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Acoustic diamond resonators with ultrasmall mode volumes

MetadataDetails
Publication Date2020-07-28
JournalPhysical Review Research
AuthorsMikoƂaj K. Schmidt, Christopher G. Poulton, M. J. Steel
InstitutionsUniversity of Technology Sydney, Macquarie University
Citations11
AnalysisFull AI Review Included

This research proposes a high-performance diamond acoustic cavity design optimized for Quantum Acoustodynamics (QAD) and enhanced coupling with solid-state emitters.

  • Ultra-Small Mode Volume: The design achieves an effective mode volume (Veff) of approximately 10-4λ3, several orders of magnitude below the diffraction limit, by leveraging a non-resonant acoustic lightning-rod effect.
  • High Cooperativity: This extreme strain localization leads to significant coupling enhancement, projecting a parametric cooperativity (CE1) of C ~ 8 and a resonant cooperativity (CE2) of C ~ 0.7 for Nitrogen-Vacancy (NV-) orbital states at 4 K.
  • Mechanism: The cavity is implemented as a defect in a quasi-one-dimensional diamond Phononic Crystal Waveguide (PnCW), utilizing a tapered, sub-wavelength bridge structure to localize the strain field.
  • Frequency Range: The cavity operates in the GHz range (mode frequency 2.838 GHz), matching the bandgap (2.3-3.2 GHz) engineered in the diamond slab.
  • Quantum Control: The high cooperativity opens pathways for efficient ground-state resonant cooling of the acoustic mode using a single NV- center, a crucial step for quantum control of macroscopic mechanical systems.
  • Scalability: The architecture is robust and can be translated to setups with multiple cavities or adapted for other emitters like Silicon-Vacancy (SiV) centers, projecting even higher cooperativity (CSiV ~ 110).
ParameterValueUnitContext
Cavity MaterialSingle-Crystalline DiamondN/ASlab thickness t = 0.5 ”m
Operating Frequency (Ωα/2π)2.838GHzTuned to the center of the bandgap
Acoustic Bandgap Range2.3 to 3.2GHzComplete bandgap for Z-symmetric/antisymmetric modes
Effective Mode Volume (Veff,α)~10-4λ3N/ANormalized by longitudinal wavelength (λp)
Mechanical Quality Factor (Q)105N/AConservative estimate for cryogenic operation
Minimum Bridge Width (d)50nmLower bound based on diamond lithography limits
Parametric Coupling (gE1/2π)5MHzMaximum calculated coupling strength
Resonant Coupling (gE2/2π)1.5MHzMaximum calculated coupling strength
Parametric Cooperativity (CE1)~8N/ACalculated at 4 K (nth ≈ 35)
Resonant Cooperativity (CE2)~0.7N/ACalculated at 4 K
NV Dephasing Rate (Γx/y/2π)~15MHzUsed in cooperativity calculation [42]
SiV Strain Susceptibility1.8GHzSignificantly larger than NV centers
Projected SiV Cooperativity (CSiV)~110N/AEstimated at 4 K
Diamond Young’s Modulus (E)1050GPaIsotropic approximation used for modeling

The design and analysis rely on combining advanced phononic crystal engineering with non-resonant strain localization techniques, validated through numerical modeling.

  1. Non-Resonant Localization: The core principle is the acoustic analogue of the lightning-rod effect. Strain is localized into a deeply sub-wavelength volume (tr’d) within a tapered 3D bridge structure, achieving a strain decay proportional to X-1 away from the tip.
  2. Phononic Crystal Waveguide (PnCW) Design: A quasi-1D PnCW was designed in a diamond slab (t = 0.5 ”m) using specific unit cell geometries (A, B, R) to create a broad, complete acoustic bandgap (2.3-3.2 GHz) along the X-direction.
  3. Cavity Implementation: The cavity is formed by a single defect (the tapered bridge) directly interfaced with the PnC Bragg mirrors, suppressing radiative phonon dissipation.
  4. Numerical Modeling: All mode properties, strain fields, and energy densities were calculated using the Finite Element Method (FEM) via COMSOL MultiphysicsÂź software, implementing Floquet boundary conditions for the PnC dispersion analysis.
  5. NV Center Coupling Analysis: The coupling Hamiltonian (Hstrain-NV) was projected onto the irreducible representations (A, E1, E2) of the C3v group. Coupling coefficients (gE1, gE2) were calculated by transforming the numerically derived strain tensor from the laboratory frame (X, Y, Z) to the local NV coordinate system (x, y, z).
  6. Performance Quantification: Cooperativity (C = 4g2/(ΓthΓx/y)) was calculated using the derived coupling strengths (g) and realistic estimates for mechanical quality factor (Q = 105) and NV dephasing rates (Γx/y).

This technology is foundational for developing next-generation quantum devices that rely on coherent interaction between mechanical motion and solid-state qubits.

  • Quantum Information Processing: Provides a platform for high-fidelity, coherent control over the orbital and spin states of NV and SiV centers in diamond, essential for solid-state quantum computing architectures.
  • Hybrid Quantum Systems: Enables the implementation of efficient transducers and quantum memories by coupling optical (NV/SiV) and mechanical (GHz phonon) degrees of freedom.
  • Acoustic Quantum Memories: The high Q (105) and strong coupling facilitate the use of GHz acoustic vibrations as robust quantum memories, potentially surpassing current limits in materials like silicon.
  • Quantum Sensing: The ultra-small mode volume and high strain localization can be utilized to create highly sensitive, nanoscale strain and force sensors based on NV center readout.
  • Integrated Quantum Photonics: The design principles (non-resonant localization) can be adapted to phoxonic crystal cavities to simultaneously co-localize high-Q optical and acoustic modes, enhancing overall optoacoustic coupling efficiency.
View Original Abstract

Quantum acoustodynamics (QAD) is a rapidly developing field of research,\noffering possibilities to realize and study macroscopic quantum-mechanical\nsystems in a new range of frequencies, and implement transducers and new types\nof memories for hybrid quantum devices. Here we propose a novel design for a\nversatile diamond QAD cavity operating at GHz frequencies, exhibiting effective\nmode volumes of about $10^{-4}\lambda^3$. Our phononic crystal waveguide cavity\nimplements a non-resonant analogue of the optical lightning-rod effect to\nlocalize the energy of an acoustic mode into a deeply-subwavelength volume. We\ndemonstrate that this confinement can readily enhance the orbit-strain\ninteraction with embedded nitrogen-vacancy (NV) centres towards the\nhigh-cooperativity regime, and enable efficient resonant cooling of the\nacoustic vibrations towards the ground state using a single NV. This\narchitecture can be readily translated towards setup with multiple cavities in\none- or two-dimensional phononic crystals, and the underlying non-resonant\nlocalization mechanism will pave the way to further enhance optoacoustic\ncoupling in phoxonic crystal cavities.\n

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