Optimizing Pulsed Optically Detected Magnetic Resonance Acquisition: A Digital Signal Processing Perspective

The gist: This work demonstrates that a digital oscilloscope can be effectively used for acquiring high-quality pulsed optically detected magnetic resonance (ODMR) data from an ensemble of nitrogen vacancy (NV) centers in diamond.

System Overview and Motivation

Ensembles of NV defect centers in diamond are promising platforms for quantum sensing and quantum information processing due to their long spin coherence time at room temperature, optical initialization, and microwave control. While single NV centers offer nanoscale spatial resolution, ensembles provide orders of magnitude improvement in sensitivity while relying on simpler instrumentation. The optical signal from the ensemble can be detected with the help of an analog avalanche photodetector (APD), and the analog output is digitized by an oscilloscope or a standalone digitizer. The oscilloscope offers several practical advantages, including testing, characterization, debugging, and configurable data-acquisition using a single instrument.

Data Acquisition Workflow

The acquisition process involves applying a pulsed ODMR sequence where nonoverlapping laser and microwave pulses are used. The system requires precise triggering to observe a stable waveform on the screen, with the trigger signal chosen to have the same periodicity as one unit cell of the laser pulse. Data is obtained by averaging over multiple waveforms, which reduces noise to some extent. The raw data is denoted by v[tn], and it can be expressed as a sum of an ideal noiseless component and a noise-induced deviation.

Signal Processing and Noise Characterization

Data processing involves defining the absolute contrast D as the difference between the mean signal and reference segments, where D = Isig − Iref. The relative contrast C is obtained by dividing D by Iref, which represents the fractional change in the mean PL. Noise characterization involves analyzing both time-domain noise and frequency-domain noise. Time-domain noise is separated into fluctuations within a single waveform, denoted as δv(fl)t'[tn], and a quasi-static shift component, denoted by δv(qs)t'.

Filtering Techniques for Noise Suppression

The data processing method is shown to effectively filter out noise in a broad spectral range. The mean filter operation, defined by equation (12), is equivalent to a finite impulse response (FIR) digital filter with an impulse response h[tn] = u[tn]u[Tro − tn]. The frequency response of this filter is the Dirichlet kernel, given by He(f) = e−iπfTro sinc(πf(Tro + Ts)). The difference filter operation, defined by equation (16), is a digital filter operation with an impulse response g[tn] = δ[tn − Tro − Tdark] − δ[tn]. The resultant filter that transforms v[tn] into d[tn] is characterized by the transfer function He(f)Ge(f), which exhibits a bandpass characteristic.

Impact of Readout Duration and Sampling Rate

The readout duration Tro is an important experimental parameter; increasing Tro leads to a narrower passband, which allows for sharper attenuation of higher-frequency noise components. The analysis shows that the standard deviation σodmr is proportional to 1/Tro. The contrast to noise ratio (CNR) is found to increase with increasing readout time, till around 260µs, after which further increases do not change the CNR significantly. The impact of sampling rate is investigated by limiting the analog noise bandwidth, and it is shown that placing an analog low pass filter before the oscilloscope improves acquisition efficiency by suppressing aliasing.

Conclusion

The key contribution of this work is the modelling of the data processing stage as a digital bandpass filter, which provides a quantitative and qualitative framework to understand how the data processing suppresses noise in the final data. Experiments confirm that the noise in the processed data depends solely on the noise level in the IF band, and is independent of the total noise present in the raw data. The optimal readout duration which gives high CNR while maintaining reasonable acquisition speed has been found. The combined influence of sampling rate and analog noise bandwidth on the CNR has been analyzed, showing that placing an analog low pass filter before the oscilloscope improves acquisition efficiency by suppressing aliasing. The insights gained are broadly applicable to the acquisition of any pulsed ODMR based protocol.

How it works

The system utilizes a digital oscilloscope for acquiring pulsed ODMR data from an ensemble of NV centers in diamond. The oscilloscope facilitates improved signal visualization and simplifies system debugging. On-board waveform averaging is used to enable more efficient measurements. The detection scheme and data processing are optimized for fast acquisition of high-quality data.

Signal and Noise Analysis

The ODMR signal is encoded in the repolarization dynamics of the photoluminescence, which deviates from simple exponential behavior due to spatially varying intensity profiles. The amplitude spectrum of the repolarization curve shows a 3-dB bandwidth of 233Hz and a 90% energy bandwidth extending to 3.88kHz. Noise in the raw data is characterized by two components: fluctuations within a single waveform, quantified by σraw, and a quasi-static shift component, denoted by δv(qs)t'. The inter-waveform noise is quantified using the Allan deviation σ(A)raw(τ), which measures the magnitude of variations in δv(qs)t' over a timescale τ.

