Linear time evolution is one of the fundamental postulates of quantum theory. Past theoretical
attempts to introduce non-linearity into quantum evolution have violated causality. However, a
recent theory has introduced non-linear state-dependent terms in quantum field theory, preserving
causality. Our experiment searches for such terms by correlating a binary macroscopic classical
voltage with the outcome of a projective measurement of a quantum bit, prepared in a coherent
superposition state. We set an upper bound of 4.7×10^{-11}, at 90% confidence level, on the parameter
that quantifies electromagnetic quantum state-dependent non-linearity. Notably, within the nonlinear
quantum theory framework, our result is also a test of the Everett many-worlds interpretation
of quantum theory.

- What is the nature of dark matter? How do we detect it in a laboratory?
- What is the difference between quantum and classical laws of physics? Does quantum wavefunction collapse create different worlds, and do they interact with each other? Is there any non-linearity in time evolution in quantum theory?

This award has supported work by the following postdocs: Alexandr Gramolin, Glenn Randall

The following scientific milestones have been accomplished by our team.

- The apparatus to search for the electron-spin interaction of axion-like dark matter has been constructed, as described in the proposal. The experimental data are being analyzed. Some delays have occurred, due to the difficulty of hiring a postdoc in the COVID-19 pandemic environment, and due to long lead times for liquid helium. Dr. Glenn Randall, who started his postdoc position in the summer of 2021, is currently leading this effort. An important scientific development is the recent analysis of XENONnT data, which showed no excess events above backgrounds [Phys. Rev. Lett., 129(16), 161805 (2022)]. This contradicts the earlier XENON1T claim of excess of electronic recoil events, which was used as the motivation for our search for electron-spin interaction of axion-like dark matter. Therefore the motivation is now significantly weakened. Nevertheless, the versatility of the apparatus we constructed will enable us to adapt it to a search for scalar ultralight dark matter, in the same mass range. The modification amounts to substituting the high-permeability magnetic rods with permanently-magnetized rods. The rest of the experiment will stay unchanged. This planned search has generated significant interest in the ultralight dark matter community in the last few months and will be completed in early 2023.
- We have completed and published a theoretical analysis of the frequency-domain lineshape of an axion-like dark matter signal in our experiment. This work is reported in ref. [5.1] and has already been used to analyze data from dark matter searches and networks, listed in the citing articles.
- We have completed and posted to the arxiv a new method of using intensity interferometry to search for ultra-light dark matter in a broad mass range. This work is reported in ref. [5.2] and may dramatically expand the science reach of experiments that search for ultralight dark matter. The proposed detection scheme is analogous to Hanbury Brown and Twiss intensity interferometry: a network of detectors with a given finite bandwidth can be used to search for bosons with Compton frequencies many orders of magnitude larger than the detector bandwidth. This work is currently under review.
- The most notable scientific result, enabled by the CFP Templeton grant so far, is our search
for causal non-linear state-dependent terms in quantum field theory. Linear time evolution is
one of the fundamental postulates of quantum theory. Past theoretical attempts to introduce
non-linearity into quantum evolution have violated causality. However, a recent theory has
introduced non-linear state-dependent terms in quantum field theory, preserving causality.
Our experiment searches for such terms by correlating a binary macroscopic classical voltage
with the outcome of a projective measurement of a quantum bit, prepared in a coherent
superposition state. We set an upper bound of 4.7×10
^{-11}, at 90% confidence level, on the parameter that quantifies electromagnetic quantum state-dependent non-linearity. Notably, within the non-linear quantum theory framework, our result is also a test of the Everett many-worlds interpretation of quantum theory. This work is reported in ref. [5.3] and is currently under review.

- In the next two years we will complete the search for the electron-spin interaction of axion-like dark matter and the search for scalar ultralight dark matter in the 10 peV – 10 neV mass range.
- We expect that our new method of using Hanbury Brown-Twiss intensity interferometry to search for ultra-light dark matter will lead to new searches for ultralight dark matter by sensor networks, with greatly expanded mass range reach.
- We expect that our work on experimental tests for non-linear quantum dynamics will generate accelerating scientific interest and progress over the next few years. There are already experimental efforts, searching for similar physics with trapped ions [arXiv:2206.12976] and with atom interferometers (Jason Hogan’s group at Stanford).

- Alexander V. Gramolin, Arne Wickenbrock, Deniz Aybas, Hendrik Bekker, Dmitry Budker, Gary P. Centers, Nataniel L. Figueroa, Derek F. Jackson Kimball, and Alexander O. Sushkov, “Spectral signatures of axionlike dark matter” Phys. Rev. D 105, 035029 (2022) (support was properly acknowledged)
- Hector Masia-Roig, Nataniel L. Figueroa, Ariday Bordon, Joseph A. Smiga, Dmitry Budker, Gary P. Centers, Alexander V. Gramolin, Paul S. Hamilton, Sami Khamis, Christopher A. Palm, Szymon Pustelny, Alexander O. Sushkov, Arne Wickenbrock, and Derek F. Jackson Kimball, “Intensity interferometry for ultralight bosonic dark matter detection”, arXiv:2202.02645 [hep-ph] (support was properly acknowledged)
- Mark Polkovnikov, Alexander V. Gramolin, David E. Kaplan, Surjeet Rajendran, Alexander O. Sushkov, “Experimental limit on non-linear state-dependent terms in quantum theory” arXiv:2204.11875 (2022) (support was properly acknowledged)

- We will publish the results of our search for the electron-spin interaction of axion-like dark matter in the 10 peV – 10 neV mass range.
- We will publish the results of our search for scalar ultralight dark matter in the 10 peV – 10 neV mass range.

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