Research ArticlePHYSICS

Constraints on bosonic dark matter from ultralow-field nuclear magnetic resonance

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Science Advances  25 Oct 2019:
Vol. 5, no. 10, eaax4539
DOI: 10.1126/sciadv.aax4539
  • Fig. 1 Nuclear spin energy levels and NMR spectra of 13C-formic acid measured in three different field conditions.

    (A) At zero magnetic field, the F = 1 levels are degenerate, resulting in a spectrum exhibiting a single peak at the J-coupling frequency. (B) In the presence of a DC magnetic field Bz ≈ 50 nT, the mF = ±1 degeneracy is lifted. The spectrum exhibits two split J-resonances. The splitting is equal to ℏBzC + γH). The asymmetry of the resonances is due to the influence of the applied field on the response characteristics of the atomic magnetometer. (C) Addition of an oscillating magnetic field along Bz modulates the mF = ±1 energy levels, resulting in sidebands located at J/2π ± BzC + γH)/2π ± ωAC with amplitude proportional to the modulation index: AsBACC + γH)/(2ωAC).

  • Fig. 2 Signal acquisition and processing schemes.

    Top: Signal acquisition scheme with simulated spectra. After polarization, each transient acquisition starts following a magnetic π-pulse (corresponding to a 180° flip of the 13C spin along any direction). The external AC magnetic field’s phase varies between transient acquisitions (orange). As a result, the sidebands generally have different phases in each transient spectrum. Averaging the transients yields a spectrum in which the sidebands are destructively averaged out (purple). Shifting each transient by a phase equal to the external field’s accumulated phase restores the sidebands’ phase coherence, yielding a spectrum with high SNR sidebands (orange). For clarity, only one of the two Zeeman-split J-coupling peaks and its two sidebands are shown. Bottom: Result of the phase-shifting procedure for actual data. (A) Transients are averaged using 2001 phase increments and stacked into a two-dimensional plot. (B) Side view of (A); sidebands are rescaled by a factor 10 for clarity. (C) Averaging with φ = 0 rad corresponds to averaging the transients without phase shift; sidebands are averaged out and carrier peaks appear with maximum amplitude. When the optimal phase (for ω/2π = 0.73 Hz, φ = 2.93 rad) is approached, sidebands appear. These spectra were acquired in an experiment during which the AC field frequency and amplitude were set to 0.73 Hz and 0.24 nT. Transient acquisitions of 30 s were repeated 850 times with a time interval between each transient of τ = 61 s.

  • Fig. 3 ALP wind nucleon linear coupling parameter space.

    The CASPEr-ZULF region is excluded by this work (90% confidence level) using a thermally polarized sample (data averaged over 850 transient acquisitions of 30 s each). The “New Force” region is excluded by searches for new spin-dependent forces (50). The SN1987A region represents existing limits from supernova SN1987A cooling (26, 35). The νn/νHg region is excluded (at 95% confidence level) by measurements of the ratio of neutron and 199Hg Larmor precession frequencies (22). The dashed line corresponds to the sensitivity of a planned second phase of CASPEr-ZULF, with a projected ~105 factor increase in sensitivity, and the bandwidth extended toward lower frequencies by using a comagnetometer technique (43) and longer integration times. The dotted lines show limits assuming a virialized ALP dark matter halo for which the field velocity and amplitude fluctuate (see section S12).

  • Fig. 4 ALP wind nucleon quadratic coupling parameter space.

    The CASPEr-ZULF region is excluded by this work (90% confidence level) using a thermally polarized sample (data averaged over 850 transient acquisitions of 30 s each). Other regions of this figure are defined in the caption of Fig. 3.

  • Fig. 5 Dark photon-nucleon couplings.

    Left: Dark photon–nucleon dEDM coupling parameter space. The SN1987A region represents existing limits for ALPs from supernova SN1987A cooling (26, 35) adjusted to constrain dark photons as discussed in (51). Right: Dark photon–nucleon dMDM coupling parameter space. The CASPEr-ZULF regions are excluded by this work (90% confidence level) using a thermally polarized sample (data averaged over 850 transient acquisitions of 30 s each). The red and purple lines correspond to the case where the dark photon field polarization is along the ε^1 and ε^3 axes of the nonrotating Celestial frame, respectively (see section S12). The dashed lines correspond to the sensitivity of a planned second phase of CASPEr-ZULF, with a projected ~105 factor increase in sensitivity.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaax4539/DC1

    Section S1. Experimental setup

    Section S2. Measurement scheme

    Section S3. Dark matter effective fields

    Section S4. Signal processing: Post-processing phase cycling

    Section S5. Sideband amplitude determination

    Section S6. Calibration: Signal scaling versus bosonic field amplitude and frequency

    Section S7. Detection threshold determination

    Section S8. Search and exclusion method

    Section S9. False alarms and false negatives

    Section S10. Coherent averaging: Signal scaling with integration time

    Section S11. Bandwidth: Accessible bosonic mass range

    Section S12. Dark matter field models

    Section S13. Search data time stamp

    Fig. S1. Calibration data.

    Fig. S2. Detection threshold determination.

    Fig. S3. Sideband amplitude, detection threshold, and SNR versus integration time.

    Fig. S4. Sideband amplitude scaling with calibration field frequency.

    References (5256)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Experimental setup
    • Section S2. Measurement scheme
    • Section S3. Dark matter effective fields
    • Section S4. Signal processing: Post-processing phase cycling
    • Section S5. Sideband amplitude determination
    • Section S6. Calibration: Signal scaling versus bosonic field amplitude and frequency
    • Section S7. Detection threshold determination
    • Section S8. Search and exclusion method
    • Section S9. False alarms and false negatives
    • Section S10. Coherent averaging: Signal scaling with integration time
    • Section S11. Bandwidth: Accessible bosonic mass range
    • Section S12. Dark matter field models
    • Section S13. Search data time stamp
    • Fig. S1. Calibration data.
    • Fig. S2. Detection threshold determination.
    • Fig. S3. Sideband amplitude, detection threshold, and SNR versus integration time.
    • Fig. S4. Sideband amplitude scaling with calibration field frequency.
    • References (5256)

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