Searches for Massive Neutrinos with Mechanical Quantum Sensors

The development of quantum optomechanics now allows mechanical sensors with femtogram masses to be controlled and measured in the quantum regime. If the mechanical element contains isotopes that undergo nuclear decay, measuring the recoil of the sensor following the decay allows reconstruction of the total momentum of all emitted particles, including any neutral particles that may escape detection in traditional detectors. As an example, for weak nuclear decays the momentum of the emitted neutrino can be reconstructed on an event-by-event basis. We present the concept that a single nanometer-scale optically levitated sensor operated with sensitivity near the standard quantum limit can search for heavy sterile neutrinos in the keV-MeV mass range with sensitivity significantly beyond existing laboratory constraints. We also comment on the possibility that mechanical sensors operated well into the quantum regime might ultimately reach the sensitivities required to provide an absolute measurement of the mass of the light neutrino states.

Popular Summary

Neutrinos are the most elusive of the known fundamental particles, typically requiring huge detectors (with masses of a kiloton or more) to identify even a handful of their interactions. However, if nuclei that decay by emitting neutrinos are implanted in tiny nanoparticles, then the momentum of the neutrino emitted in the decay can be measured not by detecting the neutrino itself but, rather, by measuring the recoil of the entire particle from which it escapes. Precise measurements of the nanoparticle recoil may then allow properties of the neutrino to be inferred, including its mass.

State-of-the-art techniques now allow the measurement of the momentum of a levitated nanoparticle in the quantum regime, where the measurement process itself provides the dominant constraints on the measurement accuracy, as required by the Heisenberg uncertainty principle. These techniques are now sensitive enough to measure the momentum of a single neutrino emitted from such a nanoparticle. If an anomalous momentum was measured for even a tiny fraction of such decays, it could indicate the existence of a previously undetected heavy type of neutrino. A single trapped nanoparticle containing specific isotopes of interest for such decays could provide world-leading searches for such heavy neutrinos in only a month of integration time.

The future potential of these techniques is significant. Extending the same ideas to large arrays of nanoparticles could probe many orders of magnitude beyond the reach of existing searches for heavy neutrinos. While beyond the state of the art, future extensions of these ideas may allow even the masses of the lighter neutrinos to be determined with similar techniques.

Figure 1

A schematic of the detection concept described in the text. (a) A close-up of a single spherical nanoparticle, schematically showing (i) a ${\beta }^{-}$ decay, for which the nuclear recoil is stopped in the nanosphere and the $e^{-}$ and ${\overline{\nu }}_e$ exit the particle, and (ii) an electron-capture (EC) decay, for which only the ${\nu }_e$ and lower-energy atomic x rays or Auger $e^{-}$ are emitted, such that the nanosphere recoils with a momentum nearly equal and opposite to that of the emitted ${\nu }_e$. (b) A cut-away view of the trap concept and surrounding detectors. The trap is formed by a low-profile high-numerical-aperture objective, with two additional long-working-distance objectives positioned perpendicularly to the trapping objective to collect scattered light. Scintillator panels instrumented with $\mathrm{Si}$PM arrays surround the trap on all sides to reconstruct emitted secondary particles. The inset shows an enlargement of the trapping region, schematically showing traps for multiple particles formed with a tweezer array [69, 70, 71, 72, 73, 74, 75, 76].

Figure 2

The simulated spectrum for the reconstructed neutrino momentum, $|{\mathbf{p}}_{\nu }|$, for a 100-nm-diameter nanosphere containing 1% by mass of the EC-unstable isotope ${}^{37}$$\mathrm{Ar}$. We assume an exposure of 30 days and 40% collection efficiency for the emitted Auger $e^{-}$ or x ray. Also overlaid (and visible in the inset) is the expected spectrum arising for a heavier sterile state with $m_4=750\mathrm{keV}$ and at the existing upper limits for a sterile $\nu$ at this mass, $|U_{e4}{|}^2=2\times {10}^{-4}$ [15]. Backgrounds and misreconstructed events are not included in the simulation (for a detailed discussion of the required background rejection to meet this assumption, see Sec. 3d). The black data points with error bars indicate the simulated counts for a typical experimental realization, along with the best fit to these data for decays to SM neutrinos (blue) and the heavier sterile state (red).

Figure 3

The calculated distribution of the reconstructed $\nu$ momentum, $|{\mathbf{p}}_{\nu }|$, versus the electron kinetic energy, $T_e$, for ${}^{32}$$\mathrm{P}$ ${\beta }^{-}$ decay, for various values of $m_4$, assuming a 100-nm-diameter nanosphere with the detection efficiencies described in the text. The probability density for this distribution for light neutrinos (with $m_i\approx 0$) is shown as the black shaded histogram, surrounded by the $2\sigma$ contour containing 95% of simulated events. The corresponding $2\sigma$ contours for nonzero $m_4$ are indicated by the colored lines.

Figure 4

The projected sensitivity to the mixing of a heavy-mass state, $|U_{e4}{|}^2$, as a function of the mass, $m_4$, for a variety of isotopes, assuming that a single 100-nm-diameter nanosphere is measured for 1 month with 1% loading by the mass of the isotope of interest, and assuming the detection efficiencies and experimental parameters described in the text. The sensitivity for isotopes decaying by EC (left) and ${\beta }^{-}$ decays (right) are shown separately. The projected sensitivity is compared to the most sensitive existing laboratory limits in this mass range (gray) [7, 8, 9, 10, 11, 12, 13, 14, 15, 17]. If sterile neutrinos constitute a significant fraction of dark matter, limits on x-ray emission from their radiative decays may also provide constraints in this mass range (not shown) [4].

Figure 5

The estimated sensitivity for a variety of nanosphere sizes, exposures, and $\beta$-decay isotopes spanning a sensitivity range from approximately 1 to 1000 keV. The background-free sensitivity for exposures of 1 nanosphere $\times$ 1 month (solid), 10 nanospheres $\times$ 1 year (dashed), and 1000 nanospheres $\times$ 1 year (dotted) are shown. The nanosphere sizes and loading fractions assumed for each isotope are described in the text. The most sensitive existing laboratory limits are also shown (gray) [7, 8, 9, 10, 11, 12, 13, 14, 15, 17]. If sterile neutrinos constitute a significant fraction of dark matter, limits on x-ray emission from their radiative decays may also provide constraints in this mass range (not shown) [4].

Figure 6

A qualitative example of the requirements for nanoparticle state preparation and measurement following the decay. (a) A comparison between the quasiprobability distribution for the zero-point motion of the COM of a 5-nm-diameter graphene flake cooled to the ground state of a weakly confining harmonic potential ($\omega =2\pi \times 100\mathrm{Hz}$) (red) and after squeezing the momentum quadrature of the motional state of the nanoparticle by 20 dB (blue). (b) The quasiprobability distribution following the decay for the nanoparticle COM (blue) and neutrino (green), assuming that all secondary particles are trapped within the flake and that the $\nu$ carries momentum $|{\mathbf{p}}_{\nu }|=100\mathrm{meV}$. The inset shows an enlargement of the region highlighted by the black dotted box in the main figure.

Figure 7

The maximum depth of the electric potential energy, $V_{\max }$, for a positively (red) or negatively (blue) charged nanosphere of radius $r_s$, assuming that the net charge is limited by field emission [99, 139]. For ${\beta }^{-}$ decay, the red dashed lines and arrows indicate the nanosphere sizes for which an electron of a given initial kinetic energy could be stopped by a nanosphere charged to this limit. The inset shows the electric potential as a fraction of $V_{\max }$ relative to a distant grounded surface as a function of the distance from the nanosphere center, $r$.