High-Accuracy Measurement of Atomic Polarizability in an Optical Lattice Clock

Abstract

Despite being a canonical example of quantum mechanical perturbation theory, as well as one of the earliest observed spectroscopic shifts, the Stark effect contributes the largest source of uncertainty in a modern optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock levels α clock = 36.2612(7) kHz (kV/cm) −2 . The clock's fractional uncertainty due to room temperature blackbody radiation is reduced an order of magnitude to 3 × 10 −17 .PACS numbers: 32.10. Dk, 32.60.+i, 06.20.fb,44.40.+a An atom immersed in an electric field E a becomes polarized -the electronic wave-function is stretched into alignment with the field. Generally, energies of the lowest-lying electronic quantum states |i are reduced by − cold alkaline-earth atoms tightly confined in an optical standing wave potential so their intrinsically narrow, largely imperturbable,may establish stable and accurate frequency and time references [4,5]. In analogy to a pendulum's oscillation slowing due to thermal expansion, a ytterbium lattice clock slows when electrically stretched, or polarized, by thermal blackbody radiation (BBR) fields [6,7]. This phenomenon has been measured in the cesium fountain primary standard [8,9] and other optical transitions [1,10,11].No shield at finite temperature protects a clock atom from the time varying electric field of BBR, the electromagnetic energy absorbed and re-emitted by all matter in thermal equilibrium according to the Stefan-Boltzmann law [12]. Inside a hollow shell of opaque matter (a blackbody), the time-averaged electric field intensity depends strongly on temperature:where α ≈ 1/137 is the fine-structure constant, k B is Boltzmann's constant, and T is the blackbody's absolute temperature [13]. Near room temperature, the spectrum of radiation is peaked strongly near 9.6 µm-invisible to the eye and also far detuned from strong electronic transitions in ytterbium.The ytterbium clock frequency (ν ≈ 518 THz) is shifted by the net BBR Stark effect of the two clock states, which can be expressed aswhere αg,e are the static polarizabilities of ground and excited states ( 1 S 0 and 3 P 0 , respectively), and η clock (T ) [7] arXiv:1112.2766v1 [physics.atom-ph]

Absolute frequency measurement of the ${{}^{1}}{{\text{S}}_{0}}$ – ${{}^{3}}{{\text{P}}_{0}}$ transition of171Yb

“…The black body radiation (BBR) emitted by bodies at temper ature T 0 K ≠ surrounding the atomic cloud induces a systematic Stark shift of the clock transition frequency according to [41] …”

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

“…For example, one of the largest contributions to the uncertainty budget of atomic clocks is the uncertainty in the blackbody radiation (BBR) shift [2,12]. The BBR shift is calculated from the difference in the electric-dipole polarizabilities between the clock states [13], and its accuracy is currently limited by uncertainty in atomic transition matrix elements.…”

“…Precise knowledge of atomic transition strengths is important in many current areas of research, including the development of ultra-precise atomic clocks [1][2][3], studies of fundamental symmetries [4,5] and degenerate quantum gases [6], quantum information [7,8], plasma physics [9], and astrophysics [10,11]. For example, one of the largest contributions to the uncertainty budget of atomic clocks is the uncertainty in the blackbody radiation (BBR) shift [2,12].…”

Horloge à réseau optique à atomes de mercure

“…Une approche très prudente que nous avions adoptée dans [39], et qui est reproduite dans le tableau 2, consiste à considérer que l'incertitude est égale à la valeur calculée. Lorsqu'on examine l'historique de ce type de calcul et son niveau d'accord avec l'expérience pour d'autres atomes [18,19,42], on peut estimer qu'une incertitude réelle est plutôt égale à 10 % de la valeur, ce qui correspondrait à 1,6 × 10 −17 . Enfin, nous avons mesuré le déplacement lumineux lié au piégeage par le réseau pour un ensemble de valeur de la profondeur et de la longueur d'onde du piège.…”