RAPID COMMUNICATIONSPHYSICAL REVIEW A 89, 021401(R) (2014)

Prospects for narrow-line cooling of KRb molecules in the rovibrational ground state
J. Kobayashi,* K. Aikawa,† K. Oasa,‡ and S. Inouye
School of Engineering, University of Tokyo, Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan(Received 13 November 2013; published 5 February 2014)
We propose and experimentally investigate a scheme for narrow-line cooling of KRb molecules in therovibrational ground state. We show that the spin-forbidden X 1 + → b 30+ transition of KRb is well suitedfor realizing narrow-line laser cooling of molecules because it has highly diagonal Franck-Condon factors
and a narrow line width. To confirm the prediction, we performed optical and microwave spectroscopy ofultracold 41 K87 Rb molecules, and determined the line width [2π × 4.9(4) kHz] and Franck-Condon factors
for the X 1 + (v  = 0) → b 30+ (v  = 0) transition [0.9474(1)]. This result opens the door towards all-opticalproduction of polar molecules at sub-microkelvin temperatures.
DOI: 10.1103/PhysRevA.89.021401

PACS number(s): 37.10.Mn, 33.40.+f, 33.20.Vq

Recently significant progress has been made in the fieldof cold molecules. Innovative ideas have been implemented
one after another, making cold molecules an attractive newtool to test fundamental physics [1–3]. However, in spiteof serious efforts by many groups, a quantum degenerate
gas of polar molecules remains an elusive goal. The JILA
group has obtained results closest to this goal by combining
magneto-association with stimulated Raman adiabatic passage(STIRAP), and they attained a phase-space density on theorder of 0.1 [4]. In that experiment, they were limited by
the magneto-association efficiency, which was determined by
the density overlap of the rubidium and potassium clouds [5].
Motivated by these results, we studied the possibility oflaser cooling bi-alkali-metal molecules in the rovibrational
ground state. Typically laser cooling of molecules is difficult
because molecules have vibrational and rotational degrees of
freedom. Recently, however, several groups succeeded in laser
cooling molecules by selecting special types of molecules(such as SrF [6], YO [7], and CaF [8]) and constructing
a quasicycling transition with minimal increase in laser
complexity. The solution to the problem was to find an opticaltransition with highly diagonal Franck-Condon factors [9]. We
have now observed such a transition in KRb: one of the mostpopular species in the field of cold molecules.
We claim that the intercombination transition X 1 + (v =0) → b 30+ (v  = 0) of KRb is well suited for realizing
narrow-line cooling of the ground-state molecule because it
has (i) near-unity spatial overlap between the ground andexcited vibrational wave functions, (ii) a narrow line width,and (iii) negligible leakage to other (i.e., triplet) ground states.
To test our expectations, we experimentally investigated
the rovibrational spectrum of ultracold 41 K87 Rb molecules
using STIRAP and RF spectroscopy. From the experimental
data, we determined the natural line width of b 30+ (v  =0) to be  = 2π × 4.9(4) kHz while the Franck-Condon
factor for the X 1 + (v  = 0) → b 30+ (v  = 0) transition wasestablished as 0.9474(1) [10]. Based on these values, weconclude that 41 K87 Rb is an ideal system for sub-microkelvinthree-dimensional laser cooling of molecules. By combining*

kobayashi@atomtrap.t.u-tokyo.ac.jp
Present address: Universität Innsbruck, 6020 Innsbruck, Austria.
‡
Present address: Toshiba Corporation, Tokyo 105-8001, Japan.
†

1050-2947/2014/89(2)/021401(5)FIG. 1. (Color online) Potential energy curves for KRb [12]. The
curves for X 1 + and b 3 states are quite similar (highlighted in red),suggesting highly diagonal Franck-Condon factors for transitions
between these two states. The decay of the v  = 0 level of theb 30+ state into the a 3  + state is strongly suppressed because of theextremely small transition dipole moments [13].

