Transcript Slide 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
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.
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).
Optimization of optical cooling
and trapping schemes
Level B
DBBR
Level A
Clock transition
T = 300 K
The temperature-dependent electric field created by the blackbody
3
radiation is described by (in a.u.) :
8
 d
2
E ( ) 
Atomic Clocks
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.
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.)
NIST Yb optical clock
For recent optical and microwave
atomic clock schemes, a major
contributor to the uncertainty
budget is the blackbody radiation
shift.
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 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).
 exp( / kT )  1
The frequency shift caused by this electric field is:
•
•
•
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.
Optimizing the fast Rydberg quantum gate, M.S. Safronova, C. J.
Williams, and C. W. Clark, Phys. Rev. A 67, 040303 (2003) .
Frequency-dependent 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).
DvBBR   A    ( ) E 2 ( ) d
Dynamic polarizability
The BBR shift of an atomic level can be expressed in terms of a scalar
static polarizability to a good approximation [1]:
4
D BBR
•
1
2  T (K ) 
  0 (0)(831.9V / m) 
 (1+ )
2
 300 
Dynamic correction
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), arXiv:1004.3567.
State-insensitive bichromatic optical trapping, Bindiya Arora, M.S.
Safronova, and C. W. Clark, Phys. Rev. A (2010), in press,
arXiv:1005.1259.
Magic wavelengths for the 5p3/2 - 5s transition of Rb
[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)
Example: BBR shift in Sr+ optical frequency standard
Polarizability
Present
0(5s1/2)
91.3(9)
0(4d5/2)
62.0(5)
We reduced the ultimate
uncertainty due the BBR shift
in this frequency standard by a
factor of 10.
BBR shift at
T=300K (in Hz)
Present
Ref.[1]
Ref. [2]
D(5s1/2 → 4d5/2)
0.250(9)
0.33(12)
0.33(9)
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
1% Dynamic correction, E2 and M1 corrections negligible
[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)
Magic wavelengths for the 5s and 5p3/2 | m| = 1/2 states
for l1 =800-810nm and l2=2 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)
Sr
Present
813.45
Expt. [1]
813.42735(40)
Zn
Cd
Present
414(5)
423(4)
Theory [2]
382
390
Hg
Present
365
Theory [3]
360
[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)