PHYSICAL REVIEW A 83, 032502 (2011)
Dynamic polarizabilities and magic wavelengths for dysprosium
V. A. Dzuba and V. V. Flambaum
School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
Benjamin L. Lev
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
(Received 22 November 2010; published 4 March 2011)
We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of
dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there is a set of
magic wavelengths of the unpolarized lattice laser field for each pair of states, which includes the ground state
and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both
states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We
present an analytical formula that, near resonances, allows for the determination of approximate values of the
magic wavelengths without calculating the dynamic polarizabilities of the excited states.
DOI: 10.1103/PhysRevA.83.032502 PACS number(s): 31.15.am, 32.70.Cs, 31.30.jg, 37.10.De
I. INTRODUCTION
The dysprosium atom has many unique features, which
makes it useful for studying fundamental problems of mod-
ern physics. This is a heavy atom that has many stable
Bose and Fermi isotopes (from A = 156 to A = 164) and
a pair of almost-degenerate states of opposite parity at
E = 19 798 cm
−1
. These features were used to study the
parity nonconservation [1–5] and possible time variation of
the fine-structure constant [6–12].
Fermionic Dy has the largest magnetic moment among all
atoms, and only Tb is as magnetic as bosonic Dy. This opens
important opportunities for studying strongly correlated matter
when gases of Dy atoms are cooled to ultracold temperatures
[13]. Recent progress in Doppler and sub-Doppler cooling is an
important step in this direction [13–17]. In addition to narrow-
line magneto-optical trapping (MOT) [18], further cooling on
narrow optical transitions might be possible using resolved-
sideband cooling [19,20].
In this method, vibrational states of the atom may be cou-
pled such that successive photon absorption and spontaneous
emission cycles reduce the vibrational quanta by one, until
the atoms are in the motional ground state of their optical
potential [19]. It is important that this resolved-sideband
cooling is performed at the magic wavelength of the laser
lattice field [21,22]. At this wavelength, the energy (ac Stark)
shift due to the laser field is the same for both states used in
the cooling. This results in a trap potential that is the same
for both states, and optical transitions between vibrational
states can be well resolved. This allows spectral selection
of cooling transitions, those which remove one vibrational
quanta, without contamination by heating transitions, which
add vibrational quanta. Other benefits to optical trapping at
magic wavelengths include enhanced precision spectroscopy
and longer-lived quantum memory for quantum information
processing (QIP) [21].
In this paper we calculate dynamic polarizabilities of
the ground and three long-lived excited states of Dy and
present a number of magic wavelengths for the transitions
between them. We also present an analytical formula that
allows the determination of approximate values of the magic
wavelengths near resonances without calculating the dynamic
polarizabilities of excited states. The optical field is assumed to
be unpolarized, although we estimate that polarization would
induce only small shifts in the magic wavelengths.
II. CALCULATIONS
A. Ab initio calculations
The dynamic scalar polarizability α
a
of atomic state a is
given by (we use atomic units: ¯h = 1,m
e
= 1,|e|=1)
α
a
(ω) =−
1
3(2J
a
+ 1)
n
×
1
E
a
− E
n
+ ω
+
1
E
a
− E
n
− ω
a||D||n
2
,
(1)
where J
a
is total momentum of state a, E
a
is its energy, and
D =−
i
r
i
is the electric dipole operator. Summation goes
over the complete set of excited states n.
We use the relativistic configuration interaction (CI) tech-
nique described in our previous papers [5,11,23] to perform
the calculations. The single-electron and many-electron basis
sets, the fitting parameters, and other details of present
calculations are exactly the same as in Ref. [5]. This simple
method provides a good accuracy for low-lying states of
a many-electron atom. However, it does not allow for the
saturation of the summation in Eq. (1) over a complete set
of many-electron states. On the other hand, the contribution
of the higher-lying states in the dynamic polarizability does
not depend on frequency at small frequencies. Therefore, for
small frequencies we can rewrite Eq. (1)as
α
a
(ω) = ˜α
a
−
1
3(2J
a
+ 1)
n
×
1
E
a
− E
n
+ ω
+
1
E
a
− E
n
− ω
a||D||n
2
,
(2)
032502-1
1050-2947/2011/83(3)/032502(6) ©2011 American Physical Society
(4 pages)
(19 pages)
Manymanuals.com
Manymanuals.de
Manymanuals.fr
Manymanuals.it
Manymanuals.pl
Manymanuals.cz
Manymanuals.es
Manymanuals-pt.com
Commentaires sur ces manuels