Detecting Single Microwave Photons with NV Centers in Diamond

At a Glance

Metadata	Details
Publication Date	2023-04-21
Journal	Materials
Authors	Olivia Woodman, Abdolreza Pasharavesh, C. M. Wilson, Michal Bajcsy
Institutions	University of Waterloo
Citations	1
Analysis	Full AI Review Included

Executive Summary

This research proposes and simulates a novel solid-state detector for single microwave photons, leveraging Nitrogen-Vacancy (NV^-) centers in diamond coupled to dual cavities.

Core Platform: A hybrid system consisting of an NV^- center simultaneously coupled to a high-Q optical cavity (e.g., Fabry-Perot) and a microwave cavity (e.g., Coplanar Waveguide, CPW).
Detection Mechanism: The scheme relies on Dipole-Induced Transparency (DIT). The presence of a microwave photon excites the NV spin from the strongly coupled ground state (|g>) to the weakly coupled spin state (|s>). This spin flip switches the optical cavity from opaque (blocked) to transparent (transmitted).
Readout: The spin state (and thus the presence of the microwave photon) is measured with high fidelity by counting the number of reflected or transmitted optical probe photons.
Performance Metrics (Simulated): Using realistic cavity parameters (Optical Q-factor Q_a = 10⁶, Microwave Q-factor Q_b = 10⁶), the simulations predict achievable detection efficiencies approaching 90% and fidelities exceeding 90%.
Robustness: The DIT process employed provides lower sensitivity to imperfections in the optical detector efficiency (e.g., maintaining high fidelity even with 75% optical detector efficiency).
Simplicity: The proposed design is simpler than alternative Raman-based microwave-to-optical transduction schemes, requiring no external control beams or highly accurate magnetic fields.

Technical Specifications

Parameter	Value	Unit	Context
NV Charge State	Negative (NV^-)	Dimensionless	Exhibits unique spin-dependent photodynamics
NV Spin States	Triplet (m_s = 0, ±1)	Dimensionless	Ground and Excited states
Zero-Field Splitting	2.87	GHz	Separation between m_s = 0 and m_s = ±1
Optical Transition (ω_dg)	2π x 470	THz	Coupled transition (
Microwave Transition (ω_sg)	2π x 3.4	GHz	Coupled transition (
Optical Cavity Q-Factor (Q_a)	10⁶	Dimensionless	Used in simulations
Microwave Cavity Q-Factor (Q_b)	10⁶	Dimensionless	Used in simulations (CPW cavity)
Optical Cavity Cooperativity (η)	0.4	Dimensionless	Based on P ≈ 26 (Purcell Enhancement)
Microwave Coupling (g_b/2π)	10	kHz	Required for >90% fidelity (with Q_b = 10⁶)
Ground State Decay (Γ_d)	1/(12)	ns^-1	Total longitudinal decay rate
Excited State Decay (Γ_e)	1/(7.5)	ns^-1	Total longitudinal decay rate
Metastable State Decay (Γ_s)	2π x 21.2	Hz	Shelving state decay rate
Optical Probe Drive Strength (Ω_d)	0.3 g_b	Dimensionless	Minimizes nonlinear effects
Empty Cavity Photon Rate	< 2 x 10⁶	photons/second	Rate of transmitted photons
Simulated Detection Efficiency	>90	%	Achieved with optimized parameters
Simulated Detection Fidelity	>90	%	Achieved with optimized parameters
Imperfect Optical Detector Efficiency	75	%	Used to model realistic SNSPD/SPAD performance

Key Methodologies

The proposed detector was evaluated using numerical simulations based on established quantum optics techniques, focusing on system dynamics and performance optimization.

System Hamiltonian Formulation: The five-level NV center model (|g>, |s>, |d>, |e>, |f>) was used. The total Hamiltonian (H) was constructed in a rotating frame, comprising three coupled Jaynes-Cummings Hamiltonians describing the interaction between the NV center and the optical cavity, the microwave cavity, and the coherent optical probe drive.
Open Quantum System Dynamics: The evolution of the system density matrix (ρ) was governed by the Lindblad master equation, dp(t)/dt = -i/ħ [H, ρ(t)] + Σ_k [2C_kρ(t)C_k^† - ρ(t)C_k^†C_k - C_k^†C_kρ(t)].
Collapse Operator Definition: Twelve collapse operators (C₁ to C₁₂) were defined to account for all dissipation channels, including population decay (with specific branching ratios), pure dephasing of excited states, and photon decay out of both the optical (κ_a) and microwave (κ_b) cavities.
Numerical Simulation: The dynamics were solved using two complementary methods implemented via the QuTiP package:
- Direct numerical integration of the Lindblad master equation.
- Monte Carlo Wave Function (MCWF) quantum trajectory approach (used for calculating photon count statistics).
Parameter Optimization: Simulations investigated the dependence of the detection gain contrast on key parameters, particularly the microwave coupling constant (g_b) and the number of incident optical probe photons, to identify optimal operating points for maximum fidelity and efficiency.
Fidelity and Efficiency Calculation: Detection fidelity (F = 1 - 1/2 (ε₀ + ε₁), where ε₀ and ε₁ are false negative and false positive rates) and efficiency (true positive rate) were calculated based on the photon count statistics relative to a set threshold (t).
Imperfect Detector Modeling: The final performance evaluation incorporated a non-ideal optical photon detector efficiency (75%) to ensure the results reflect practical experimental limitations.

Commercial Applications

The development of high-fidelity, efficient single microwave photon detectors is critical for advancing several quantum and classical technologies:

Quantum Computing (cQED): Essential for non-destructive readout and control of superconducting qubits, which operate in the microwave frequency domain.
Quantum Networking and Communication: Enables coherent microwave-to-optical transduction, necessary for linking distant superconducting quantum processors via optical fiber networks.
Quantum Sensing and Metrology: Used in high-sensitivity quantum spectroscopy and vector magnetometry, particularly where ultra-low energy detection is required.
Fundamental Physics Research: Provides a tool for searching for extremely weak signals, such as dark matter axions, which require detection in the 5 to 500 GHz range.
Quantum Cryptography: Meets the stringent requirements (high efficiency, low dark count rate) for advanced quantum key distribution (QKD) protocols.
Quantum Radar: Potential application in next-generation radar systems that utilize quantum entanglement for enhanced detection capabilities.

View Original Abstract

We propose a scheme for detecting single microwave photons using dipole-induced transparency (DIT) in an optical cavity resonantly coupled to a spin-selective transition of a negatively charged nitrogen-vacancy (NV−) defect in diamond crystal lattices. In this scheme, the microwave photons control the interaction of the optical cavity with the NV− center by addressing the spin state of the defect. The spin, in turn, is measured with high fidelity by counting the number of reflected photons when the cavity is probed by resonant laser light. To evaluate the performance of the proposed scheme, we derive the governing master equation and solve it through both direct integration and the Monte Carlo approach. Using these numerical simulations, we then investigate the effects of different parameters on the detection performance and find their corresponding optimized values. Our results indicate that detection efficiencies approaching 90% and fidelities exceeding 90% could be achieved when using realistic optical and microwave cavity parameters.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma16083274

References

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