this narrow-line cooling with photoassociation and STIRAP,
cooling of polar molecules to the sub-microkelvin temperatures is possible by all-optical means [11].
Figure 1 shows the potential energy curve of KRb as
a function of internuclear separation. The potential energy curves of X 1 + and b 3 look surprisingly similar,
which suggests highly diagonal Franck-Condon factors for
X 1 + → b 30+ transitions. Furthermore, radiative decay
from b 30+ (v  = 0) into the dissociative continuum of thea 3  + triplet ground state is strongly suppressed because of
the small electronic transition dipole moment (TDM) of thea 3  + -b 30+ transition at the bottom of the b 30+ potential[d = 0.006(4) ea0 , where e is the electron charge and a0 is theBohr radius] [13,14]. The calculated decay rate of the v  = 0
level of the b 30+ to both the continuum and bound states ofa 3  + is on the order of 1 Hz, which does not play a major rollunless narrow-line cooling is applied for more than 100 ms.
To test our prediction, we performed an experiment involving ultracold KRb molecules. Our experimental procedure for
producing KRb molecules in the rovibrational ground stateis described in detail in Ref. [11]. In brief, KRb molecules

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J. KOBAYASHI, K. AIKAWA, K. OASA, AND S. INOUYE

J=2
J=1
J=0

X 1Σ+, v = 0
J=1
J=0

(b)
AC-Stark shift (kHz)(a) b 3Π0+ , v = 0

60

J = 1→0

PHYSICAL REVIEW A 89, 021401(R) (2014)

J = 0→1 J = 1→2(a)b 3Π0+ , v = 0

40
20
0

J=1
~0.02 %

1028.7 nm

-20

63 %

-40

v

-60

Microwave

5%

410 412 414 416 418 420 422
Laser frequency - 291000 (GHz)X 1Σ+, v = 0

J=0FIG. 2. (Color online) (a) Schematic of double-resonance spectroscopy for locating the |X,0-|b,0 transition. The ac Stark shift
induced by a laser beam tuned close to the |X,0-|b,0 transition was
detected by the microwave transition between the rotational levels in
the |X,0 state. (b) The observed ac Stark shifts. The measured shifts
exhibited a dispersive feature characteristic of ac Stark shifts. The
solid curve is a fit to the data for extracting resonance frequencies.

J=1

1, J = 0, 2

J=2

(b)
Ion Counts (arb. units)

in the X 1 + (v = 91,J = 0) state (or |X,91,0 state, forshort) were made by photoassociation in a magneto-opticaltrap (MOT) of 87 Rb and 41 K atoms. Next, the molecules in
the |X,91,0 state were transferred to the |X,0,0 state by
STIRAP via the intermediate state |(3)1 + ,41,1 by using twolasers of wavelength 875 and 641 nm. The use of 5 ns pulses
from a tunable dye laser and a micro-channel plate provides
for vibrationally selective detection by resonance-enhanced
multiphoton ionization (REMPI).
Until now, the X 1 + (v  = 0) → b 30+ (v  = 0) transition(or |X,0-|b,0 transition, for short) of KRb has not been
observed. The transition wavelengths predicted by ab initio
calculations range from 1026.4 to 1036.9 nm [12,15–17],
which is nine orders of magnitude larger than the expectednatural line width. To overcome this uncertainty, we looked fora dispersive signal rather than an absorptive signal because thesignal falls off as 1/ instead of 1/2 (where  is the detuningfrom resonance). We monitored the microwave transition
frequency between rotational levels (|X,0,0 and |X,0,1), andlooked for the ac Stark shift induced by near-resonant light,
as described in Fig. 2(a). Employing this method resulted in
the observance of three transitions |X,0-|b,0, |X,0-|b,1,and |X,0-|b31 ,0 with clearly resolved rotational structures,as shown in Fig. 2(b). Their transition wavelengths without
rotational energies were determined to be 1028.7397(7),1020.9746(7), and 1022.6870(7) nm, respectively, where theaccuracies were limited only by the accuracy of our wave
meter.
We determined the natural line width and Doppler broadening of the |X,0-|b,0 transition by directly exciting moleculeswith a narrow-line width laser [18]. Figure 3(a) shows aschematic of the transitions examined by the experiment.
Assuming almost diagonal Franck-Condon factors, prolonged
excitation optically pumps molecules into different rotational
states (in this case, mostly to |X,0,2). The number ofmolecules in the |X,0,2 state was detected by REMPI, which
is sensitive to the rotational state [19]. First, we saturated thetransition using a laser beam with an intensity three orders ofmagnitude greater than the saturation intensity. Here power
broadening of the transition was larger than the hyperfine

