Contents - Max-Planck-Institut für Physik komplexer Systeme

−Eij [MHz] theory exp.: Rb +
2 exp.: Rb +
E3 7.8 — —
E2 10.7 9.9(7) 8.9(7)
E1 16.5 16.6(5) 16.5(5)
E0 ♦ 23.1 22.4(5) 22.8(5)
E−1 25.9 26.3(7) —
E12 33.8 26.3(7) —
E10 39.6 39.6(12) —
E00 46.2 45.0(8) 45.5(8)
Table 1: Binding energies oft the 35s dimer Eν and trimer E ν ′ ν (in
blue) of Rb, measured from the atomic n = 35 Rydberg line. The
experimental positions are given with uncertainties and correspond
to the two different decay channels in Fig. 1. The diamond indicates
the “ground state” in the outer well, labeled as ν = 0.
Figure 2: Molecular potential curve for n = 35 obtained from the
Green function calculation (solid line) and from a model potential
(dotted line) taking V in Eq.(2) as a perturbation with an effective
scattering length A (eff)
s to reproduce the outermost potential well.
The grey area around R ≈ 1200a.u. marks the region of quantum reflection
where the WKB-approximation is not valid. The baseline of
the shown molecular wave functions corresponds to their respective
vibrational energies. The inset demonstrates the rapid potential drop
at the avoided crossing and illustrates the variable inner boundary
condition R0 used for stabilization plot of Fig.3.
Life time of dimer states To experimentally double
check the decay rates γIQR of the states controlled by
IQR as predicted in Fig. 3 is not straightforward, since
the dimers are embedded in an ultracold gas of Rb
atoms. Collisions lead to loss of dimers reducing their
lifetime in addition to the finite lifetime of the Rydberg
atom. The γIQR are only an additive contribution
to the widths due to these decay mechanisms.
However, the γIQR can be extracted by measuring experimental
linewidths γexp(ρ) as a function of atomic
density which allows to separate the collision induced
life time by extrapolating the (linear) dependence on
atomic density to ρ = 0. Moreover, by comparing
γexp(ρ) for a state stabilized by IQR with the width
for the ground state E0, which is stable against the
molecular decay, one can deduce from the experiment
γIQR. Since the procedure is quite involved, experimental
data has been obtained only for the ground
state E0 of 35s and E1. The residual experimental decay
rate γ1 = 3.3(12) × 10 4 s −1 is slightly larger than
γ1 = τ −1
1 ≡ (dθ/dE)−1 = 2.47 ×10 4 s −1 calculated from
the Wigner time delay (see Fig. 3) as discussed in [9],
where also the theoretical decay widths for the other
states are given.
binding energy [MHz]
-5
-10
-15
-20
-25
(a) (b) (c)
300 310 320 330 340
position of inner boundary [a.u.]
0 10 20 0 2 4 6
dos [µs] θ [mod. 2π]
Figure 3: Stabilization plot with the vibrational energies as a function
of the position R0 of the inner boundary (see Fig.2). The density
of states (dos) obtained by binning the data of (a) and shown in (b),
reveals the energies and widths of the molecular resonances, in perfect
agreement with the corresponding results from the Wigner time
delay (c).
Dipole moment of the 3 Σ(5s − 35s) dimer molecule
A homonuclear molecule as discussed here with Rb ∗ 2
does normally not possess a permanent dipole moment,
whose signature is a linear Stark effect in a small
electric field. However, the Rydberg dimer does show a
linear Stark effect pointing to a dipole moment of about
1 Debye experimentally as well as theoretically [3]. The
reason for this unusual property is again the p-wave
scattering resonance which mixes to the dominant 35s
atomic Rydberg wavefunction other Rydberg components
allowing for the formation of a dipole moment.
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2.2. Molecular bond by internal quantum reflection 45