Transcript BCF OSU 2011.pptx

Prospects for rapid deceleration of
diatomic molecules with optical
bichromatic forces
M. A. Chieda and E. E. Eyler
Physics Department, University of Connecticut
Supported by the University of Connecticut, the Air Force Office of
Scientific Research (MURI), and the National Science Foundation
Topics
1. Introduction to the optical bichromatic force
(BCF).
2. Example: deceleration of a metastable atomic
He* beam.
3. Plans for deceleration and deflection of CaF, SrF,
and other small molecules.
Cooling and slowing atoms by photon recoil
Laser
|b
Δ𝐸 = ℏ𝜔
Δ𝑝 = ℏ𝑘
𝑘, 𝜔𝐿
|a
Scattered
photon
FRad  k sc
In saturation,  sc   2, and FRad  k  2
Typically, d v = 1–9 cm/s per photon scattered.
 = 1/t
BCF π-pulse model
a  d
a  d

a  d
a  d
d

d
• In each direction, two plane waves shifted by ±d form an
amplitude-modulated traveling wave with beat notes.
• Power is chosen so that each beat note has an area of
approximately  , true if  R  4 d .
• Each  -pulse drives one half-cycle of a 2-level system.
• Synchronized  -pulses lead to coherent momentum transfer,
rate >> radiative decay rate γ=1/τ.
π-pulse synchronization
-pulse train
-pulse train
Delay
Stimulated
k
Emission
Excitation k
FB, ideal
P 2 k 2 kd



.
t  d

Optimal delay  8 d , or   2 .
The atom spends ¼ time in the
wrong excited state cycle, so:
FB 
kd

Numerical solution of OBEs
Code provided by Harold Metcalf’s
group, based on Grimm and
Solomon’s.
BCF Profile, r=1.2d
100
250MHz
Force (k)
80
60
Sharp edges make cooling possible.
40
Predicts a different optimum Rabi
frequency than π-pulse model:
20
0
-150
-100
-50
0
50
100
150
Velocity (m/s)
Calculated force profile for 4He
with d = 250 MHz.
Velocity range is v d /2k = 135 m/s.
Ω𝑅 = 𝜋4δ
Ω𝑅 =
3
δ
2
π-pulse model
OBE solutions
Comparison of optical forces
Force
kd
FB 
v   d 2k

FRad 
FDipole
Velocity Range
k
2
v    k
k 2 I 0

sin(2kz )
8d I SAT
Sensitive to
Doppler Shift
Typical BCF δ ~ 150γ
For more, see H. Metcalf, Entropy exchange in laser cooling, Phys. Rev. A 77, 061401 (2008).
Application to metastable helium beams
v
0  d + kv
0  d - kv
For He 23S  23P at 1083 nm, if d = 154  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/ = 98 ns.
• FB = 3.1 × 10-19 N  100 FRad.
• Velocity range is Δv = d /2k= 135 m/s.
𝑚Δ𝑣 𝑚(𝛿 𝑘) 𝜋 2
=
=
• Slowing time is Δ𝑡 =
𝐹
ℏ𝑘𝛿 𝜋
𝜔𝑟
ℏ𝑘 2
𝜔𝑟 =
2𝑚
Δt = 5.8 μs for helium, independent of velocity range.
Metastable helium source
Based on a design by Kawanaka with modifications as
proposed by Mastwijk. Same source as Metcalf Group
with minor external modifications.
Metastable helium source output
He Metastable Source Velocity Distribution
0.18
0.7
Metastable Helium Source TOF Spectrum
0.16
0.14
0.6
Signal (arb)
0.12
Population (arb)
0.5
0.10
0.08
0.06
0.4
0.04
0.02
0.3
0.00
0.0000
0.0005
0.0010
0.0015
0.0020
Time (s)
0.2
0.1
He* flux
0.0
400
600
800 1000 1200 1400 1600 1800 2000 2200 2400
Velocity (m/s)
6 × 1013 atoms
sr∙s
He* fraction = 5x10-5
UConn bichromatic force decelerator
Bichromatic detuning δ = 2π fAOM
Doppler shifts ±2Δ
Producing the frequency shifts
with acousto-optic modulators
AOM
 d

