Experimental determination of the E2-M1 polarizability of the strontium clock transition S. D orscher J. Klose S. Maratha Palliand Ch. Lisdaty

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Experimental determination of the E2-M1 polarizability of the strontium clock

transition

S. D¨orscher, J. Klose, S. Maratha Palli,∗and Ch. Lisdat†

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany

(Dated: October 27, 2022)

To operate an optical lattice clock at a fractional uncertainty below 10−17, one must typically

consider not only electric-dipole (E1) interaction between an atom and the lattice light ﬁeld when

characterizing the resulting lattice light shift of the clock transition but also higher-order multipole

contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However,

strongly incompatible values have been reported for the E2-M1 polarizability diﬀerence of the clock

states (5s5p)3P0and (5s2)1S0of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018);

Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium

clocks with uncertainties of few 10−18, as the resulting lattice light shift corrections deviate by up

to 1 ×10−17 from each other at typical trap depths. We have measured the E2-M1 polarizability

diﬀerence using our 87Sr lattice clock and ﬁnd a value of ∆αqm =−987+174

−223 µHz. This result is in

very good agreement with the value reported by Ushijima et al.

The interaction between the optical lattice and the

trapped atom plays an important role in optical clocks

with neutral atoms and has been investigated in several

publications: As the accuracy of optical lattice clocks in-

creases, one must take into account not only the electric-

dipole (E1) interaction between atom and laser ﬁeld [1]

but also higher-order multipole interactions and two-

photon coupling [2–6]. In electric-dipole approximation,

the lattice light shift on the clock transition cancels for

all lattice depths if the lattice is operated at the magic

wavelength [1], but the higher-order contributions render

this general cancellation impossible. Lastly, the individ-

ual contributions to the lattice light shift depend intri-

cately on the motional state of the individual atom and

thus on the population distribution of the atoms in the

lattice [4, 5, 7].

Although the description of the light shift as a function

of lattice depth can be simpliﬁed [4], the necessary con-

ditions require careful testing and are not met in many

cases. In the general case, however, several atomic pa-

rameters need to be known accurately, including the dif-

ference of the polarizabilities by electric-quadrupole (E2)

and magnetic-dipole (M1) coupling, ∆αqm, at the given

lattice light frequency and polarisation. The most accu-

rate determinations of this atomic parameter for stron-

tium lattice clocks have been reported by Ushijima et al.

[5] using an experimental approach, where the diﬀerent

contributions to the lattice light shift are separated by

their diﬀerent dependences on the motional state of the

atoms and on the lattice light intensity, and by Porsev

et al. [6] based on atomic structure calculations. Worry-

ingly, these two values are extremely incompatible with

each other, as they diﬀer by about twenty-two times their

combined standard uncertainty (see Fig. 4)

Given this discrepancy, it becomes diﬃcult at best to

accurately correct for the lattice light shift at an uncer-

tainty of few 10−18 or less in units of the clock transition

frequency (referred to as fractional units hereafter): Us-

Δαqm

Porsev

Δαqm

Ushijima

-10 -5 0

fraconal lace light shi (10 -18)

Δαqm

Porsev

Δαqm

Ushijima

}

cold atoms

}

hot atoms

FIG. 1. Lattice light shifts estimated using either the value

of ∆αqm reported by Porsev et al. [6] or by Ushijima et al.

[5], for diﬀerent models (dots: Ref. [4]; squares: Ref. [5]) and

experimental conditions (see text) when the lattice light shift

is equalized for trap depths of 77Erand 149Er.

ing either value of ∆αqm, the E2-M1 contribution to the

lattice light shift diﬀers by about 1 ×10−17 in fractional

units (see Fig. 1) under typical conditions, including a

trap depth of around 100Er, where Er=h2/(2mλ2

m) is

the photon recoil energy at the lattice wavelength λm

for an atom of mass m, regardless of which light shift

model [4, 5] is used. Even in the motional ground state,

i.e., in the limit of zero temperature, the diﬀerence ex-

ceeds 3 ×10−18 for any reasonable [8, 9] lattice depth.

Hence, the discrepancy cannot be mitigated by operating

at lower lattice depth or by preparing the atomic sam-

ple closer to the motional ground state, e.g., by cooling

to sub-recoil temperatures as demonstrated recently for

ytterbium [10].

Here, we report on an independent experimental deter-

mination of ∆αqm(λm) of the clock transition in neutral

strontium (mF=±9/2, ∆mF= 0). Our measurement

procedure follows a similar approach as the one presented

in Ref. [5]. We measure the diﬀerential light shift be-

tween samples with diﬀerent motional state distributions

at a ﬁxed lattice depth in a new experimental apparatus

that uses the same interrogation laser [11] as our previ-

ous system [12] and a vertically oriented, one-dimensional

optical lattice. The procedure used to measure diﬀeren-

arXiv:2210.14727v1 [physics.atom-ph] 26 Oct 2022

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摘要：

ExperimentaldeterminationoftheE2-M1polarizabilityofthestrontiumclocktransitionS.Dorscher,J.Klose,S.MarathaPalli,andCh.LisdatyPhysikalisch-TechnischeBundesanstalt,Bundesallee100,38116Braunschweig,Germany(Dated:October27,2022)Tooperateanopticallatticeclockatafractionaluncertaintybelow1017,onemusttyp...

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Experimental determination of the E2-M1 polarizability of the strontium clock transition S. D orscher J. Klose S. Maratha Palliand Ch. Lisdaty

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