Reducing Decoherence in Quantum Sensors

1
Reducing Decoherence in Quantum Sensors Charles
W. Clark1 and Marianna Safronova2 1Joint Quantum
Institute, National Institute of Standards and
Technology and the University of Maryland,
Gaithersburg, Maryland 2 Department of Physics
and Astronomy, University of Delaware, Delaware
Blackbody Radiation Shifts
Abstract
Optimization of optical cooling and trapping
schemes
The operation of atomic clocks is generally
carried out at room temperature, whereas the
definition of the second refers to the clock
transition in an atom at absolute zero. This
implies that the clock transition frequency
should be corrected in practice for the effect of
finite temperature. The most important
temperature correction is the effect of black
body radiation (BBR).
We have the ability to explore and quantify
decoherence effects in quantum sensors using
high-precision theoretical atomic physics
methodologies. We propose to explore various
atomic systems to assess their suitability for
particular applications as well as to identify
approaches to reduce the decoherence effects.
In this presentation, we give examples of our
calculations relevant to those goals. Two
separate but overlapping topics are considered
development of ultra-precision atomic clocks and
minimizing decoherence in optical cooling and
trapping schemes.
Level B

• Cancellations of ac Stark shifts
  state-insensitive optical cooling and
  trapping
• State-insensitive bichromatic optical trapping
  schemes
• Optimization of multiple-species traps
• Calculations of relevant atomic properties
  dipole matrix elements, atomic polarizabilities,
  magic wavelengths, scattering rates, lifetimes,
  etc.

DBBR
Level A

Clock transition
T 300 K
The temperature-dependent electric field created
by the blackbody radiation is described by (in
a.u.)
Optimizing the fast Rydberg quantum gate, M.S.
Safronova, C. J. Williams, and C. W. Clark,
Phys. Rev. A 67, 040303 (2003) . Frequency-depend
ent polarizabilities of alkali atoms from
ultraviolet through infrared spectral regions,
M.S. Safronova, Bindiya Arora, and Charles W.
Clark, Phys. Rev. A 73, 022505 (2006). Magic
wavelengths for the ns-np transitions in
alkali-metal atoms, Bindiya Arora, M.S.
Safronova, and C. W. Clark, Phys. Rev. A 76,
052509 (2007). Theory and applications of atomic
and ionic polarizabilities (review paper), J.
Mitroy, M.S. Safronova, and Charles W. Clark,
submitted to J. Phys. B (2010), arXiv1004.3567.
State-insensitive bichromatic optical trapping,
Bindiya Arora, M.S. Safronova, and C. W. Clark,
Phys. Rev. A (2010), in press, arXiv1005.1259.
Atomic Clocks
The frequency shift caused by this electric field
is
The International System of Units (SI) unit of
time, the second, is based on the microwave
transition between the two hyperfine levels of
the ground state of 133Cs. Advances in
experimental techniques such as laser frequency
stabilization, atomic cooling and trapping, etc.
have made the realization of the SI unit of time
possible to 15 digits. A significant further
improvement in frequency standards is possible
with the use of optical transitions. The
frequencies of feasible optical clock transitions
are five orders of magnitude larger than the
relevant microwave transition frequencies, thus
making it theoretically possible to reach
relative uncertainties of 10-18. More precise
frequency standards will open ways to more
sensitive quantum-based standards for
applications such as inertial navigation,
magnetometry, gravity gradiometry, measurements
of the fundamental constants and testing of
physics postulates.
Dynamic polarizability
The BBR shift of an atomic level can be expressed
in terms of a scalar static polarizability to a
good approximation 1

Magic wavelengths for the 5p3/2 - 5s transition
of Rb
Dynamic correction
1 Sergey Porsev and Andrei Derevianko, Physical
Review A 74, 020502R (2006)

Example BBR shift in Sr optical frequency
standard
Polarizability Present
a0(5s1/2) 91.3(9)
a0(4d5/2) 62.0(5)
We reduced the ultimate uncertainty due the BBR
shift in this frequency standard by a factor of
10.
Decoherence Effects in Atomic Clocks
New clock proposals require both estimation of
basic atomic properties (transition rates,
lifetimes, branching rations, magic wavelengths,
scattering rates, etc.) and evaluation of the
systematic shifts (Zeeman shift, electric
quadrupole shift, blackbody radiation shift, ac
Stark shifts due to laser fields, etc.)

Surface plot for the 5s and 5p3/2 m 1/2 state
polarizabilities as a function of laser
wavelengths l1 and l2 for equal intensities of
both lasers
BBR shift at T300K (in Hz) Present Ref.1 Ref. 2
D(5s1/2 ? 4d5/2) 0.250(9) 0.33(12) 0.33(9)
1 Dynamic correction, E2 and M1 corrections
negligible
NIST Yb optical clock
For recent optical and microwave atomic clock
schemes, a major contributor to the uncertainty
budget is the blackbody radiation shift.
1 A. A. Madej et al., PRA 70, 012507 (2004) 2
H. S. Margolis et al., Science 306, 19 (2004).
Sr Dansha Jiang, Bindiya Arora, M. S.
Safronova, and Charles W. Clark, J.
Phys. B 42 154020 (2010). Ca Bindiya Arora,
M.S. Safronova, and Charles W. Clark,
Phys. Rev. A 76, 064501 (2007)
Review Blackbody Radiation Shifts and
Theoretical Contributions to Atomic Clock
Research, M. S. Safronova, Dansha Jiang, Bindiya
Arora, Charles W. Clark, M. G. Kozlov, U. I.
Safronova, and W. R. Johnson, Special Issue of
IEEE Transactions on Ultrasonics, Ferroelectrics,
and Frequency Control 57, 94 (2010).

Magic wavelengths for the 5s and 5p3/2 m 1/2
states for l1 800-810nm and l22 l1 for various
intensities of both lasers. The intensity ratio
(e1/e2)2 ranges from 1 to 2.

Magic Wavelengths in atomic frequency standards
(nm)
Magic Wavelength
Optical atomic clocks have to operate at magic
wavelength, where the dynamic polarizabilities
of the atom in states A and B are the same,
resulting in equal light shifts for both states.
Theoretical determination of magic wavelengths
involves finding the crossing points of the ac
polarizability curves. H. Katori, T. Ido, and
M. Kuwata-Gonokami, J. Phys. Soc. Jpn. 68, 2479
(1999).
1 A. D. Ludlow et al., Science 319, 1805
(2008) 2 V. D. Ovsiannikov et al., Phys. Rev.
A 75, 020501R ( 2007) 3 H. Hachisu et al.,
Phys. Rev. Lett. 100, 053001 (2008)