## Abstract

The standard model of particle physics accurately describes all particle physics measurements made so far in the laboratory. However, it is unable to answer many questions that arise from cosmological observations, such as the nature of dark matter and why matter dominates over antimatter throughout the Universe. Theories that contain particles and interactions beyond the standard model, such as models that incorporate supersymmetry, may explain these phenomena. Such particles appear in the vacuum and interact with common particles to modify their properties. For example, the existence of very massive particles whose interactions violate time-reversal symmetry, which could explain the cosmological matter–antimatter asymmetry, can give rise to an electric dipole moment along the spin axis of the electron. No electric dipole moments of fundamental particles have been observed. However, dipole moments only slightly smaller than the current experimental bounds have been predicted to arise from particles more massive than any known to exist. Here we present an improved experimental limit on the electric dipole moment of the electron, obtained by measuring the electron spin precession in a superposition of quantum states of electrons subjected to a huge intramolecular electric field. The sensitivity of our measurement is more than one order of magnitude better than any previous measurement. This result implies that a broad class of conjectured particles, if they exist and time-reversal symmetry is maximally violated, have masses that greatly exceed what can be measured directly at the Large Hadron Collider.

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## Data availability

The data that support the conclusions of this article are available from the corresponding authors on reasonable request.

## Additional information

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## Acknowledgements

This work was supported by the NSF. J.H. was supported by the Department of Defense. D.G.A. was partially supported by the Amherst College Kellogg University Fellowship. We thank M. Reece and M. Schwartz for discussions and S. Cotreau, J. MacArthur and S. Sansone for technical support.

### Reviewer information

*Nature* thanks E. Hinds and Y. Shagam for their contribution to the peer review of this work.

## Author information

### Author notes

- V. Andreev

Present address: Max Planck Institute of Quantum Optics, Garching, Germany

- A. D. West
- & E. P. West

Present address: Department of Physics and Astronomy, UCLA, Los Angeles, CA, USA

A list of participants and their affiliations appears at the end of the paper.

### Affiliations

#### Department of Physics, Harvard University, Cambridge, MA, USA

- V. Andreev
- , D. G. Ang
- , J. M. Doyle
- , G. Gabrielse
- , J. Haefner
- , N. R. Hutzler
- , C. Meisenhelder
- , C. D. Panda
- , E. P. West
- & X. Wu

#### Department of Physics, Yale University, New Haven, CT, USA

- D. DeMille
- , Z. Lasner
- , B. R. O’Leary
- , A. D. West
- & X. Wu

#### Center for Fundamental Physics, Northwestern University, Evanston, IL, USA

- G. Gabrielse

#### Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA, USA

- N. R. Hutzler

### Consortia

### ACME Collaboration

- V. Andreev
- , D. G. Ang
- , D. DeMille
- , J. M. Doyle
- , G. Gabrielse
- , J. Haefner
- , N. R. Hutzler
- , Z. Lasner
- , C. Meisenhelder
- , B. R. O’Leary
- , C. D. Panda
- , A. D. West
- , E. P. West
- & X. Wu

### Contributions

All authors contributed to one or more of the following areas: proposing, leading and running the experiment; design, construction, optimization and testing of the experimental apparatus and data acquisition system; setup and maintenance during the data runs; data analysis and extraction of physics results from measured traces; modelling and simulation of systematic errors; and the writing of this article. The corresponding authors are D.D., J.M.D. and G.G. (acme@physics.harvard.edu).

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to D. DeMille or J. M. Doyle or G. Gabrielse.

