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

• 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 d /p >> radiative decay rate γ=1/τ.

• If relative phase = p / 2, after each radiative decay the chance of excitation from the right is 0.75 Force is directional.

w0 d w0 d

v

p / dp / d

The left-hand and right-hand beat notes are time-reversed images of one another, so the BCF:

• Is very tolerant of deviations from p-pulses.

• Is not affected by moderate Doppler shifts kv, which do not break this symmetry!

• Upper velocity limit: is grossly disrupted if kv ~ W0, , leading to a velocity range of Dv d /k.

• Has a huge range compared to Dv g /k for FRad!

BCF magnitude and velocity range

But the atom spends ¼ time in thewrong (accelerating) cycle, so:

B, ideal2 2

.P k k

Ft

B

kF

2 2Rabi 0 ( )kv

Given two momentum transfersper stimulated cycle,

B

Rad

2 and thus, .

F

F

g

e

Numerical solution of OBEs

Force profiles are calcu-lated for 4He, using code based on previous ver-sions by Metcalf, Grimm, Solomon groups.

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

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 p / (2 wrecoil), 5.9 ms for He*.

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

3 2 vs. 4 .

0 + kv 0 - kv

v

Application to metastable He* atoms

For He 23S 23P at 1083 nm, if d = 154 = g 250 MHz × 2p,

• Required laser power from each direction = 23.8 W/cm2.

• Beat note period is p /d = 2 ns, much faster than t = 1/g = 98 ns.

• FB = 3.1 × 10-19 N 100 FRad.

• Velocity range is Δv = d /2k= 135 m/s, still much smaller than beam velocity of ~1000 m/s.

• Slowing time is Δt = 5.8 μs, independent of velocity range.

UConn bichromatic force decelerator for He*

DL100Seed Laser

Nufern 7WFiber Amp

He*Source

Detector

AOM

l/4

l/4

l/4PBC

PBC

PBC CouplerCollimator

50/50Splitter

PhaseDelay

D

a

a+2D

a-2D

AO

M

AO

M

D

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 UConnHe* decelerator

• 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.

With BCFWithout BCF

Difference

M. A. Chieda and E. E. Eyler, to be published (2012),

Upper limits of static BCF slowing

g

e

• 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 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!

Chirped slowing of He*

Initial tests: Detuning of 74g gives a velocity range of only 1.57 d /k = 200 m/s, but the lasers are linearly chirped in about 20-40 ms to follow the changing Doppler shift.

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 74g or 120 MHz.

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),

Direct laser slowing and cooling of moleculesA 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 AX and BX in CaF are near-cycling transitions: rotationally closed, with Franck-Condon factor of 0.99 for the (0-0) band of AX, and 0.999 for BX!

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 × 2p (30×natural width), needs I ~ 60 W/cm2; velocity range is Dv = 150 m/s.

Remaining Problem: Hyperfine structure and unresolved m sublevels.

-98.3 MHz

-22.6

24.248.9F

=2F

=1

F =1

J =3/2

J =1/2, F

=0,1, (+) parity

F =0X 2+, N

=1

606.3 nm or 530.96 nm

J =1/2

A 21/2 or B 2+, N=0

Finding an effective two-level system

The 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 BX the upper state also has a J =3/2 component, but the spin-orbit splitting of 2.06 GHz is >> d.

0 1N N

J =1/2(–), N=0

F =0

F =1

0

10

F =1

-91.5 MHz

m = -1

F =0

30.5 MHz

X 2+, N =0, J

=1/2

A 21/2, or B 2+,

For more details on AX, see M. A. Chieda and E. E. Eyler, Phys. Rev. A 84, 063401 (2011).

Estimated BCF parameters for CaF

These values are for Q11(0.5) of AX without vibrational repumping.With one repump laser, Dvloss exceeds Dvb.

For BX , Dvloss is larger by at least a factor of five.

Bichromatic detuning d / 2p 250 MHzDeceleration a 1.4 × 106 m/s2

Bichromatic velocity range Dvb150 m/s

BCF slowing time Tb108 ms

Loss time Tloss14 ms

Loss-limited velocity range Dvloss19.4 m/s

Optimal irradiance Ib60 W/cm2

Ratio of BCF to rad. force Fb : Frad12.4

Experimental tests now underway!

Test of BCF in a multi-level system:He 2S-2P with pi-polarized light

23S, J=1

23P, J’=2

23P, J’=1

Transition Strengths in units of from NIST Atomic Database

15

110

215

110

-1 0 +1

-1 0 +1

-1 0 +1 +2-2

16

16

f1,1=0.29958

f1,2=0.17974

BCF in a system with multiple mj levels

600 800 1000 1200 1400 1600 1800 2000-0.2

0.0

0.2

0.4

0.6

0.8

1.0-polarized light, = 2*300MHz

Pop

ulat

ion

(arb

)

Velocity (m/s)

600 800 1000 1200 1400 1600 1800 2000-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-polarized light, = 2*300MHz

Pop

ulat

ion

(arb

)

Velocity (m/s)

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

Low-cost 531 nm BCF lasers

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.

Þ 5-15 mW expected at 531 nm.

Detection laser: 585 nm cw dye laser (existing).

531

B 2S+

X 2S+

BCF

585

A 2P

X 2S+

Detection

v = 1v = 0

605

DL100 TA (1.5W)

PPLN

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; BX 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

|a

|bΔ 𝐸=ℏ𝜔

Laser

�⃗� ,𝜔𝐿

Scatteredphoton

Δ �⃗�=ℏ�⃗�

Typically, dv = 1–9 cm/s per photon scattered.

Rad sc

sc Rad

In saturation, 2, and 2

F k

F k

g = 1/t

Metastable helium energy levels

11S0

23S1

23P2

23P1

23P0

62.6 nm

1083 nm

𝜏=8000 s

2.2912 GHz

29.617 GHz

2sat

2

Bich sat

98 ns

1.62 MHz2

0.17 mW/cm

3 , each beam.

I

I I

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).

4lMHzx

A O M

P BC

, 2

,

2a

, a ckv

, a ckv

Image from M. Partlow, Ph.D. thesis, Stony Brook

Producing the frequency shiftswith acousto-optic modulators