Digital Filtering Implementation

The data processing stage is modeled as an effective filter implicitly implemented by the processing algorithm. The mean filter operation, defined by equation (12), has a frequency response He(f) = e−iπfTro sinc(πf(Tro + Ts)). The difference filter operation, defined by equation (16), has an impulse response g[tn] = δ[tn − Tro − Tdark] − δ[tn]. The resultant filter is characterized by the transfer function He(f)Ge(f), which exhibits a bandpass characteristic.

Contrast to Noise Ratio (CNR)

The contrast to noise ratio (CNR) is introduced as a figure of merit that accounts for both signal contrast and noise, defined by equation (11), CNR(X) = Xmax σ(X)odmr. The analysis shows that the noise in the processed data depends solely on the noise level in the IF band, and is independent of the total noise present in the raw data. The optimal readout duration which gives high CNR while maintaining reasonable acquisition speed has been found.

Sampling Rate and Aliasing Effects

The aliasing effect introduced in Section IV is central to understanding how the sampling rate and noise bandwidth influence the CNR. The condition for avoiding an increase in the PSD within the IF band due to aliasing is given by relation (27), Fs > Frnbw + Fu. This condition ensures that the analog low pass filtering provided by the preamplifier enables high-CNR measurements even at low sampling rates.

Waveform Averaging Effect

The waveform averaging operation can be approximated by a digital filter with an impulse response Ke(f) of the Dirichlet kernel, given by equation (24), Ke(f) = sinc(πfNavgTtrig)sinc(πfTtrig). The discrete PSD for averaged waveforms is approximated by equation (25), Seδv(avg)[fk] ≈ 1/Navg Seδv[fk]. The ODMR contrast is approximately independent of Navg, as shown in Figure 5(d).

Final Summary

The work presents a complete workflow for acquiring pulsed ODMR data using an oscilloscope, including raw data acquisition and subsequent processing steps to obtain the final ODMR contrast. The key contribution is the modelling of the data processing stage as a digital bandpass filter, which provides a quantitative and qualitative framework to understand how the data processing suppresses noise in the final data. The optimal readout duration which gives high CNR while maintaining reasonable acquisition speed has been found.

1. No-board waveform averaging enables more efficient measurements by reducing noise; this capability allows AI systems to perform on-board signal processing that dynamically optimizes acquisition based on real-time noise characteristics of the ODMR signal.

2. The data processing method effectively suppresses a broad range of noise spectral components, thereby reducing the total noise in the processed data; an AI system can be trained to learn and implement this optimal filtering algorithm automatically for any new experimental setup or material platform.

3. The framework developed in this work can be extended to other detection techniques and material platforms for ODMR; an AI system could use this framework to rapidly adapt its measurement protocols and noise suppression strategies when deployed on novel quantum sensing hardware.

4. The analysis of the impact of waveform averaging on the contrast to noise ratio (CNR) shows that the CNR scales linearly with p[Navg], as seen in Figure 5, which means an AI system could be programmed to automatically select the optimal number of waveform averages for a desired trade-off between CNR and acquisition time.

5. The analysis demonstrates that the introduction of an analog low pass filter in the signal path is shown to improve the measurement by removing aliasing; an AI system could dynamically adjust or select the appropriate analog filter based on real-time spectral analysis to ensure minimal aliasing effects during high-speed measurements.

6. The identification of an intermediate frequency (IF) band whose noise spectral components make the dominant contribution to the noise in the processed ODMR data allows an AI system to focus its noise mitigation efforts precisely on this band, as it is independent of the total noise present in the raw data.

Ensembles of nitrogen vacancy (NV) defect centers in diamond have attracted considerable interest for fundamental studies and applications in quantum sensing and quantum information processing. Pulsed optically detected magnetic resonance (ODMR) and related pulse-sequence protocols are essential for the coherent manipulation and characterization of the NV spins. Here, we introduce a novel framework for analyzing pulsed ODMR data acquisition and subsequent processing from the perspective of digital signal processing (DSP). As a central part of this approach, we model the data processing procedure as an effective digital bandpass filter that suppresses a broad range of noise spectral components, thereby reducing the noise in the processed data. This analysis identifies an intermediate frequency (IF) band whose spectral contribution to this noise is maximum. The proposed DSP-based analysis is experimentally validated using an oscilloscope based acquisition method, and is also applied to optimize key measurement parameters. In particular, the introduction of an analog low pass filter in the signal path is shown to remove aliasing of noise into the IF band, and thus improve signal quality. Our results also establish the oscilloscope as a viable data acquisition device for pulsed ODMR, with practical advantages including on-board waveform averaging, real-time signal visualization, and simplified system debugging. The proposed framework can be extended to other detection techniques and material platforms for ODMR.