## Extended data figures and tables

### Extended Data Fig. 1 Switching timescales.

**a**, Fluorescence signal amplitude versus time in an \(\hat{{\boldsymbol{X}}},\hat{{\boldsymbol{Y}}}\) polarization cycle. The red line corresponds to the signal from the \(\hat{{\boldsymbol{X}}}\)-polarization laser and the black line to the signal from the \(\hat{{\boldsymbol{Y}}}\)-polarization laser.**b**, Measured molecular trace (25 averaged pulses) versus time. Signal averaged over the entire \(\hat{{\boldsymbol{X}}},\hat{{\boldsymbol{Y}}}\) polarization cycles shown in**a**are shown in red and black for the \(\hat{{\boldsymbol{X}}}\) and \(\hat{{\boldsymbol{Y}}}\) laser polarizations, respectively.**c**, Switches performed within a block. The \(\tilde{\mathcal{N}}\) and \(\tilde{\mathcal{B}}\) switches randomly alternate between a (−+) and a (+−) pattern, and the \(\tilde{\mathcal{E}}\) and \(\tilde{\theta}\) switches randomly alternate between (−++−) and (+−−+) between blocks.**d**, Switches performed within a superblock. The \(\tilde{\mathcal{P}}\)-state order is selected randomly, while \(\tilde{\mathcal{L}}\) and \(\tilde{\mathcal{R}}\) are deterministic.**e**, Run-data structure. We alternate between ‘normal’ EDM data, taken at three values of \(|{{\mathcal{B}}}_{z}|\), and monitoring of known systematic effects by performing intentional parameter variations (IPVs). For several days data were taken with \(|{{\mathcal{B}}}_{z}|=2.6\,{\rm{m}}{\rm{G}}\) instead of \(|{{\mathcal{B}}}_{z}|=0.7\,{\rm{m}}{\rm{G}}\), which is shown in the figure. Each IPV corresponds to one superblock, where a control parameter (*A*–*E*) is deliberately offset from its ideal value. Here,*A*=*P*_{ref}(the refinement beam is completely blocked, to determine the intrinsic \({\omega }_{{\rm{S}}{\rm{T}}}^{{\mathcal{N}}{\mathcal{E}}}\)), \(B={{\mathcal{E}}}^{{\rm{n}}{\rm{r}}}\), \(C={P}^{{\mathcal{N}}{\mathcal{E}}}\), \(D={\phi }_{{\rm{S}}{\rm{T}}}^{{\mathcal{N}}{\mathcal{E}}}\) and \(E={\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z\). The magnetic-field magnitude for the IPV of parameter*E*was varied between three experimental values within a run.**f**, The EDM dataset. The electric-field magnitude was varied from day to day. The magnetic-field magnitude for the IPVs for parameters*A*,*B*,*C*and*D*was varied between three experimental values.### Extended Data Fig. 2 The \({\boldsymbol{\partial }}{\pmb{\mathcal{B}}}_{{\boldsymbol{z}}}/{\boldsymbol{\partial }}{\boldsymbol{z}}\times {\boldsymbol{\delta }}\times {\boldsymbol{\partial }}{\pmb{\mathcal{E}}}^{{\bf{n}}{\bf{r}}}/{\boldsymbol{\partial }}{\boldsymbol{z}}\) systematic error.

**a**, A \({\rm{\partial }}{{\mathcal{E}}}^{{\rm{n}}{\rm{r}}}/{\rm{\partial }}z\) gradient (blue arrows) causes a*z*-dependent two-photon detuning correlated with \({\mathcal{N}}{\mathcal{E}}\) (\({\delta }_{z}^{{\mathcal{N}}{\mathcal{E}}}\)), due to the Stark shift \(D{\mathcal{E}}\). When*δ*≠ 0, the combination of a non-zero \({\delta }_{z}^{{\mathcal{N}}{\mathcal{E}}}\) and a dependence of the STIRAP efficiency on the two-photon detuning, ∂*η*/∂*δ*(shown as black lines), acts to translate the detected molecular cloud (purple gradient ellipse) position by \({\rm{d}}{z}_{{\rm{c}}{\rm{m}}}^{{\mathcal{N}}{\mathcal{E}}}\) (purple arrow). A non-zero \({\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z\) (teal-colour gradient) causes molecules to accumulate more (less) precession phase if their position has a smaller (larger)*z*coordinate. The effects combine to create the dependence of \({\omega }^{{\mathcal{N}}{\mathcal{E}}}\) on \({\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z\). The scales are exaggerated for clarity.**b**, The effect of changing the STIRAP two-photon detuning,*δ*, on the \({\omega }^{{\mathcal{N}}{\mathcal{E}}}\) versus \({\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z\). We note that the slope \({\rm{\partial }}{\omega }^{{\mathcal{N}}{\mathcal{E}}}/{\rm{\partial }}({\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z)\) is consistent with zero when*δ*is set to zero.**c**, Dependence of \({\omega }^{{\mathcal{N}}{\mathcal{E}}}\) on*δ*and \({\rm{\partial }}{{\mathcal{B}}}_{z}/{\rm{\partial }}z\). Fits (dashed curves) to a simple lineshape model (see Methods) show good agreement with the data.*δ*= 0 is defined as the point where all curves cross. The error bars in**b**and**c**represent 1*σ*statistical uncertainties.

## Supplementary information

### Supplementary Information

The supplementary methods section contains text describing in detail the mechanisms leading to the systematics effects referenced in the main text.

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