Reducing Decoherence in Quantum SensorsCharles W. Clark1 and Marianna Safronova2

1Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, Gaithersburg, Maryland2 Department of Physics and Astronomy, University of Delaware, Delaware

Reducing Decoherence in Quantum SensorsCharles W. Clark1 and Marianna Safronova2

1Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, Gaithersburg, Maryland2 Department of Physics and Astronomy, University of Delaware, Delaware

AbstractAbstractAbstractAbstract

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.

Blackbody Radiation Blackbody Radiation ShiftsShifts

Blackbody Radiation Blackbody Radiation ShiftsShifts

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).

T = 300 K

Level A

Level B

BBR

The temperature-dependent electric field created by the blackbody radiation is described by (in a.u.) : 3

2 8( )

exp( / ) 1

dE

kT

The frequency shift caused by this electric field is:

2BBR ( ) ( ) v A E 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]:

42

BBR 0

1 ( )(0)(831.9 / ) (1+ )

2 300

T KV m

Dynamic correctionDynamic correction

[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)

Clock transition

Magic Magic WavelengthWavelength

Magic Magic WavelengthWavelength

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).

Magic Wavelengths in atomic frequency Magic Wavelengths in atomic frequency standards (nm)standards (nm)

Magic Wavelengths in atomic frequency Magic Wavelengths in atomic frequency standards (nm)standards (nm)

[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)

Sr Present Expt. [1]813.45 813.42735(40)

Present Theory [2]Zn 414(5) 382Cd 423(4) 390

Present Theory [3]Hg 365 360

Atomic ClocksAtomic ClocksAtomic ClocksAtomic 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 Decoherence Effects in Atomic

ClocksClocksDecoherence Effects in Atomic Decoherence Effects in Atomic

ClocksClocks

NIST Yb optical clock

For recent optical and microwave atomic clock schemes, a major contributor to the uncertainty budget is the blackbody radiation shift.

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.)

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).

Example: BBR shift in SrExample: BBR shift in Sr++ optical optical frequency standardfrequency standard

Example: BBR shift in SrExample: BBR shift in Sr++ optical optical frequency standardfrequency standard

BBR shift at T=300K (in Hz)

Present Ref.[1] Ref. [2]

(5s1/2 → 4d5/2) 0.250(9) 0.33(12) 0.33(9)

Polarizability Present

0(5s1/2) 91.3(9)

0(4d5/2) 62.0(5)

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)

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).

We reduced the ultimate uncertainty due the BBR shift in this frequency standard by a factor of 10.

Optimization of optical Optimization of optical cooling and trapping cooling and trapping

schemesschemes

Optimization of optical Optimization of optical cooling and trapping cooling and trapping

schemesschemes• 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).

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.

Surface plot for the 5s and 5p3/2 |m| = 1/2 state polarizabilities as a function of laser wavelengths

1 and 2 for equal intensities of both lasers

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

Magic wavelengths for the 5p3/2 - 5s transition of Rb