Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state.

doi:10.1103/PHYSREVLETT.113.205301

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Takekoshi, Tetsu and Reichsollner, Lukas and Schindewolf, Andreas and Hutson, Jeremy M. and Le Sueur, C.

Ruth and Dulieu, Olivier and Ferlaino, Francesca and Grimm, Rudolf and Nagerl, Hanns-Christoph (2014)

'Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperne ground state.', Physical

review letters., 113 . p. 205301.

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Reprinted with permission from the American Physical Society: Tetsu Takekoshi, Lukas Reichsollner, Andreas

Schindewolf, Jeremy M. Hutson, C. Ruth Le Sueur, Olivier Dulieu, Francesca Ferlaino, Rudolf Grimm, and

Hanns-Christoph Nagerl (2014) 'Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperne

ground state.', Physical review letters., 113 . p. 205301.

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Ultracold Dense Samples of Dipolar RbCs Molecules in the Rovibrational

and Hyperfine Ground State

Tetsu Takekoshi,

1,2

Lukas Reichsöllner,

1

Andreas Schindewolf,

1

Jeremy M. Hutson,

3

C. Ruth Le Sueur,

3

Olivier Dulieu,

4

Francesca Ferlaino,

1

Rudolf Grimm,

1,2

and Hanns-Christoph Nägerl

1

Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria

2

Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria

3

Joint Quantum Centre (JQC) Durham/Newcastle, Department of Chemistry, Durham University, South Road,

Durham DH1 3LE, United Kingdom

4

Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, Bâtiment 505, 91405 Orsay Cedex, France

(Received 23 May 2014; published 12 November 2014)

We produce ultracold dense trapped samples of

87

Rb

133

Cs molecules in their rovibrational ground state ,

with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with

efficiencies of 90%. We observe the onset of hype rfine-changing collisions when the magnetic field is

ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift of the

transition frequencies as a function of applied electric field shows the strongly dipolar character of the RbCs

ground-state molecule. Our results open up the prospect of realizing stable bosonic dipolar quantum gases

with ultracold molec ules.

DOI: 10.1103/PhysRevLett.113.205301 PACS numbers: 67.85.-d, 05.30.Rt, 33.20.-t, 42.62.Fi

Samples of ultracold molecules with dipole moments

that can be tuned with applied electric fields offer a platform

for exploring many new areas of physics. They are good

candidates to form many-body systems with features such

as supersolidity, unconventional forms of superfluidity,

and novel types of quantum magnetism [1–3].Theyallow

exquisite control over all quantum degrees of freedom and

offer the possibility of implementing quantum simulation

protocols [4] that require genuine long-range interactions.

The most advanced experiments with ultracold polar

molecules to date have been on KRb. Ni et al. [5] produced

ultracold

40

K

87

Rb molecules in states very close to dis-

sociation by tuning a magnetic field across a Feshbach

resonance and transferred the resulting Feshbach molecules

to the rovibrational absolute ground state by stimulated

Raman adiabatic passage (STIRAP). Similar work has

been carried out on nondipolar Cs

2

[6,7]. The ground-state

KRb molecules can be transferred between hyperfine

states using microwave radiation [8] and confined in

one-dimensional [9] and three-dimensional [10] optical

lattices. However, pairs of KRb molecules can undergo an

exothermic chemical reaction to form K

2

þ Rb

2

; this

provides an opportunity for studies of quantum-state-

controlled reactions [8,9,11] but also constitutes a loss

mechanism for the trapped molecules.

There is great interest in producing samples of ultracold

dipolar molecules that are collisionally stable. Żuchowski

and Hutson [12] have shown that the molecules NaK,

NaRb, NaCs, KCs, and RbCs in their absolute ground

states are stable to all possible two-body collision proc-

esses. We have previously demonstrated that

87

Rb

133

Cs

Feshbach molecules can be produced from ultracold atoms

by magnetoassociation [13,14]. Similar work has been

reported by Köppinger et al. [15]. In this Letter, we describe

the transfer of these molecules to their rovibrational ground

state by STIRAP. We also demonstrate magnetic control

and show that the resulting molecules decay much more

slowly when they are in their hyperfine ground state than

when they are in an excited hyperfine state.

