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arXiv:2304.02523 · Annalen der Physik

A Quantum Perspective on Oscillation Frequencies in Axion Dark Matter Experiments

Joerg Jaeckel, Valentina Montoya, Cedric Quint

Published Sep 21, 2023• 0 citations
arXivHTMLPDF

Abstract

Abstract In this paper, the time evolution of signals in axion dark matter experiments is considered from a quantum perspective. The aim is to illuminate the specific case of axion experiments and not to contribute new results to the general discussion of the quantum/classical connection. Classically, one expects a signal oscillating with a frequency equal to the axion mass whose amplitude is slowly rising due to the tiny interaction of the axions with ordinary matter. Quantum mechanically the latter time‐scale arises from the small splitting in the energy levels induced by the interaction between the axions and the experiment. It is always present in suitable, sensitive experiments. Signals that oscillate with the axion mass arise from processes changing the axion number. For certain observables such oscillations are absent for special initial quantum states of the axions. Examples are shown where these special states can be affected by the experiment such that a signal oscillating with the axion mass re‐appears. Suitable correlators that feature an oscillation with the axion mass are discussed, and comments on the connection to the classical treatment are provided. Explicitly, the Cosmic Axion Spin Precession Experiment (CASPEr) is studied, but these findings are expected to be adaptable to other axion dark matter searches.

DOI
10.1002/andp.202300151

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Abstract In this paper, the time evolution of signals in axion dark matter experiments is considered from a quantum perspective. The aim is to illuminate the specific case of axion experiments and not to contribute new results to the general discussion of the quantum/classical connection. Classically, one expects a signal oscillating with a frequency equal to the axion mass whose amplitude is slowly rising due to the tiny interaction of the axions with ordinary matter. Quantum mechanically the latter time‐scale arises from the small splitting in the energy levels induced by the interaction between the axions and the experiment. It is always present in suitable, sensitive experiments. Signals that oscillate with the axion mass arise from processes changing the axion number. For certain observables such oscillations are absent for special initial quantum states of the axions. Examples are shown where these special states can be affected by the experiment such that a signal oscillating with the axion mass re‐appears. Suitable correlators that feature an oscillation with the axion mass are discussed, and comments on the connection to the classical treatment are provided. Explicitly, the Cosmic Axion Spin Precession Experiment (CASPEr) is studied, but these findings are expected to be adaptable to other axion dark matter searches.
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Quantum phase measurements offer a complementary route to axion searches. We show that axion-photon interactions can imprint both Aharonov-Bohm (AB) and Berry phases in experimentally motivated quantum setups. For a coherently oscillating axion dark matter background, the induced effective current generates a time dependent magnetic flux in an rf-SQUID, leading to a measurable voltage signal through the Josephson phase. For representative benchmarks, this AB phase search reaches the minimum axion-photon coupling gaγγmin∼7.8×10−14 GeV−1g_{aγγ}^{\mathrm{min}}\sim 7.8\times10^{-14}~\mathrm{GeV}^{-1}gaγγmin​∼7.8×10−14 GeV−1 at axion mass ma∼10−10 eVm_a\sim 10^{-10}~\mathrm{eV}ma​∼10−10 eV, with projected sensitivity that can improve on existing limits in that parameter space by roughly one to two orders of magnitude. We also identify a geometric phase observable in a Mach-Zehnder interferometer with an adiabatically rotating magnetic field, providing a proof-of-principle phase-based probe of meV-scale axions even when they do not constitute the dark matter, although sensitivity on the coupling remains weaker than current bounds with conservative tabletop benchmarks. Extending the analysis to a three level photon-axion quasiparticle (AQP)-axion system, with the AQP realized in a topological magnetic insulator, we find a potentially measurable THz Berry phase dominated by the AQP sector, furnishing a nontrivial validation of the formalism in a richer coupled system. These setups establish quantum phase observables as a useful new framework for axion searches, with immediate phenomenological promise in superconducting circuits and longer term potential in quantum enhanced interferometry.
Quantum coherence is one of the most striking features of quantum mechanics rooted in the superposition principle. Recently, it has been demonstrated that it is possible to harvest the quantum coherence from a coherent scalar field. In order to explore a new method of detecting axion dark matter, we consider a point-like Unruh–DeWitt detector coupled to the axion field and quantify a coherent measure of the detector. We show that the detector can harvest the quantum coherence from the axion dark matter. To be more precise, we consider a two-level electron system in an atom as the detector. In this case, we obtain the coherence measure [Formula: see text] where [Formula: see text] and [Formula: see text] are an observation time and the Lorentz factor. At the same time, the axion mass [Formula: see text] we can probe is determined by the energy gap of the detector.
We provide a fully quantum-mechanical description of the continuous measurement of wavelike dark matter. Our focus is cavity haloscopes, although our results inform a broad range of axion searches. We extend the input-output formalism by treating the axion as a quantum field, finding how its quantum state is imprinted onto higher-order moments of observables of the outgoing transmission-line modes. We further develop a novel measurement-record formalism, which computes the joint probability distribution of all measurement outcomes and is well suited to studying the axion in the time domain. With it, we compute the exact axion-induced number distribution for the first time, demonstrating that it is not Poisson. We argue that virialized axion dark matter is expected to be in a Gaussian quantum state, and show that number or quadrature measurements can distinguish this from the predictions of a coherent state or even a Bose-Einstein condensate. Finally, we show that intrinsically quantum effects, such as those from Fock or squeezed axion states, are far too weak to detect.
We propose a magnetic resonance force microscopy (MRFM) search for axion dark matter around 1 GHz. The experiment leverages the axion's derivative coupling to electrons, which induces an effective A.C. magnetic field on a sample of electron spins polarized by a D.C. magnetic field and a micromagnet. A second pump field at a nearby frequency enhances the signal, with the detuning matched to the resonant frequency of a magnet-loaded mechanical oscillator. The resulting spin-dependent force is detected with hih sensitivity via optical interferometry. Accounting for the relevant noise sources, we show that current technology can be used to put constraints competitive with those from laboratory experiments with just a minute of integration time. Furthermore, varying the pump field frequency and D.C. magnetic field allows one to scan the axion mass. Finally, we explore this setup's capability to put constraints on other dark matter - Standard Model couplings.
These notes summarize lectures given at the 2019 Les Houches summer school on Quantum Information Machines. They describe and review an application of quantum metrology concepts to searches for ultralight dark matter. In particular, for ultralight dark matter that couples as a weak classical force to a laboratory harmonic oscillator, quantum squeezing benefits experiments in which the mass of the dark matter particle is unknown. This benefit is present even if the oscillatory dark matter signal is much more coherent than the harmonic oscillator that it couples to, as is the case for microwave frequency searches for dark matter axion particles.