Abstract
Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters. Here we study the dependence of the lock-in spectral slope on the modulation of the spin-driving microwave field. Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is ≳ 1/4, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation. We formulate a model for calculating lock-in spectra which shows excellent agreement with our experiments, and which shows that an optimum slope is achieved when the linewidth/separation ratio is ≲ 1/4 and the modulation depth is less then the resonance linewidth, irrespective of the modulation function used.
Highlights
One of the primary tools for precision measurements in modern experimental physics is phasesensitive detection
Their combination with phase-sensitive detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters
Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is 1/4, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation
Summary
One of the primary tools for precision measurements in modern experimental physics is phasesensitive detection. Previous NV-related work which addresses the use of lock-in detection has focused on single NV based sensing through multi-pulsed phase estimation schemes [15], or their incorporation within a scanning-probe based schemes [16] It has been presented as an integral component for NV ensemble magnetometery using optical fibre-based read-out [17], using the diamond as a light trapping-waveguide [7], through the absorption of the spin-singlet state [18], when avoiding the use of a MW drive field [19], or for sensing biologically generated magnetic fields [20]. To our knowledge, there has been no published investigation of the technicalities on optimising the modulation parameters to maximise the slopes in the measured lock-in spectrum While this technique is conceptually undemanding, the optimum modulation function for NV ensemble magnetometry is not obvious as it is dependent on the systems spin resonance spectrum and its unique response to optical and microwave drive fields. Experimental and theoretical results are compared and discussed, which show that the optimum modulation function and depth are dependent on the linewidth-to-separation ratio of the measured peaks
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