t=9 s - University of Virginia€¦ · Long-range Rydberg-Rydberg molecules bound by the...
Transcript of t=9 s - University of Virginia€¦ · Long-range Rydberg-Rydberg molecules bound by the...
Long-range Rydberg-Rydberg molecules bound by the dipole-dipole interaction
Hyunwook Park1, Martin Kiffner2, Wenhui Li2, and T. F. Gallagher1,2
1Department of Physics, University of Virginia
2Center for Quantum Technologies, National University of Singapore
II. Existence of the wells: θ=0 well
III. Robustness of wells
IV. Dynamics
Fig. 1 Rb ground-Rydberg diatomic potential (5s+30f) resembles a trilobite [1].
I. Introduction
Rydberg atoms, which are highly excited atoms with one or more electrons with a large principal quantum number n, are
a fascinating system to study a broad range of quantum mechanical problems due to their exaggerated properties, such as, huge
geometrical cross sections, long radiative life times, and large polarizabilities, etc [1]. As one of the most fundamental problems in atoms and molecules, the dipole-
dipole interaction has been intensively studied and observed in diverse disciplines, physics, chemistry, and bio-science, etc [2-4]. Recently, it has garnered much
attention due to its potential application to quantum gates through the notion of dipole blockade [5].
For the quantum manipulation of atoms, an intriguing question was raised about the possibility of forming Rydberg molecules by Greene et al. [6]. It was claimed
that when two closely spaced atoms make a pair, one of the atoms in the pair can be excited to Rydberg state while the other one remains in the ground state,
forming a trilobite-like potential, as shown in Fig. 1. Similarly, the existence of Rydberg-Rydberg (RR) dimers was also predicted [7]. However, such Rydberg
molecules have not been observed, although RR pairs were produced in an optical lattice potential[8, 9].
Here, we present a new approach to produce a RR molecule bound in a dipole-dipole potential. Specifically, we discuss the Rb ns1/2np3/2 state which generates
long range dipole-dipole potential wells in the presence of a small electric field. This new method should be able to produce a larger RR dimer than the trilobite-
like potential and provide a new way for the quantum information physics.
VI. Concluding Remarks
A. It is found that a very large diatomic pot well exists in the ns1/2np3/2 dipole-dipole potential when an electric field is applied.
B. For a given n, R0 can be adjusted to match, for example, lattice spacing by adjusting the electric field.
C. We have observed the suppressed attractive dipole-dipole potentials as an evidence of the dipole-coupled anti-crossings induced by the electric field.
D. In the future work, the microwave field can be used to engineer the large Rydberg-Rydberg dimers.
* This research was supported by the Air Force Office of Scientific Research
Basis states M=0 : 4 states
ns1/2np-1/2 np-1/2ns1/2 ns-1/2np1/2 np1/2ns-1/2
M=1 : 4 states
ns1/2np1/2 np1/2ns1/2 ns-1/2np3/2 np3/2ns-1/2
M=-1 : 4 states
ns-1/2np-1/2 np-1/2ns-1/2 ns1/2np-3/2 np-3/2ns1/2
M=2 : 2 states
ns1/2np3/2 np3/2ns1/2
M=-2 : 2 states
ns-1/2np-3/2 np-3/2ns-1/2 2 4 6 8 10 12
-40
-20
0
20
40
n=40,=0,=0
En
erg
y [
MH
z]
R [m]
ns1/2
np3/2
levels
θ
R atom1
(μ1)
atom2
(μ2)
z
A simple example of Vdd in E:
when two atoms are aligned along the field E, R // E (θ=0)
3
2121 )ˆ)(ˆ(3
R
RRVdd
The dipole-dipole interaction in ns1/2np3/2 pair of atoms [10]
where μ1= μ2 = μsp in this work
θ
R
atom1
(μ1)
atom2
(μ2)
z
E
The well exists at θ=0. How wide is the well in θ?
In a realistic problem, two atoms are randomly oriented.
2 4 6 8 10 12
-10
0
10 n=40
=-10 MHz
=o
En
erg
y [
MH
z]
R [m]
The potential well is plotted in a 3-dimensional
space. The pot well has two minima along the z-
axis (θ=0) and becomes shallow at other θ. The
deep wells are in -20o < θ < 20o.
