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Enhanced Dark Matter Quantum Sensing via Geometric Phase

Xiaolin Ma, Jie Sheng

Abstract

We propose a quantum sensing protocol for coupled qubit-oscillator systems that surpasses the standard quantum limit by exploiting a geometric phase for dark matter searches. Instead of letting the cavity evolve freely under a weak dark matter background, we combine large coherent displacements and squeezing operations within the evolution protocol, thereby mapping the signal onto an enhanced geometric phase. This new protocol increases the quantum Fisher information to surpass standard quantum limit and leads to a substantial improvement in dark photon and axion detection sensitivity, opening a new paradigm for cavity-based dark matter detection.

Enhanced Dark Matter Quantum Sensing via Geometric Phase

Abstract

We propose a quantum sensing protocol for coupled qubit-oscillator systems that surpasses the standard quantum limit by exploiting a geometric phase for dark matter searches. Instead of letting the cavity evolve freely under a weak dark matter background, we combine large coherent displacements and squeezing operations within the evolution protocol, thereby mapping the signal onto an enhanced geometric phase. This new protocol increases the quantum Fisher information to surpass standard quantum limit and leads to a substantial improvement in dark photon and axion detection sensitivity, opening a new paradigm for cavity-based dark matter detection.
Paper Structure (12 sections, 150 equations, 4 figures)

This paper contains 12 sections, 150 equations, 4 figures.

Table of Contents

  1. Appendix A -- DM coupling with Cavity
  2. Axion
  3. Appendix B -- Deviation of Evolution under the Dark Matter Drive
  4. Appendix C -- Details of the Evolution under geometric protocol
  5. Communications
  6. geometric Protocol and Total Phase
  7. Appendix D -- Details Concerning the Quantum Fisher Information
  8. Appendix E -- The Impact of Decoherence from geometric protocol
  9. Appendix F -- The signal profile and experimental parameter choices
  10. Appendix G -- Power Spectrum Density
  11. Case I: $t_{\mathrm{obs}}<\tau_{\rm DM}$
  12. Case II: $t_{\mathrm{obs}}>\tau_{\rm DM}$

Figures (4)

  • Figure 1: Geometric sensing protocol for DM detection. (a) A transmon qubit is dispersively coupled to a cavity mode, which is weakly driven by a DM field. (b) The sensing sequence: (1) A large, squeezed displacement operation $\hat{D}(\beta)$ is applied to the cavity. (2) The system evolves freely under DM interaction for $2\tau_0$ with a spin-echo $\pi$-pulse at $\tau_0$. (3) The final opposite squeezed displacement operation $\hat{D}(-\beta)$. (c) Phase space trajectories for the qubit in its ground $\ket{g}$ (blue) and excited $\ket{e}$ (red) states. The DM signal is the geometric phase $\delta \Phi$ proportional to the area enclosed by the two paths.
  • Figure 2: Upper panel: Quantum Fisher information versus detuning $\Delta \equiv \omega_c-\omega_D$ of the geometric protocol (yellow) and free evolution (blue) with $\beta = 20$. Lower panel: Signal profile for 1 GHz mass DM after convolution with the DM spectrum for the cases of $\beta=20$ (yellow), $\beta=1$ (green), and free evolution (blue) with $\chi \tau_0 = \pi$ and cavity frequency $\omega_c=(1+3\times10^{-7})m_{\rm DM}$.
  • Figure 3: Left panel: Comparison between the projected 95% C.L. sensitivity to the dark-photon kinetic mixing parameter $\epsilon$ from the geometric protocol (blue solid) with existing bounds AxionLimits (colored regions) and the benchmark cavity sensitivity SHANHE:2023kxz (black dotted). Right panel: Comparison between the projected 95% C.L. sensitivity to the axion-photon coupling $g_{a\gamma\gamma}$ (blue solid) with current limits AxionLimits (colored regions). See main text for parameter choices for both figures.
  • Figure 4: Shown here are the signal power dependencies on the protocol time with parameter chosen as aforementioned main-text. They show piece-wise behavior before and after the coherence time.