Prospects for relic neutrino detection using nuclear spin experiments

TL;DR

This work presents an open-quantum-system treatment of relic neutrino interactions with large spin ensembles, using a Lindblad master equation in the Dicke basis to capture both coherent N^2-enhanced neutrino-spin couplings and realistic local noise. Through perturbative, steady-state, and fast second-order numerical methods, the authors quantify how coherence, sample size, and initial polarisation shape observables such as ⟨J_z⟩ and ⟨J_z^2⟩, and project two-time covariances for experimental inference. Forecasts for CASPEr-like experiments show potential δν sensitivities of order 10^12–10^13 in optimistic-to-realistic scenarios, though achieving such polarisation and noise performance remains a major challenge. The results underscore the viability of quantum-sensing techniques to probe fundamental physics beyond dark matter searches, while setting realistic expectations for direct CνB detection in the near term.

Abstract

Direct detection of the cosmic neutrino background (C$ν$B) remains one of the most formidable experimental challenges in modern physics. In this work, we extend recent studies of C$ν$B-induced coherent transitions in polarised nuclear spin ensembles. Adopting an open quantum system framework, we model coherent neutrino effects in large spin ensembles using a Lindblad master equation that also incorporates realistic experimental imperfections such as local dephasing and imperfect polarisation. We solve the Lindblad equation numerically by way of a fast and computationally inexpensive method that can be extended to an arbitrarily large number of spins. Using our numerical solutions, we forecast the sensitivities of future experiments such as CASPEr to the local C$ν$B overdensity parameter $δ_ν$. Our findings indicate that a CASPEr-like experiment, though primarily aimed at axion dark matter search, could also constrain the C$ν$B overdensity to $δ_ν\sim 10^{13}$ in configurations achievable by currently planned experimental efforts, and down to $δ_ν\sim 10^{11}$ in the most optimised scenario. While C$ν$B detection remains out of reach in the foreseeable future, our results highlight the potential of using quantum sensing to probe fundamental physics.

Figures (13)

• Figure 1: Typical neutrino-spin interaction rates for a single neutrino species at a standard number density $n_\nu \sim 110~{\rm cm}^{-3}$ and with a typical momentum $p_\nu \sim 27~{\rm cm}^{-1}$. Left: The total rate $\Gamma_{\rm tot} \equiv \Gamma_++\Gamma_-$ in the parameter space of system energy splitting $\omega_0$ and sample size $R$, where we have assumed a spin density of $n_s\sim 3\times 10^{22}$ cm$^{-3}$ and a single neutrino mass of $m_{\nu}=0.1$ eV. The regions that exhibit coherent effects are in the top-left corner. Right: Dissipation ratio $\gamma_+/\gamma_-$ in the parameter space of neutrino mass $m_\nu$ and system energy splitting $\omega_0$ in units of neV $=10^{-9}$ eV. The ratio quantifies the imbalance between neutrino-induced excitation ($\gamma_+$) and de-excitation ($\gamma_-$) single-spin processes, setting the dynamics of the system in the absence of other interactions. We find $\gamma_+/\gamma_- < 1$ across the entire parameter space shown, indicating a net de-excitation effect from relic neutrinos on the spin ensemble. The two horizontal red dashed lines denote the splitting energies for an ensemble of $^{129}$Xe spins achieved with two different sub-Tesla magnetic field values.
• Figure 2: Visual representations of collective spin states in an ensemble of spin-$1/2$ particles. Left: The Dicke triangle shows the structure of permutational invariant Dicke states $\vert j, m\rangle$, including the ground state $\vert j, -j\rangle$, excited state $\vert j, j\rangle$, and intermediate states such as the superradiant state $\vert j=N/2, 0\rangle$. The vertical coordinate $m$ parameterises the energy of the system, while the horizontal coordinate $j$ represents the cooperativity of the system, i.e., the degree of coherence in the system. Blue shading indicates regions of enhanced collective effects, as determined by the expectation value of the emission rate operator $\langle \Gamma_+ \Gamma_- \rangle$. Centre: The density matrix for the coherent spins state (or product state) $\vert P\rangle$ in the symmetric subspace basis $\vert N/2, m\rangle\langle N/2, m'\vert$, with $m\in (-N/2, N/2)$ and for $N=30$. We also depict the excited and the ground states, which lie in the opposite extremities of the matrix. Right: Bloch sphere depiction of collective spin states. The ground and the excited Dicke states point in the negative and positive $z$-directions, respectively. The product state $\vert P\rangle$ also has a well-defined classical direction: in this figure, it aligns with $+y$ and relates to the ground state by a $\pi/2$ pulse.
• Figure 3: Time evolution of the standard deviation of the first order observable ${\cal J}_z$, as defined in Eq. \ref{['eq:variance_z']}, for $N=10^8$ and $\gamma_+/\gamma_-=0.997$. The perturbative solution is taken from the approximation in Eq. \ref{['eq:variance_z']}, $\sigma_{{\cal J}_z}=\sqrt{N/4+\gamma_{\rm tot}N^2t}$, whereas the numerical solution is obtained with the second-order approximation method, introduced in Sec. \ref{['sec:2ndorder']}. We highlight the departure from the spin projection noise at $t\gtrsim t_{\rm diss}$ and the breakdown of the perturbative solution at $t\gtrsim (N\gamma_{\rm net})^{-1}$.
• Figure 4: Steady-state scaling of the collective expectation value $\langle {\cal J}^2_x\rangle_{|G\rangle}$ as a function of the number of spins $N$, in the presence of neutrino collective interactions only. The nine curves shown here correspond to different values of the dissipation ratio $\gamma_+ / \gamma_-$ as indicated by the colour scale. For a given $\gamma_+ / \gamma_-$, the observable exhibits convergence at $N \gtrsim \mathcal{O}(10^3)$, with the convergence point shifting to larger values of $N$ as $\gamma_+/\gamma_-$ moves closer to unity.
• Figure 5: Time evolution of collective spin variance $\langle {\cal J}_x^2 \rangle$. We highlight three distinct regimes: (i) coherence-dominated ($\gamma_\pm \gg \gamma_\phi^{\mathrm{loc}}$), where collective dynamics are preserved; (ii) intermediate ($\gamma_\pm \ll \gamma_\phi^{\mathrm{loc}}$, but $N\gamma_\pm \gg \gamma_\phi^{\mathrm{loc}}$), where partial coherence remains; and (iii) dephasing-dominated ($N\gamma_\pm \ll \gamma_\phi^{\mathrm{loc}}$), where local noise suppresses collectivity. Time is scaled by $N\gamma_-$, and the spin variance is shown in units of $N/4$ for $N=100$.