Science - USA (2022-04-08)

driven. If true, this would have certain impli-
cations for the symmetry of the superconduct-
ing order parameter ( 33 , 34 ). Recent transport
measurements that indicate reentrant super-
conductivity at high magnetic field are com-
patible with a spin-triplet order parameter
that would be sensitive to disorder of the type
we observed ( 5 ).
Confirmation of this hypothesis requires
direct measurements of the effect of disorder
on superconductivity. Future work that sys-
tematically explores this expanded phase space
by controllably tuning moiré defect density
through the angle mismatchdqhas the po-
tential to further shed light on the pairing
mechanism in TTG by determining its sensi-
tivity to nonmagnetic impurity scattering, as
has been done in a range of other uncon-
ventional systems ( 35 – 37 ).

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ACKNOWLEDGMENTS
We thank D. Halbertal, H. Ochoa, and A. Tsvelik for fruitful
discussions.Funding:Studies of the electronic structure of twisted
trilayer graphene were supported as part of Programmable

Quantum Materials, an Energy Frontier Research Center funded by

the US Department of Energy (DOE), Office of Science, Basic

Energy Sciences (BES), under award DE-SC0019443. The synthesis

of the trilayer samples was supported by the NSF MRSEC

program through Columbia in the Center for Precision-Assembled

Quantum Materials (PAQM) DMR-2011738 and by DMR-2004691.

Support for cryogenic STM measurements was provided by the Air

Force Office of Scientific Research through grant FA9550-21-1-0378.

Z.Z. and E.K. are supported by STC Center for Integrated

Quantum Materials, NSF grant DMR-1231319, ARO MURI grant

W911NF14-0247, and NSF DMREF grant 1922165. Relaxation

calculations were performed on the Odyssey cluster supported

by the FAS Division of Science, Research Computing Group

at Harvard University. M.C. and S.S. are supported by NSF grant

DMR-2002850. K.W. and T.T. acknowledge support from the

Elemental Strategy Initiative conducted by the MEXT, Japan (grant

JPMXP0112101001) and JSPS KAKENHI (grants 19H05790 and

JP20H00354).Author contributions:S.T. and J.S. conceived the

experiment. J.S. fabricated samples and performed AFM and PFM

measurements. S.T. performed STM measurements, analyzed

the experimental data, and performed single-particle band structure

calculations. Z.Z. performed structural relaxation calculations.

M.C. and M.S.S. performed interacting band structure calculations.

K.W. and T.T. provided the BN crystals. S.S., E.K., C.R.D., and

A.N.P. advised. S.T. wrote the manuscript, with contributions from all

authors.Competing interests:The authors declare no competing

interests.Data and materials availability:Data and calculations that

support the conclusions of this work are available in ( 38 ).

SUPPLEMENTARY MATERIALS

science.org/doi/10.1126/science.abk1895

Materials and Methods

Supplementary Text

Figs. S1 to S17

References ( 39 – 53 )

27 June 2021; accepted 9 March 2022

10.1126/science.abk1895

PHYSICS

Measurement of a helium tune-out frequency:

an independent test of quantum electrodynamics

B. M. Henson^1 †, J. A. Ross^1 †, K. F. Thomas^1 , C. N. Kuhn^2 , D. K. Shin^1 , S. S. Hodgman^1 ,

Yong-Hui Zhang^3 , Li-Yan Tang^3 *, G. W. F. Drake^4 *, A. T. Bondy^4 , A. G. Truscott^1 , K. G. H. Baldwin^1 *

Despite quantum electrodynamics (QED) being one of the most stringently tested theories underpinning

modern physics, recent precision atomic spectroscopy measurements have uncovered several small

discrepancies between experiment and theory. One particularly powerful experimental observable

that tests QED independently of traditional energy level measurements is the“tune-out”frequency,

where the dynamic polarizability vanishes and the atom does not interact with applied laser light. In this

work, we measure the tune-out frequency for the 2^3 S 1 state of helium between transitions to the 2^3 P

and 3^3 Pmanifolds and compare it with new theoretical QED calculations. The experimentally determined

value of 725,736,700(260) megahertz differs from theory [725,736,252(9) megahertz] by 1.7 times

the measurement uncertainty and resolves both the QED contributions and retardation corrections.

Q

uantum electrodynamics (QED) describes

the interaction between matter and light.

It is so ubiquitous that the theory is con-

sidered a cornerstone of modern phys-

ics. QED has been remarkably predictive

in describing fundamental processes, such as

spontaneous emission rates of photons from

atoms and the anomalous electron magnetic

moment ( 1 ). However, as the precision of atomic

spectroscopy approaches the part-per-trillion

level, discrepancies between such predictions

and experiments have come to light, such as

the“proton radius puzzle”( 2 ). Spectroscopic

measurements [of muonic hydrogen ( 3 ), hy-

drogen ( 4 , 5 ), and muonic deuterium ( 6 )] yield

determinations of the proton radius that dis-

agree with other approaches [electron-proton

scattering ( 7 ) and hydrogen spectroscopy ( 8 )]

by up to five standard deviations.

Helium is an ideal testing ground for QED

because its simple two-electron structure makes

high-precision predictions tractable and test-

able. Notably, helium also presents a nuclear

“puzzle,”with precision measurement of iso-

tope shifts of the 2^3 S 1 → 23 P(0,1,2)( 9 ) and 2^3 S 1 → 21 S 0

( 10 ) transitions disagreeing by two standard

deviations in the derived nuclear charge ra-

dius. Further, recent measurements of the ion-

ization energy for the helium 2^1 S 0 state ( 11 )

confirm similar discrepancies in the Lamb

shift to those recently revealed theoretically

( 12 ). These puzzles raise the possibility that

the issue lies with QED itself ( 13 ). Thus, we

look to challenge QED directly by precision

spectroscopy in helium beyond the usual en-

ergy interval measurements.

An atom in an optical field experiences an

energy shift in proportion to the real part of

the frequency-dependent polarizability, a fun-

damental atomic property dictated by the

SCIENCEscience.org 8 APRIL 2022•VOL 376 ISSUE 6589 199

(^1) Department of Quantum Science and Technology, Research
School of Physics, The Australian National University,
Canberra, ACT 2601, Australia.^2 Centre for Quantum and
Optical Science, Swinburne University of Technology,
Melbourne, VIC 3122, Australia.^3 State Key Laboratory of
Magnetic Resonance and Atomic and Molecular Physics,
Innovation Academy for Precision Measurement Science and
Technology, Chinese Academy of Sciences, Wuhan 430071,
People’s Republic of China.^4 Department of Physics,
University of Windsor, Windsor, Ontario N9B 3P4, Canada.
*Corresponding author. Email: [email protected]
(K.G.H.B.); [email protected] (G.W.F.D.); [email protected]
(L.-Y.T.)
†These authors contributed equally to this work.
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