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Fundamental quantum limits for detecting ultrahigh frequency gravitational waves

Xinyao Guo, Haixing Miao, Zhi-Wei Wang, Huan Yang, Ye-Ling Zhou

Abstract

The ultrahigh-frequency (above 10 kHz) gravitational waves (GW) window provides a unique opportunity to detect primordial GWs, free from astrophysical foregrounds that dominate lower frequencies. A stochastic GW background in this range is generically predicted from cosmological phase transitions and topological defects associated with grand unification and other ultra-high energy theories. We establish a universal quantum limit framework for various detection schemes, setting a fundamental bound on GW detectability. Our analysis reveals that backgrounds in the kHz-MHz range are in principle observable, whereas higher-frequency signals lie below the quantum limit. These results offer theoretical guidance for future detector designs and open new avenues for probing early universe physics.

Fundamental quantum limits for detecting ultrahigh frequency gravitational waves

Abstract

The ultrahigh-frequency (above 10 kHz) gravitational waves (GW) window provides a unique opportunity to detect primordial GWs, free from astrophysical foregrounds that dominate lower frequencies. A stochastic GW background in this range is generically predicted from cosmological phase transitions and topological defects associated with grand unification and other ultra-high energy theories. We establish a universal quantum limit framework for various detection schemes, setting a fundamental bound on GW detectability. Our analysis reveals that backgrounds in the kHz-MHz range are in principle observable, whereas higher-frequency signals lie below the quantum limit. These results offer theoretical guidance for future detector designs and open new avenues for probing early universe physics.

Paper Structure

This paper contains 20 sections, 86 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Fundamental limits
  3. FQL-based conceptual design
  4. Implications
  5. Conclusion
  6. Acknowledgements
  7. Energetic quantum limit
  8. Proof of the upper bound of gain
  9. Derivation of energy fluctuation(Eq. \ref{['eq:lineshape']})
  10. Model of quantum loss
  11. Review of Different Measurement Schemes
  12. Review of Fisher Information
  13. Linear Measurement
  14. Photon Counting
  15. Channel Limit
  16. ...and 5 more sections

Figures (5)

  • Figure 1: Fundamental quantum limits for different experimental setups over $10^3$–$10^7$ Hz. Here, the integration time $T_{\rm int}$ is set to 10 years, and the frequency bin width is set as the entire resonant bandwidth of individual detector. The EM cavity (fixed ratio) line assumes a cylindrical cavity with aspect ratio of 1:5, while benchmark values of other sensitivity lines are summarized in Tab. \ref{['table:scaling']}. A representative binary neutron-star foreground (equation of state of SHFo Steiner:2012rk, data extracted from L-shaped) rapidly decays above $4$ kHz. The UHF band is therefore well-suited to probe GUT-motivated phase transitions (B1 at $10^8$ GeV, B2 at $10^9$ GeV, with specific lineshape given in Eq. \ref{['eq:GWsignal']}), collapsing domain walls (B3), or metastable strings (B4).
  • Figure 2: Left: schematic diagram of concept and layout of detection proposals in Fig \ref{['fig:limits']}. Right: Fundamental limits and single-detector sensitivity under different classical noise levels, corresponding to the worked example of fundamental-limit-based detector design.
  • Figure 3: Non-SUSY $SO(10)$ GUT breaking chains as motivations of ultra-high frequency GWs via phase transition. Conventions, e.g., $G_{422} = SU(4)_c\times SU(2)_L\times SU(2)_R$, are understood King:2021gmj. $G_{\rm SM}\equiv SU(3)\times SU(2)_L \times U(1)_Y$ denotes the gauge symmetry of the Standard Model. Topological defects (cosmic strings, monopoles and domain walls) associated with the symmetry breaking Jeannerot:2003qv are marked. Gauge symmetries which might provide phase transition at scales lower than $10^{10}$ GeV and consistent with cosmological observations are highlighted in blue.
  • Figure 4: Constrained and unconstrained fundamental limit for linear readout within laser interferometer, with $T_{\rm int}=10\, \rm y$ and $\Delta f= 1\,\rm kHz$. Individual detectors with different lengths saturates the fundamental limit at different frequencies, similar to the standard quantum limit (where interferometers with varying circulating power touch the bound at different frequencies).
  • Figure 5: Minimum integration time to achieve unity SNR under different $\bar{\dot{n}}_0$ levels.