32 %

a 3Σ+

35
30
25
20
15
10
5
0

100

200 300 400 500
Pulse Width (μs)

600FIG. 3. (Color online) (a) Schematic of optical pumping spectroscopy of the |b,0,1 state (see text). The branching ratios for transitions from the |b,0,1 state were calculated using the Hönl-London
and Franck-Condon factors. Most of the molecules in the |X,0,0 state
were optically pumped into the |X,0,2 state by the 1028.7 nm laser,which was resonant with the transition between |X,0,0 and |b,0,1.
Subsequently molecules in |X,0,2 were selectively detected byresonance-enhanced multiphoton ionization based on their rotational
state [19]. (b) Measurement of the time constant of optical pumping inthe saturated regime. Ion counts of the molecules in the |X,0,2 state
were measured as a function of the pulse duration of the opticalpumping laser. The measured time constant for optical pumping[95(7) μs] was converted into the lifetime of |b,0,1 [32.5(24) μs]
using the branching ratios shown in panel (a).

splitting in the ground state, which is ∼ 2π × 5 kHz for|X,0,0 [20,21]. From the optical pumping time constant,determined as shown in Fig. 3(b) and the branching ratios
shown in Fig. 3(a), we obtained the lifetime and natural line
width of the |b,0,1 state, which was 32.5(24) μs and 2π ×4.9(4) kHz, respectively. Second, we measured the moleculetemperature by observing the optical pumping spectrum inthe nonsaturating regime. The typical temperature and mean
velocity were 130 μK and 130 mm/s, respectively. The
observed velocity is about 43 times the recoil velocity of the|X,0-|b,0 transition.
Franck-Condon factors are sensitive to rotational constantsbecause both are directly related to the equilibrium internuclear
distance. To exploit this, we performed detailed analysis
of |b,0,0, |b,0,1, |b,1,0, and |b,1,1 states by acquiring
hyperfine-resolved optical pumping spectra, as shown in Fig. 4.
We assigned the hyperfine structures based on the Hamiltonian
discussed in Refs. [20,21], which describes the interactions
between two atomic nuclear spins and the rotation of diatomic
molecules [22]. The potential energy curve for a ground-state
molecule was also refined using STIRAP spectra of the |X,1,0
and |X,1,2 states.

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Ion Counts (arb. units)

PROSPECTS FOR NARROW-LINE COOLING OF KRb . . .

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PHYSICAL REVIEW A 89, 021401(R) (2014)
TABLE II. Obtained parameters for molecular potentials of
X 1 + and b 30+ states. Similarity between the two potentials can beseen by the values obtained for a2 ,a3 , and re (see text). Only statisticalerrors are shown. For estimates on systematic errors, see text.

4 3,1,2 2 1

F=3 2 1 0

25
20
15
10

a2 (cm−1 Å−2 )a3 (cm−1 Å−3 )re (Å)V0 (cm−1 )

5
0

4

12
8
Frequency (MHz)16

FIG. 4. (Color online) Spectrum of the |b,0,1 state obtained by
optical pumping as described in Fig. 3(a). The horizontal axis shows
the frequency of the optical pumping laser relative to the leftmost
signal (which has been assigned a frequency of zero). The hyperfine
structure of the |b,0,1 state was thereby observed.

