EGAS41 - Swansea University

41 st EGAS CP 37 Gdańsk 2009
Optical lattice clock without atom-motion-dependent
uncertainties
E.Yu. Ilinova 1 , V.D. Ovsiannikov 1 , H. Katori 2 , K. Hashiguchi 3
1 Faculty of Theoretical Physics,Voronezh State University, Universitetskaya pl. 1, Voronezh,
Russia
2 Department of Applied Physics, Graduate School of Engineering, The University of Tokyo,
Bunkyo-ku, 113-8656 Tokyo, Japan
3 CREST, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, 332-0012 Saitama,
Japan
∗ Corresponding author: sweraji@yandex.ru,
Excellent controllability of system parameters for atoms in optical lattices has found broad
applications in condensed matter physics, quantum information science and metrology.
Polarization gradient lattice led to efficient laser cooling mechanisms and controlled atomic
transport. The long coherence times of atoms in far-detuned intensity lattices make them
attractive for precision measurement. In these applications, so far, the lattice potentials
are well characterized by the electric dipole (E 1 ) interaction, hence, the higher order
multipole interactions, such as the magnetic-dipole (M 1 ) and electric-quadrupole (E 2 )
interactions, are rarely discussed as an experimental concern. Besides controlling atomic
motion, engineering light shift potential of a far-detuned intensity lattice opens up possibilities
for novel atomic clocks. Optical lattice clocks are attracting growing interest as
candidates for future redefinition of the second. It was pointed out, that different spatial
distributions of multipolar (E 1 ,M 1 ,E 2 ) atom-field interactions may critically affect the
uncertainties of highly accurate clocks based on atoms in an optical lattice of a ”magic”
wavelength [1], introducing difficulties in canceling out the light shift in clock transitions.
There are two possibilities to overcome this problem: (i) to use an optical lattice, where
the spatial distribution of the E 1 Stark effect coincided with the distributions of the M 1
and E 2 Stark energies; (ii) to shift the magic wavelength so, as to equalize the spatial
distributions of the Stark-effect corrections to the energies of atoms in their excited and
ground states, which for equal amplitudes E 0 of the waves is:
△E g(e)
St (r) = − E2 0
2
[
α
g(e)
E 1
(ω)g E1 (r) + α g(e)
M 1
(ω)g M1 (r) + α g(e)
E 2
(ω)g E2 (r) ] (1)
where α g(e)
E 1
(ω), α g(e)
M 1
(ω), α g(e)
E 2
(ω) are the polarizabilities of the ground-state (excited) atom
at the frequency ω , and the factors g E1 (r), g M1 (r), g E2 (r)are the spatial distribution
factors of the corresponding light shifts. A thorough analysis demonstrates, that 2D
and 3D lattices exist with standing waves produced by running waves with mutually
orthogonal polarization, where the E 1 distribution g E1 (r) could coincide with either g M1 (r)
or g E2 (r). E.g., in a 3D lattice with running waves polarized along the standing-wave
axes Ox, Oy and Oz the M1 and E1 distributions coincide: g E1 (r) = g M1 (r) = 3 +
cosk(x + y) + cos k(x + z) + cosk(y + z), while g E2 (r) = 6 − g E1 (r). In the case of
polarization at the angle π/4 to the axes the E2 distribution coincides with that of the
E1: g E1 (r) = g E2 (r) = 3 + 2 sin kx sin kz + 2 cosky coskz, while g M1 (r) = 6 − g E1 (r). In
every case, the position-dependent Stark shift of the clock frequency may be eliminated
by corresponding choice of the magic wavelength, while the residual position-independent
multipole offset may be correctly taken into account.
References
[1] A.V. Taichenachev et al., Phys. Rev. Lett. 101, 193601 (2008)
97