d  x MHz


4
  a  d 2
PBC
 ,   2d
 d ,  d
 ,   d  a  d  kvc
  d ,   d  a  d  kvc
Image from M. Partlow, Ph.D. thesis, Stony Brook
Microcontroller-based RF frequency synthesizer
In-house designs offer precise and agile control of
frequencies over one-octave ranges, selectable from
50 MHz to 3 GHz.
Used for driving AOMs and offset-locking of lasers
using beat notes measured with a photodiode.
Apparatus for testing helium deceleration
Typical results from the UConn
He* decelerator
Without BCF
With BCF
Difference
• In these tests, at most 20% of the atoms within range v can be slowed.
• Caused by small size of laser beam, needed for tests at very large
detunings d.
BCF “deceleration” at δ = 2π  450MHz
Failure of the adiabatic approximation?
800 MHz
Prospects for direct laser slowing
and cooling of molecules
Ordinary laser slowing/cooling requires a quasi-cycling transition. OH, CH, etc. are
candidates. Best are CaF and SrF: visible-light transitions; nuclear spin I of just ½.
The DeMille group at Yale recently achieved transverse slowing of SrF,1 using multiple
vibrational and hyperfine repumping lasers as shown in their figure 1:
1E.S.
Shuman, J.F. Barry, and D. DeMille, Laser cooling of a diatomic molecule, Nature 467, 820 (2010).
Results from Yale for
transverse cooling of SrF
• Initial beam: cryogenic beam source
with v ~ 200 m/s, collimated to a
transverse spread v ~ 1.9 m/s.
• An extended transverse cooling
region is used, with imaged LIF for
detection.
• Doppler (left) and Sisyphus (right)
cooling and heating are seen as
detuning (blue/red) and other
parameters are varied.
Figure from E.S. Shuman, J.F. Barry, and D. DeMille, Laser cooling of a diatomic molecule, Nature 467, 820 (2010).
Level scheme for CaF
Level diagram for CaF shows a near-cycling
transition: rotationally closed, with FranckCondon factor of 0.99 for the (0-0) band.
The BCF avoids excessive radiative cycling:
system is in the upper state ~3/14 of the
time, and there are many BCF cycles per
radiative cycle.
If d = 250 MHz × 2 (30 × natural width),
needs I ~ 60 W/cm2; velocity range is v =
150 m/s.
Velocity change of v ~ 40 m/s without
vibrational loss, much more with a repump.
Remaining Problem: Hyperfine structure
and unresolved m sublevels.
A 21/2
J =1/2, F=0,1
N =0
606.3 nm
J =3/2
N =1
X 2
+
F =2
F =1
48.9
24.2
F =0
-22.6
F =1
-98.3
J =1/2
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) branch (shown). A
rotational repump laser at 609 nm is needed, but
the four transitions shown all have the same line
strength.
1E.S.
Shuman, J.F. Barry, and D. Demille, Laser cooling of a
diatomic molecule, Nature doi:10.1038/nature09443 (2010).
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
Bichromatic Detuning Asymmetry
Bichromatic Force Magnitude (hk)
250
Asym = 0d
Asym = 0.1d
Asym = 0.2d
Asym = 0.3d
200
150
100
50
0
-150
-100
-50
0
Velocity (/k)
50
100
150
BCF in a system with multiple mj levels
Population (arb)
1.0
s-polarized light, d = 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, d = 2*300MHz
0.6
0.4
0.2
0.0
-0.2
600
800
1000
1200
1400
Velocity (m/s)
1600
1800
2000
Single-pulse BCF deflection or slowing
• Can very high detunings be used, with long-pulsed lasers (Nd:YAG or
flashlamp-pumped)? Is limit for d the same as for atomic He?
• No repumping: just use the force available from a single pulse,
comparable to a single radiative period (19 ns × 14/3 for CaF).
• Applicable to nearly any molecular beam.
• Acceleration of CaF with a detuning of 4 GHz (480 Grad) is 4.5×107 m/s2,
yielding v = 8 m/s for one radiative period.
• Can easily provide a deflected beam in a pure quantum state for
spectroscopy or scattering experiments.
Summary
• The BCF is hundreds of times larger than the
radiative force with a wider velocity range.
• It appears there is an upper limit to the bichromatic
force.
• Application to molecules looks quite promising,
especially for near-cycling systems.
• Transverse deflection of molecules should be
possible even for non-cycling levels.
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).
Metastable helium energy levels
2 3 P0
2 3 P1
2 3 P2
29.617 GHz
𝜏 = 98 ns
2.2912 GHz
𝛾
= 1.62 MHz
2𝜋
1083 nm
2 3 S1
62.6 nm
11S0
𝜏 = 8000 s
𝐼𝑠𝑎𝑡 = 0.17 mW cm2