The states and transitions involved in our ground-state

molecule production process are shown in Figs. 1(a)–1(c).

A pump laser beam L

p

at 1557 nm couples a Feshbach state

jii with mostly a

3

Σ

þ

character to the jv

0

¼ 29i level of the

b

3

Π

1

state with Rabi frequency Ω

p

. This state has a small

admixture of the A

1

Σ

þ

state [13] (Supplemental Material

[16]), and a dump laser beam L

d

at 977 nm couples it to

the rovibrational ground-state level jv

00

¼ 0;J

00

¼ 0i of the

X

1

Σ

þ

potential with Rabi frequency Ω

d

. This level is made

up of 32 Zeeman sublevels, as shown in Fig. 1(c) [26].

At magnetic field B ¼ 0 the levels are grouped according to

the total molecular nuclear spin I

00

¼ 2,3,4,or5.The

stretched state with M

I

00

¼ M

tot

¼ 5 is the absolute ground

state for B larger than about 90 G. It can be accessed at

B ¼ 181 G using crossed vertical and horizontal linear

polarizations (v

p

,h

d

) for L

p

and L

d

copropagating in the

horizontal plane.

We start by generating a sample of

87

Rb

133

Cs Feshbach

molecules via magnetoassociation in an ultracold, magneti-

cally levitated and nearly quantum-degenerate mixture of

Rb and Cs atoms. The molecules are initially produced using

the Feshbach resonance at B ¼ 197.06 G and then trans-

ferred by magnetic field ramps to the state j−2ð1; 3Þdð0; 3Þi

near B ¼ 180 G as sketched in Fig. 1(b) and described

in more detail in Ref. [14]. Here, states are labeled with

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quantum numbers jnðf

Rb

;f

Cs

ÞLðm

f

Rb

;m

f

Cs

Þi, where n is

the vibrational quantum number counted downwards from

the ðf

Rb

;f

Cs

Þ dissociation threshold, f indicates the atomic

total angular momentum with projection m

f

, and L is the

molecular rotational angular momentum. We take the quan-

tization axis to lie along the magnetic field direction, which is

vertical in our setup (Supplemental Material [16]).

Thehigh-field-seeking molecules in statej− 2ð1;3Þdð0;3Þi

are separated from the remaining atoms by the Stern-

Gerlach effect. The magnetic field B is then ramped

back up through the nearest avoided crossing to transfer

the molecules into the strongly low-field-seeking state

jii¼j− 6ð2; 4Þdð2; 4Þi at a binding energy of approxi-

mately 2 MHz × h at B ¼ 181 G (marked with a dot in

Fig. 1(b)). This state is chosen because it has the greatest

triplet fraction and the largest amplitude at short range,

giving the most favorable Franck-Condon overlap for the

STIRAP process described below. To reduce spatial Zeeman

broadening and gravitational sag, the field gradient used

for levitation is turned off and a vertical one-dimensional

optical lattice (Supplemental Material [16]) is super-

imposed on the molecular cloud to hold it against gravity.

The molecular sample is, thus, held in a stack of pancake-

shaped two-dimensional traps with their tight axis along the

vertical direction. This additional step, combined with the

shorter collisional lifetime of molecules in the n ¼ −6 state

(about 30 ms), reduces the cloud population from 3000

to between 1000 and 1500 trapped molecules with a 1=e

2

-

cloud radius of between 30 and 40 μm. The translational

temperature measured in expansion after sudden release

from the trap is 240(30) nK. The overall sample preparation

procedure takes about 13 s.

STIRAP is based on a pulse sequence in which the dump

laser is turned on before the pump laser to generate a

transient dark superposition of the initial and final states

[28]. We perform ground-state STIRAP from jii to jv

00

¼ 0;

J

00

¼ 0i and characterize its efficiency by reversing the

STIRAP process as shown in Fig. 2 [29]. Molecules are

transferred to the hyperfine-Zeeman ground state with

M

tot

¼ 5 between t ≈ 15 and 30 μs and back to the

Feshbach state jii between t ≈ 40 and 55 μs. Both lasers

are tuned to one-photon resonance for fixed B ¼ 181 G.

