Measurement of the Zeeman-like ac Stark shift
Chang Yong Park, Heeso Noh, Chung Mok Lee, and D. Cho*
Department of Physics, Korea University, Seoul 136-701, Korea
Received 4 May 2000; revised manuscript received 25 August 2000; published 9 February 2001
We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an
alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the
laser frequency is between the D1 and D2 transition frequencies, with the size of the detuning from the D2
resonance twice that from the D1 resonance. The direction of the effective magnetic field is along the laser
propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser
intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-
optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar
polarizability vanishes at the particular detuning.
DOI: 10.1103/PhysRevA.63.032512 PACS numbers: 32.10.Dk, 32.60.+i
I. INTRODUCTION
The ac Stark effect is the result of an interaction between
an oscillating electric field and an atom. The electric field
induces an electric dipole moment in the atom, and the in-
duced moment interacts with the field again to produce an
energy shift, the ac Stark shift. The shift can be a problem in
a precision measurement 1, but a field gradient leads to an
optical dipole force, which is useful in the study of cooling
and trapping of atoms 2 and in atom optics 3.
The ac Stark shift of an atom in its ground state consists
of two components due to the scalar and vector polarizabil-
ities. The scalar part is from the induced electric dipole mo-
ment parallel to the electric field, and the vector part is from
the moment perpendicular to the field. It has been known
since 1972 4 that when the light is circularly polarized, the
vector part results in an energy shift analogous to a Zeeman
shift. This ‘‘fictitious magnetic field’’ was used to demon-
strate optically induced spin echoes 5 and spin precessions
6. In most studies of this phenomenon, the atom is modeled
as a two-level system with Zeeman substructure and a near
resonant light beam is used to make the effect large. When
the ac Stark shift is used to produce a dipole force, however,
it is often advantageous to have a far detuned light beam to
reduce unwanted photon scattering. In this case the multi-
level nature of an atom becomes important. For alkali atoms,
which play a central role in both precision measurements and
atom optics, the fine structure, whose spin-orbit coupling is
responsible for the vector polarizability, is important. We
pointed out 7 that when the laser light is properly detuned
between the D 1 and D 2 transitions of an alkali-metal atom,
the scalar polarizability vanishes and the contributions from
the D 1 and D 2 couplings to the vector polarizability add
constructively. When this condition is satisfied and the laser
light is circularly polarized, the ac Stark shift takes the same
form as a Zeeman shift, and the laser intensity gradient pro-
duces a pure Stern-Gerlach type force.
Using the Zeeman-like ac Stark effect one may replace a
magnetic field with a laser beam when such a replacement
leads to a more convenient or interesting experimental situ-
ation. The laser-induced Stern-Gerlach force provides a new
tool in optically manipulating atomic motion in a spin-
dependent way. Recently it was used in an experiment where
an optical dipole trap, which behaved like a magnetic trap,
was constructed to trap spin-polarized rubidium atoms 8. In
the spin precession experiment 6 a similar situation was
exploited for lithium atoms. It is also possible to perform the
classic Stern-Gerlach experiment using a laser intensity gra-
dient in place of a magnetic-field gradient, or to produce a
standing wave along which the effective magnetic-field
strength changes from zero to maximum in half a wavelength
of the light. Such a ‘‘magnetic grating’’ cannot be built with
conventional coils.
In this paper we briefly outline the theory and report the
spectroscopic measurement of the Zeeman-like ac Stark
shift. In the first part of the experiment we study the vector
part under various detunings and polarizations of the laser
light using a slow atomic beam from a magneto-optical trap.
We apply the standard atomic beam resonance methods in-
cluding optical pumping, stimulated Raman excitation, and
detection by shelving technique to the slow atomic beam.
The experimental procedures are described in detail. In the
second part we show that the scalar polarizability vanishes at
the expected detuning using saturated absorption spectros-
copy in a vapor cell.
II. THEORY
When an alkali-metal atom in its ground state | nS
1/2
, m
j
is irradiated by a laser field E( t ) =E
0
e
-i t
+E
0
* e
i t
, its ac
Stark shift, to the lowest order, is
U nS
1/2
, m
j
=
E
0
• E
0
*
+i
E
0
* E
0
• S
1/2
, m
j
| | S
1/2
, m
j
.
1
Here and are the scalar and vector polarizabilities, re-
spectively, and is the Pauli spin operator 9. Explicit
forms of the polarizabilities are given in Ref. 7. The vector
part vanishes either in the dc Stark effect or when the applied
light is linearly polarized. However, when the light is circu- *Email address: cho@korea.ac.kr
PHYSICAL REVIEW A, VOLUME 63, 032512
1050-2947/2001/633/0325127/$15.00 ©2001 The American Physical Society 63 032512-1