From the spectra, we determined vibrational and rotationalenergies, which are listed in Table I. The X-state values agree
well with the predictions of Ref. [23]. To calculate the FranckCondon factors, we determined the potential energy curves of
X and b states. We assumed that the potential energy curvesin the low energy region of X and b states could be written as
V (r) =nmax
an (r − re )n + V0 ,

(1)

n=2

where r is the internuclear distance. re (the equilibrium
distance), an , and V0 are the fitting parameters. Setting
nmax = 3 and fitting these curves to the experimental data, we
determined these parameters for X and b potentials, as listed
in Table II [24]. Because the difference in equilibrium distance
between X and b states (∼4.1 pm) is much smaller than theharmonic oscillator lengths for both potentials (∼80 pm), theFranck-Condon factors between these states are highly diagonal. Using the obtained potential energy curves, we determined
the Franck-Condon factors of|X,0-|b,0, |X,1-|b,0, and|X,v  2-|b,0 transitions to be 0.9474(1), 0.0500(1), and2.60(1) × 10−3 , respectively, as illustrated in Fig. 5 [25].
The model dependence of the Franck-Condon factors isimportant because it could be a major source of systematic
errors. In addition to the polynomial expansion shown in
Eq. (1), we also tried other fitting functions like the expanded

73.845(3)1095.3772(1)1091.93(1)73.936(3)1118.37(1)1116.26(1)2286.3(2)−1133.5(8)4.067792(5)02279.2(2)−906.5(1.5)
4.02698(2)9720.531(3)v=0Γ = 2π x 4.9(4) kHz

0.9474(1)E(v = 1) − E(v = 0) (cm−1 )B(v = 0) (MHz)B(v = 1) (MHz)b 3Π0+

X 1Σ+

b 30+

b 30+

Morse oscillator function [26] and the function adopted by the
Hannover group [27]. Surprisingly, the Franck-Condon factors
obtained by all these methods were nearly identical to eachother, well within the confines of statistical error. This factindicates that the shape of the potential around the equilibrium
point is not sensitive to the details of the model. We also
replaced the potential energy curve for the X state with that described in Ref. [23] and calculated the Franck-Condon factors,
but the difference was again smaller than the statistical error.
We now discuss using the X 1 + → b 30+ transition forrealizing narrow-line cooling of KRb molecules. The proposed
scheme is as follows. Ground-state KRb molecules at a few
hundred microkelvin are prepared by photoassociation in adual-species MOT followed by STIRAP. The cooling beam is
red-detuned from the |X,0,1-|b,0,0 transition, whereas therepumping beam is resonant with the |X,1,1-|b,0,0 transition. Both beams irradiate molecules from all six directions.
Because the cooling beam is red detuned, molecules should
predominantly scatter photons from the counterpropagating
beam; therefore their velocities are reduced. The actual spectraof the cooling and repumping beams must be optimized bothfor accessing all the hyperfine states and for increasing theranges of the capture velocity.
Several necessary conditions must be satisfied for coolingthe molecules. First, the cooling transition should be highly
closed. From the experimentally obtained Franck-Condon
factors, KRb molecules can scatter ∼ 1/2.60(1) × 10−3 ∼ 400
photons before being pumped into other vibrational levels.
This number is sufficiently large for capturing molecules inthis setup because the mean velocity of the initial cloud was∼ 43 times the recoil velocity.

TABLE I. Experimentally obtained rotational and vibrationalenergies for molecular potentials of X 1 + and b 30+ . The energy
difference between v = 0(J = 0) and v = 1(J = 0) states is givenby E(v = 1) − E(v = 0). The accuracy was limited by the accuracyof our wavemeter (∼ 100 MHz). B is the rotational constant. The
accuracy of the rotational transition frequencies is higher since
the measurement was done using narrow line-width lasers and astable optical cavity (see Ref. [18] for details). The value with thehighest accuracy (B for |X,0) was obtained by directly driving the
microwave transition.
X 1 +

X 1 +

v=0

v=1

v

2

FIG. 5. (Color online) Franck-Condon factors and natural line
width for X 1 + -b 30+ transitions. A cooling laser red-detuned fromthe |X,0,1-|b,0,0 transition and repumping laser resonant with the|X,1,1-|b,0,0 transition can form a highly closed cooling transition.