The Feshbach molecules are then detected by dissociating

them at the Feshbach resonance at 197.06 G and using

absorption imaging on the atomic clouds [14]. The round-

trip transfer efficiencies are typically about 80%, implying

one-way transfer efficiencies of about 90%. For compari-

son, the solid line in Fig. 2(a) is the result of a simulation

that takes laser linewidth into account, but not beam shape

and laser noise pedestal effects (Supplemental Material

[16]). It gives a somewhat higher efficiency.

Scanning the dump laser detuning Δ

d

reveals hyperfine

and Zeeman substructure of the X

1

Σ

þ

, jv

00

¼ 0;J

00

¼ 0i

180 190

-2

-1

0

0 50 100 150 200

-800

-600

-400

-200

0

5101520

0

5

10

|

-6(2,4)

d(2,3)

〉

|-1(1,3)s(1,3)

〉

|

-2(1,3)d(0,3)

〉

energy/h (MHz)

magnetic field B (G)

|

i

〉

=

|

-

6(2,4)d(2,4)

〉

M

tot

=3

M

tot

=5

energy/h (kHz)

magnetic field B (G)

X

1

Σ

+

, v'' =0,J'' =0

|v' =29

〉

|

i

〉

|

v'' =0,J'' =0

〉

(c)

(b)

b

3

Π

c

3

Σ

+

A

1

Σ

+

B

1

Π

a

3

Σ

+

Rb 5s + Cs 6p

energy/(hc)(10

3

cm

-1

)

internuclear distance R (a

0

)

Rb 5s + Cs 6s

X

1

Σ

+

Ω

p

Ω

d

(a)

FIG. 1 (color online). STIRAP scheme and levels involved.

(a) Ground- and excited-state molecular potentials of the RbCs

molecule [13]. The transfer from the Feshbach state jii at

threshold to the rovibrational ground-state level jv

00

¼ 0;J

00

¼ 0i

involves the v

0

¼ 29 level belonging to the b

3

Π

1

electronically

excited state. The red and green solid lines indicate the

wave functions that are coupled by the STIRAP pump and

dump lasers L

p

and L

d

with Rabi frequencies Ω

p

and Ω

d

.

(b) Zeeman diagram for the states with M

tot

¼ 4 just below

the ground-state two-atom ðf

Rb

;f

Cs

Þ¼ð1; 3Þ threshold. The red

dot marks the position from which STIRAP takes place. The

magnetoassociation path is marked with a blue line. Energies are

given relative to the field-dependent atomic dissociation thresh-

old. (c) Zeeman diagram showing the ground-state hyperfine

structure (32 states). The magnetic field during STIRAP is

indicated by the arrow. The energy levels are calculated using

the Hamiltonian and parameters from Ref. [27] . The thick lines

show the final states allowed by the selection rule ΔM

tot

¼1 for

vertical pump and horizontal dump polarization (v

p

,h

d

).

0.0

0.5

1.0

(b)

STIRAP time t (µs)

(a)

0 1020304050607080

0

5

10

15

20

N

F

(10

3

)

pump

power (mW)

dump

FIG. 2 (color online). Efficient ground-state STIRAP transfer.

(a) Number of Feshbach molecules N

F

as a function of STIRAP

time t during a typical forward and reverse on-resonance STIRAP

pulse sequence as shown in (b). The peak Rabi frequencies

are Ω

p

¼ 2π × 0.77ð22Þ MHz and Ω

d

¼ 2π × 2.3ð6Þ MHz. The

one-way STIRAP efficiency is 90%. The red curve is the result of

a master equation model (Supplemental Material [16]). Error bars

denote the 1σ standard statistical error. (b) Laser power as a

function of time t as recorded by photodiodes.

PRL 113, 205301 (2014)

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state as shown in Fig. 3. For (v

p

,h

d

) polarization, the

transfer is mostly into the level with M

tot

¼ 5. For (v

p

,v

d

)

polarization, the transfer is primarily into one of the two

hyperfine-excited levels with M

tot

¼ 4. The most important

terms in the ground-state hyperfine Hamiltonian [27] are

the nuclear Zeeman shift and the scalar nuclear spin-spin

interaction, which are governed by the electronic and

nuclear g factors, and the nuclear spin-spin parameter c

4

,

respectively. The second of these two terms dominates at

low field. The g factors are very precisely known, and a

simulation (Supplemental Material [16]) using them and

the c

4

parameter of Ref. [27] agrees well with the observed

spectrum for both choices of polarization.

