 ns, much faster than t = 1/g = 98 ns.
• FB = 3.1 × 10-19 N  100 FRad.
• Velocity range is Δv =  /2k= 135 m/s, still much smaller than beam
velocity of ~1000 m/s.
• Slowing time is Δt = 5.8 μ s, independent of velocity range.
UConn bichromatic force decelerator for He*
Bichromatic detuning δ = 2π fAOM
Doppler shifts ±2Δ
Microcontroller-based lab instruments
• The project uses numerous homemade timing/control/frequency generation circuits.
• We now use 32-bit Microchip PIC processors with a USB interface to an Android
tablet for graphics and user input.
• Designs include a ramp/timing generator (pictured), temperature controller, and rf
frequency synthesizer/offset lock circuit.
USB interface
Dual 12-bit and
16-bit DACs
Touch-screen tablet controls
For more, see http://www.phys.uconn.edu/~eyler/microcontrollers/ , also E. E. Eyler, RSI 82, 013105 (2011).
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 .
M. A. Chieda and E. E. Eyler, to be published (2012),
Upper limits of static BCF slowing
 e
Non-directional!
 g
• Results at 450 MHz are consistent with a 1-D random walk.
• Mechanism 1: Cumulative dephasing due to left-right 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
, cannot avoid phase differences along beam path due to beat note length of 10-20 cm.
• Both effects are predicted to be large when  > 250 g!
Chirped slowing of He*
Initial tests: Detuning of 74g gives a velocity range of only 1.57  / k = 200 m/s, but the
lasers are linearly chirped in about 20-40 m s to follow the changing Doppler shift.
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
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  / k = 370 m/s
Simulations match well, and clearly show that efficient slowing to rest is feasible if rf
phasing is improved and detuning  is slightly increased.
M. A. Chieda and E. E. Eyler, to be published (2012),
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).
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).
Level scheme for cw slowing of CaF
Both AX and BX in CaF are near-cycling
transitions: rotationally closed, with FranckCondon 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  = 250 MHz × 2 (30×natural width), needs
I ~ 60 W/cm2; velocity range is Dv = 150 m/s.
2 +
J =1/2, F =0,1, (+) parity
606.3 nm or 530.96 nm

J =3/2
X 2 , N =1
+
J =1/2
Remaining Problem: Hyperfine structure and
unresolved m sublevels.

A 21/2 or B  , N =0
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   0  N   1 transition is rotationally
closed, but has several (F, mF) levels that cannot
be optically pumped with circular polarization.
Three approaches are possible:
(1) Live with it. The BCF is zero or positive for
every level. If rapid level mixing is
maintained, the net force is still large.
(2) Alternate BCF pulses (s - polarization) with
optical pumping (s +) for state selection.
(3) Switch to the Q11(0.5)/RQ21(0.5) branch
(shown). A rotational repump laser is needed,
but the four transitions shown all have the
same line strength. For BX the upper state
also has a J =3/2 component, but the spinorbit splitting of 2.06 GHz is >> .
2 +
A 21/2, or B  ,

F =1
J =1/2(–), N =0
F =0
F =1
m = -1
0
1
30.5 MHz
X 2 , N =0, J =1/2
+
F =0
0
-91.5 MHz
Estimated BCF parameters for CaF
Bichromatic detuning
Deceleration
 / 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).
Test of BCF in a multi-level system:
He 2S-2P with pi-polarized light
23P,
23P,
J’=1
J’=2
-2
-1
0
+1
-1
0
+1
1
10
2
15
1
6
23S, J=1
-1
Transition Strengths in units of
f1,2=0.17974
+2
1
10
1
5
1
6
0
f1,1=0.29958
+1
𝜉′𝐽′ 𝑑 𝜉𝐽
2
from NIST Atomic Database
BCF in a system with multiple mj levels
Population (arb)
1.0
s-polarized light,  = 2*300MHz
0.8
0.6
0.4
0.2
0.0
-0.2
600
800
1000
1200
1400
1600
1800
2000
Velocity (m/s)
Population (arb)
1.0
0.8
-polarized light,  = 2*300MHz
0.6
0.4
0.2
0.0
-0.2
600
800
1000
1200
1400
1600
1800
2000
Velocity (m/s)
From M. A. Chieda and E. E. Eyler, Phys. Rev. A 84, 063401 (2011).
Low-cost 531 nm BCF lasers
DL100
Main BCF laser: Toptica DL100 external-cavity
diode laser at 1062 nm, amplified to ~1.5 W
with a tapered amplifier laser diode, 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 cw
laser!) with a PPKTP waveguide doubler
 All components have arrived.
5-15 mW expected at 531 nm.
PPLN
B 2 +
v=1
v=0
531
A 2
585
605
X 2 +
X 2 +
Detection laser: 585 nm cw dye laser (existing).
TA (1.5W)
BCF
Detection
Summary
• The BCF can be up to 300 times larger than the radiative force,
with a much wider velocity range.
• Upper limit is set by by dephasing of Rabi cycling and of rf
beat notes between the counterpropagating beams.
• Chirped BCF slowing can slow a He* beam to rest.
• For molecules, limitations due to “dark state” decay are
reduced greatly.
• CaF has two near-cycling systems; BX will be used for tests.
Expect Dv > 150 m/s with one repump.
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).
• Applicable to 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 circumvents rf phase problems.
Cooling and slowing atoms by photon recoil
Laser
|b
Δ𝐸 = ℏ𝜔
Δ𝑝 = ℏ𝑘
𝑘, 𝜔𝐿
|a
Scattered
photon
FRad  kg sc
In saturation, g sc  g 2, and FRad  k g 2
Typically,  v = 1–9 cm/s per photon scattered.
g = 1/t
Metastable helium energy levels
2 3 P0
29.617 GHz
2 3 P1
2 3 P2
2.2912 GHz
1083 nm
2 3 S1
𝜏 = 8000 s
t  98 ns
g
 1.62 MHz
2
I sat  0.17 mW/cm 2
2
I Bich
62.6 nm
11S0
 
 3I sat   , each beam.
g 
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).
Producing the frequency shifts
with acousto-optic modulators
AOM
w 
w
  x MHz
w

4
w  wa -  2
PBC
w , w  2
w  , w -
w , w    wa    kvc
w -  , w    wa   - kvc
Image from M. Partlow, Ph.D. thesis, Stony Brook