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PHYSICAL REVIEW A 89, 021401(R) (2014)

Second, the dark Zeeman substates, which are inevitably
formed in this (J  = 1 → J  = 0) type of rotationally closed
transition, should be eliminated. As described in Ref. [28],these dark states can be mixed with bright states by applying
a proper magnetic field such that the Larmor precession
frequency in the ground state nearly equals the natural line
width of the cooling transition. For the 41 K87 Rb molecule, thiscondition can be fulfilled by a magnetic field of about 4 G,
which is easily applied in the experiment.
Finally, the cooling transition should be sufficiently strong.
The natural line width obtained for the X 1 + → b 30+transition is 2π × 4.9(4) kHz; therefore, the thermal expansionof the molecular cloud during laser cooling (∼6 ms [29]) is
estimated to be only ∼ 1 mm. Thus, we can apply narrow-line
cooling to molecules in free space, since we can complete thecooling process before the molecules diffuse away from thetrap center. In addition, the maximum acceleration for thistransition, which is ∼ 22 m/s2 (=k/4m, where m is themass of the molecule), is more than twice the acceleration
due to gravity.
From the above considerations, we conclude that threedimensional laser cooling can be achieved by this system [30].
Because the natural line width of the cooling transition iscomparable to its recoil frequency (2π × 1.5 kHz), laser
cooling to the recoil temperature (140 nK) can be realized, as
has been successfully performed with strontium atoms [31].

In summary, we investigated the optical transitions between
the low-lying vibrational states of the X 1 + and b 30+states for KRb molecule and determined its natural line
width and Franck-Condon factors. These results suggest
a novel all-optical scheme for producing sub-microkelvinmolecules, where molecules formed by photoassociation (andSTIRAP) are cooled to the photon recoil temperature by
three-dimensional laser cooling using |X,0,1-|b,0,0 and|X,1,1-|b,0,0 transitions. Because alkali-metal dimers have
similar properties, this scheme is applicable to other homo- andheteronuclear alkali-metal-dimers, in addition to other isotopic
KRb molecules. Because this scheme allows sub-microkelvinmolecules to be rapidly produced, it could prove a powerful
method for molecular precision spectroscopies. Furthermore,
optically trapping molecules cooled by this scheme can be anovel strategy for realizing a quantum degenerate moleculargas.

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[18] K. Aikawa et al., Opt. Express 19, 14479 (2011).
[19] For clarity, the molecules remaining in |X,0,0 are optically
pumped into higher vibrational states before ionization.
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[22] We will discuss the quantitative analyses of the hyperfine
structures in detail elsewhere.
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[24] The obtained equilibrium distance (re ) of the X state did
not completely match the value in the Ref. [23]. This small
difference may have resulted from the models describing
potential energy curves.
[25] We checked the contributions of the variation of the TDMof X-b transition with internuclear distance to the branchingratios via a rough calculation. The variation of the TDM of X-btransition is mainly due to the variation of the spin-orbit coupling
between b and A 1 + states. Therefore the TDM is larger in thelonger internuclear distance due to the smaller energy separation
between the b and A 1 + potentials. In our calculations including
this variation, branching ratios to |X,0 and |X,v  2 states
are larger than 0.95 and smaller than 2 × 10−3 , respectively.
This still supports our discussions about laser cooling ofmolecule.
[26] E. G. Lee et al., J. Mol. Spectrosc. 194, 197 (1999).
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We thank Olivier Dulieu for providing his calculations of
the TDM of KRb. This work was supported by a Grant-in-Aid
for Young Scientists (A) of JSPS (No. 23684034), a Grant-inAid for Scientific Research on Innovative Areas of JSPS (No.
24104702), and the Matsuo Foundation. K.A. acknowledges
the support of the Japan Society for the Promotion of
Science.

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PHYSICAL REVIEW A 89, 021401(R) (2014)[29] The time it takes for capturing molecules traveling with 43 times
1
×4×
the recoil velocity can be estimated as tcapture ∼ 2π ×5kHz
43 ∼ 6 ms.
[30] Although Doppler cooling is our prime interest, threedimensional MOT is also a possible extension [7]. Repump-ing lasers, which are resonant to the |X,v  2,1 − |b,0,0transitions, should make the trapping time of molecular MOT
longer.
[31] H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, Phys.
Rev. Lett. 82, 1116 (1999).

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