There are usually 50 to 100 Feshbach molecules that

remain after the transfer to the ground state [offset in

Figs. 2(a) and 3]. We believe this is mainly due to a slight

beam misalignment and the fact that the molecular cloud

and STIRAP beams have similar radii. We exclude these

molecules when calculating the transfer efficiency. The

efficiency is most likely limited by laser power, in the sense

that Feshbach molecules at the edge of the cloud see lower

laser intensities. Laser phase noise pedestals may also play

a role, as discussed in Ref. [30].

To explore the molecules’ collisional properties, we load

oursampleofground-statemoleculesinto a three-dimensional

crossed dipole trap (Supplemental Material [16]). The

trap is comparatively stiff with a geometrically averaged

trap frequency of 409(20) Hz to hold the sample against

gravity. The sample’s peak particle density is now

1.1ð1Þ × 10

11

cm

−3

. The compression of the sample leads

to a marked increase in temperature to 8.7ð7Þ μK.

Nevertheless, we expect that s-wave collisions dominate

the collision process at zero electric field. Figure 4 shows

the ground-state population in the M

tot

¼ 5 state as a

function of hold time t

h

between forward and reverse

STIRAP transfer for various values of the magnetic field B.

For this measurement, we first prepare the molecular

sample as before at B ¼ 181 GinM

tot

¼ 5 and then ramp

the magnetic field to the chosen value within about 1 ms.

After time t

h

, we reverse the process and determine the

remaining number of molecules. The results show ground-

state molecule loss that depends strongly on B. Using a

two-body decay model (Supplemental Material [16]),

we determine the two-body loss rate coefficient L

2

. Its

dependence on B is shown in the inset to Fig. 4. The value

of L

2

is considerably greater at fields below about 90 G.

The state with M

tot

¼ 5 is not the absolute ground state at

fields below this threshold, as seen in Fig. 1(c), and we

attribute the greatly reduced lifetime to hyperfine-changing

collisions to form the lower-energy states. We note that L

2

is nonzero even for fields above 90 G; this may be due to

thermal population of excited hyperfine states or to losses

involving long-lived collision complexes [31,32]. We also

note that our ground-state sample is not 100% pure,

-200 0 200 400 60

0

0.0

0.5

1.0

M

tot

=4

M

tot

=3

M

tot

=3

M

tot

=4

M

tot

=3

(v

p

, h

d

) polarization

(v

p

, v

d

) polarization

N

F

(10

3

)

dump laser detuning

Δ

d

(kHz)

M

tot

=5

FIG. 3 (color online). STIRAP spectrum showing the number

of Feshbach molecules N

F

after round-trip STIRAP as a function

of dump laser detuning Δ

d

for two different choices of the

polarization of the dump laser. The energies of the hyperfine

components of the ground state (calculated using the parameters

of Ref. [27]) are marked with dashed vertical lines and labeled

with their total angular momentum projection M

tot

.For(v

p

,h

d

)

polarization (black squares), the Feshbach molecules (M

tot

¼ 4)

are primarily transferred into the absolute hyperfine ground state

with M

tot

¼ 5. For (v

p

,v

d

) polarization (red triangles), hyperfine-

excited levels are addr essed. The solid curves are master equation

simulation results (Supplemental Material [16]). The black curve

centered around zero detuning is a fit to the data to determine

the dump Rabi frequency. The Rabi frequencies are Ω

p

¼ 2π ×

0.26ð7Þ MHz and Ω

d

¼ 2π × 2.3ð6Þ MHz.

0 200 400 600 800 1000

0

200

400

600

800

181.45 G

104.7 G

90.0 G

0G

number of ground-state molecules

hold time in trap t

h

(ms)

0 50 100 150

1

10

ground state

L

2

(10

-10

cm

3

/s)

magnetic field B (G)

M

tot

=5isNOT

M

tot

=5is

ground state

FIG. 4 (color online). Decay of ground-state molecules as a

result of collisions at zero electric field. The number of ground-

state molecules in M

tot

¼ 5 is plotted against hold time t

h

in

the crossed dipole trap for different values of the magnetic field B

as indicated. The initial peak density is 1.1ð1Þ × 10

11

cm

−3

. The

solid lines are fits based on a two-body decay model to determine

the two-body loss rate coefficient L

2

(Supplemental Material [16]).