2 4 6 8 10 12
-10
0
10n=40
=-10 MHz
=90o
En
erg
y [
MH
z]
R [m]
5.3 5.4 5.5 5.6 5.7 5.8
-7.0
-6.5
-6.0
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0-7.0
-6.5
-6.0
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0-7.0
-6.5
-6.0
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0
(c) =0.08 rad
R [m]
(b) =0.02 rad
En
erg
y [
MH
z]
|M|=1 |M|=2
(a) =0
2 fold degenerate
|M|=0
|M|=2
|M|=1
|M|=0
around R=5.5 m (a) At θ=0, ΔM=0 and |M|=0, 1, and 2 levels cross. If θ ≠ 0, M is not
conserved. (b) and (c) at θ ≠ 0, |M|=0, 1, and 2 levels are coupled, resulting in anti-crossings.
2 4 6 8 10 12
-20
-10
0
10
20
30
mj=3/2
Dash M=0
Solid |M|=1
Dot |M|=2
: Stark shift due to E
n=40, =-10 MHz=0
En
erg
y [
MH
z]
R [m]
mj=1/2
ns1/2
np3/2
levels
=-10 MHz
Potential well
Question: What happens to the dipole-dipole interaction
in the presence of an electric field, E ?
Degenerate potential wells
with equilibrium at R0=5.5 μm
(≈ 105 Bohr radius a0) Huge Rydberg-Rydberg molecule R0 can be adjusted independent of n by changing δ, R0≈δ-1/3
2cos)(93)(3)(28)(436
1)( 2 RVRVRVRVRV dddddddd
An analytic formula for the bound state of the potential is given by, The vibrational frequency around the equilibrium position ,R0=5.5 μm, is computed to be 15 kHz, which is so slow
that the atom’s motion remains on the adiabatic potential curves. Accordingly, this potential well keeps the atoms
from collisional ionization, maintaining the Rydberg-Rydberg molecular state.
References [6]Chris H. Greene et al. Phys. Rev. Lett. 85, 2458 (2000)
[7] Christophe Boisseau et al. Phys. Rev. Lett. 88, 133004 (2002)
[8] B. Vaucher et al. Phys. Rev. A 78 043415 (2008)
[9] S. E. Anderson et al. Phys. Rev. Lett. 107, 263001 (2011)
[10] Hyunwook Park et al. Phys. Rev. A 84, 022704 (2011)
[1] T. F. Gallagher. Rydberg Atoms. Cambridge University Press (1994)
[2] R. Vincent et al. Phys. Rev. B 83, 165426 (2011)
[3] David Beljonne et al. J. Phys. Chem. B 113 19 (2009)
[4] K. Autumn et al. Nature (London) 405, 681 (2000)
[5] M. D. Lukin et al. Phys. Rev. Lett. 87, 037901 (2001)
[11] Hyunwook Park et al. Phys. Rev. A 84, 052708 (2011)
The degenerate ns1/2np3/2 levels split and shift up and down
due to Vdd as the atoms approach close each other
V. Preliminary evidence of the well: probing attractive potentials
Experimental approach [11]:
1. Transfer atoms to an attractive
potential by a microwave field
2. Allow a time for atoms to
move and collide in the
attractive potential between
the microwave and detection
3. Detect ions produced by the
atom-atom collision 2 4 6 8 10 12
-30
-20
-10
0
10
20
30
n=40
=45o
En
erg
y [
MH
z]
R [m]
mj=1/2
=+10 MHz
mj=3/2
12375 12380 12385 12390 12395 12400
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0.006
0.008
0.010
0.012
0.014
I2io
n
Microwave frequency [X6 MHz]
I1
t=0
t=9 s
ion
38
p3
/2 [a
rb. u
nits]
allowed time
t=0
mj=1/2 3/2
Two resonances occur due
to Stark shift.
The ionization from mj=1/2,
I1, is much stronger than
that of mj=3/2, I2, because
seven attractive potentials
exist in mj=1/2, contrast to
only one attractive potential
in mj=3/2.
Due to the dipole-dipole coupling in the presence of the electric
field, only one of mj=3/2 levels (red solid line) shifts down to form
an attractive potential, which leads to ionizing collisions which can
be detected.
The dipole-dipole potential with δ>0 θ=90o well with δ>0 (mj=3/2 above mj=1/2 in this case) We obtain a ring shaped potential about the z-axis
2/3p 2/3p
2/1p 2/1p
2/1s 2/1s
δ
Internal level structure of each Rydberg atom.
The Stark shift of the |p±3/2 > levels is denoted by
δ = W(|p±3/2>)- W(|p±3/2>) (δ < 0 for the above configuration). The dipole transitions indicated by solid, dashed, and dotted lines couple to π, σ-, and σ+ polarized light, respectively.