COL 10(Suppl.), S22702(2012) CHINESE OPTICS LETTERS December 30, 2012
A staggered dual Mott insulator in a 3D optical lattice
Jianfang Sun (
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)
1,2
, Guodong Cui (
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1,2
, Yafan Duan (
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, Jun Qian (
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1,2∗
,
Tao Hong (
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3
, and Yuzhu Wang (
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)
1,2∗∗
1
Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics,
Chinese Academy of Sciences, Shanghai 201800, China
2
Center for Cold Atom Physics, Chinese Academy of Sciences, Shanghai 201203, China
3
Center for Macroscopic Quantum Phenomena, Shanghai Advanced Research Institute,
Chinese Academy of Sciences, Shanghai 201203, China
∗
Corresponding author: jqian@mail.siom.ac.cn;
∗∗
corresponding author: yzwang@mail.shcnc.ac.cn
Received April 20, 2012; accepted September 4, 2012; posted online December 28, 2011
We propose a novel scheme for trapping ultracold rubidium and ytterbium atoms in a three-dimensional
(3D) optical lattice simultaneously, in which the two species of atoms locate on two staggered lattices with
the same spatial period and have a spatial separation of 133 nm. Furthermore, we calculate the tu nneling
and intra- and interspecies interactions of rubidium and ytterbium atoms as a function of light intensity,
and find that the mixture of quantum degenerate gases in optical lattices can exhibit more intriguing
quantum phases, especially a staggered dual Mott insulator of alkali-metal and alkaline-earth metal atoms.
OCIS codes: 270.0270, 270.5585.
doi: 10.3788/COL201210.S22702.
Ultracold atoms in optical lattices have proven to be
a versatile model system to simulate complex quantum
phases and investigate unsolved many-body problems
from condensed-matter physics in a highly controllable
fashion
[1−3]
. As an outstanding example, phase transi-
tion of superfluid (SF) to Mott insulator (MI) has be e n
predicted theoretically
[4]
and observed experimentally
[3]
.
In addition, ultracold multi-flavor gases offer new in-
sight into the atomic interspecies interaction and ultra-
cold molecule
[5−7]
. Recently, the mixtures of bosonic
and fermonic atoms in optical lattices have draw much
attention due to the occurrence of complex quantum
phases, such as phase sepa ration
[8]
, supersolid phase
[9]
,
and unexpected large shift of the phase transition
[10]
. Up
to now, experimental efforts to load two-species alkali-
metal atoms in an optical lattice have succeeded in
several groups
[11−14]
. The mixture of alkali-metal and
alkaline-earth(-like) atoms has been also investigated,
such as rubidium (Rb)-ytterbium (Yb)
[15,16]
and lithium
(Li)-Yb
[17,18]
. In this paper, more unexpected phases
have been theoretically predicted and investigated ex-
perimentally. Espe cially, the appearance of a dual MI
of bosons and fermions is a paradigmatic example of this
diversity
[6]
.
In this letter, we propose a novel scheme to trap both
87
Rb and
174
Yb atoms in a staggered three-dimensional
(3D) lattice with a laser field, and predict a new dual MI
of the mixture of alkali-metal and alkaline-earth atoms,
which is greatly different from the dual MI rea lize d by
Takahashi group in Kyoto University
[6]
. Experimental
realization is also discussed.
Now we b e gin to describe the scheme in detail. First, a
two-flavor quantum degenerate gas of Rb and Yb atoms
is prepa red
[15,16]
. Then a laser at 532 nm is used to pro-
duce a 3D lattice, which is red-detuned for
1
S
0
to
1
P
1
transition of Yb atoms but blue-detuned for D line tran-
sitions of Rb atoms. Therefore, the Rb and Yb atoms
are trapped in the regions of the minimum and maxi-
mum light intensity, respectively, and lattice potentials
of Rb and Yb atoms can be w ritten as
V l
Rb
= V
Rb
cos
2
(kx), (1)
V l
Yb
= V
Yb
sin
2
(kx), (2)
where k and V
Rb/Yb
describe the wave vector and the
potential depth of Rb/Yb atoms, respectively.
From Eqs. (1) and (2), we plotted the sketch of one
dimensional (1D) potentials in Fig. 1. The lattice poten-
tials for two species have equal spatial periods (266 nm)
but stag gered with a spatial sepa ration of 133 nm. It is
clear that the lattice depth of Yb atoms is larger than
that of Rb atoms, which is in accordance with our calcu-
lation on lattice depth below. To obtain the trap depth
of the mixture in an optical lattice, we use the following
expressions
[19]
Fig. 1. Light potentials for Rb and Yb atoms in a staggered
lattice. The solid and hollow b alls depict the Rb and Yb
atoms, respectively. The dash and solid lines represent the po-
tential experienced by Rb and Yb atoms, respectively. They
are staggered with a spatial separation of 133 nm.
1671-7694/2012/S22702(4) S22702-1
c
2012 Chinese Optics Letters