The fits are constrained to run through the first data point at zero

hold time. The inset plots L

2

as a function of B. A greatly reduced

L

2

is seen at magnetic fields B greater than about 90 G, where the

molecules are mostly in the hyperfine-Zeeman ground state.

PRL 113, 205301 (2014)

PHYSICAL REVIEW LETTERS

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14 NOVEMBER 2014

205301-3

because it initially contains some molecules left behind in

the Feshbach state jii. The cross section for inelastic

collisions between molecules in states jM

tot

¼ 5i and jii

is likely to be large and will lead to some loss of ground-

state molecules on the time scales considered here.

A crucial property of RbCs molecules is their permanent

electric dipole moment μ, calculated to be 1.25 D in the

absolute ground state [33,34]. We have measured the

Stark shift of the hyperfine ground state by applying

voltages to a set of four parallel electrodes external to

the fused silica cell vacuum chamber [16] and tracking the

shift E

S

of the M

tot

¼ 5 peak position (as in Fig. 3) from

that recorded at zero electrode potential. The potential is

pulsed to reduce charging effects from the alkali-coated cell

walls (Supplemental Material [16]) [35]. The resulting shift

is shown in Fig. 5. Both the dump and the pump laser must

be detuned considerably, because of the large excited-state

shift shown in the inset of Fig. 5. The quadratic shift is

observed to be 1.60ð7Þ Hz=V

2

, which implies a permanent

dipole moment of 1.17(2)(4) D. Here, the first error is

statistical and the second is the estimated systematic error

due to geometrical uncertainty that enters when calculating

the dielectrically enhanced electric field inside our quartz

cell apparatus (Supplemental Material [16]).

In conclusion, we have formed dense samples of ultra-

cold RbCs molecules in their electronic and rovibrational

ground state. The molecules are initially formed in near-

dissociation states by magnetoassociation and transferred

to the ground state by the STIRAP method. The efficiency

of the ground-state transfer is about 90%. With an appro-

priate choice of laser polarization, we can produce the

molecules in their absolute hyperfine ground state. RbCs

molecules in their ground state are stable to all possible

two-body collision processes, so our results offer the

prospect of producing the first collisionally stable quantum

gas of dipolar molecules.

In future work, we will attempt to increase the sample size

and density by creating Feshbach molecules from atomic

Mott insulators in a three-dimensional optical lattice [36],in

generalization of work on homonuclear Cs

2

[7]. The dynam-

ics will then be dominated by nearest-neighbor interactions

with interaction strength on the order of h × 1 kHz. This will

allow us to study important problems in quantum many-body

physics, such as the phase diagram of the Bose-Hubbard

model extended by a long-range interaction term [37,38].

We acknowledgecontributions by V. Pramhaas, M. Kugler,

and M. Debatin and thank N. Bouloufa, R. Vexiau,

A. Crubellier, and J. Aldegunde for fruitful discussions.

We acknowledge support by the Austrian Science Fund

(FWF) through the Spezialforschungsbereich (SFB)

FoQuS within project P06 (FWF project No. F4006-N23),

the European Office of Aerospace Research and

Development through Grant No. FA8655-10-1-3033 and

the Engineering and Physical Sciences Research Council

through Grant No. EP/I012044/1.

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0 100 200 300 400 500 600

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

Stark shift E

S

/h (MHz)

field rod p otential U (V)

0 200 400 600

0

10

20

30

FIG. 5 (color online). Stark shift of the M

tot

¼ 5 state of the

RbCs ground state. The two-photon STIRAP resonance shift E

S

is plotted as a function of the electrode potential U. The solid line

is a quadratic fit. The inset shows an expanded range in which the

excited-state shift can be seen as well (triangles).

PRL 113, 205301 (2014)

PHYSICAL REVIEW LETTERS

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14 NOVEMBER 2014

205301-4

Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state.

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