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Colloquium - Quantum limits to the energy resolution of magnetic field sensors

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-04-28
JournalReviews of Modern Physics
AuthorsMorgan W. Mitchell, Silvana Palacios
InstitutionsInstitució Catalana de Recerca i Estudis Avançats, Institute of Photonic Sciences
Citations110
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This colloquium reviews the fundamental quantum limits constraining the performance of low-frequency magnetic field sensors, focusing on the Energy Resolution per Bandwidth (ER).

  • Technology-Spanning Limit: The best-performing magnetometers across various technologies (dc SQUIDs, Optically-Pumped Magnetometers (OPMs), and Nitrogen-Vacancy (NV) centers in diamond) all approach, but have not surpassed, a quantum limit of ER ≈ ħ (reduced Planck constant).
  • Dissipation as the Source: The technology-specific limits are consistently linked to dissipation mechanisms necessary for sensor operation, such as shunt resistances (SQUIDs), spin-destruction collisions (OPMs), or magnetic dipole-dipole coupling (NV ensembles).
  • ER as a Figure of Merit: ER serves as a critical metric, combining field resolution (sensitivity), measurement duration/bandwidth, and the size of the sensed region (volume or area). Smaller ER values indicate better overall performance.
  • Unconvincing General Limits: General quantum speed limits (like the Margolus-Levitin bound) and zero-point magnetic field fluctuations were assessed as potential technology-spanning limits, but the analysis suggests they do not fundamentally constrain the ER of a well-designed sensor.
  • Proposed Evasion Strategies: Several sensor designs are proposed to potentially surpass ER = ħ by evading known dissipation mechanisms, including non-dissipative superconducting sensors (SQUIPTs), localized single quantum systems, and spin-precession sensors utilizing low-entropy reservoirs (e.g., Bose-Einstein Condensates).

Technical Specifications

Section titled “Technical Specifications”

The following table summarizes key performance metrics and limiting factors for high-sensitivity magnetometers discussed in the paper, based on reported experimental results (Figure 2 and Tables I/II).

ParameterValueUnitContext
Fundamental Quantum Limit (ERL)~1.05 x 10-34J¡s (ħ)Theoretical minimum action per measurement
Best Achieved ER (SQUID)~2ħdc SQUID sensors (approaching the limit)
Best Achieved ER (OPM)~44ħ87Rb SERF-regime OPMs
Best Flux Sensitivity (SQUID, Label 39)9.3 x 10-23Wb/Hz1/2Micro-SQUID, effective area 1.0 x 10-12 m2
Best Field Sensitivity (OPM, Label 2)1.6 x 10-16T/Hz1/2Alkali-vapor OPM, effective volume 4.5 x 10-7 m3
Best Field Sensitivity (NV, Label 58)5.3 x 10-8T/Hz1/2Single NV center, radio-frequency measurement
SQUID Limiting MechanismZero-point current fluctuationsN/ADissipation in shunt resistances
OPM Limiting MechanismSpin-destruction collisionsN/ATwo-body relaxation processes in vapor
NV Ensemble Limiting MechanismDipole-dipole couplingN/ASelf-depolarization in spatially-disordered spins

Key Methodologies

Section titled “Key Methodologies”

The paper analyzes existing sensor methodologies and proposes modifications aimed at reducing dissipation and surpassing the ER = ħ limit.

  1. Non-Dissipative Superconducting Sensors:

    • Method: Eliminate the dissipative shunt resistances typically used in dc SQUIDs to prevent hysteresis.
    • Examples: Superconducting Quantum Interference Proximity Transistors (SQUIPTs) and Superconducting Kinetic Impedance Magnetometers (SKIMs).
    • Goal: Remove the source of zero-point current fluctuations that impose the TC (Tesche and Clarke) limit.

  2. Localized Single Quantum Systems (SQSs):

    • Method: Utilize single, isolated quantum systems (e.g., single NV centers, trapped ions, single Rydberg atoms) as sensors.
    • Goal: Completely evade internal decoherence mechanisms, particularly the dipole-dipole coupling that limits spin ensembles.

  3. Dynamical Decoupling (DD) in Spin Ensembles:

    • Method: Apply strong, impulsive spin operations (pulse sequences) to sensor spin ensembles (like NV centers).
    • Goal: Prevent or reverse the buildup of coherent rotations caused by neighboring spin interactions, effectively decoupling the spins from their neighbors while maintaining coupling to the external field.

  4. Low-Entropy Reservoirs (Quantum Degenerate Gases):

    • Method: Employ quantum degenerate gases, such as spinor Bose-Einstein Condensates (BECs), where two-body interactions induce coherent spin evolution rather than introducing entropy.
    • Goal: “Freeze out” the center-of-mass degrees of freedom, minimizing angular momentum loss and achieving sensitivity scaling (dB2)T proportional to T-2 for long measurements.

  5. OPMs with Low Spin-Destruction Rates:

    • Method: Select atomic species for OPMs (e.g., Potassium (K) or gaseous 3He) that exhibit significantly lower spin-destruction cross-sections (σsd) compared to standard 87Rb OPMs.
    • Goal: Reduce the intrinsic noise floor imposed by two-body relaxation processes, potentially lowering the ERL below ħ.

Commercial Applications

Section titled “Commercial Applications”

The research on fundamental energy resolution limits directly impacts the design and optimization of high-sensitivity magnetometers used across several critical sectors:

  • Biomedical Imaging:
    • Magnetoencephalography (MEG) and Magnetocardiography (MCG) using OPMs and SQUIDs for non-invasive brain and heart function studies.
  • Quantum Sensing and Computing:
    • Development of localized single quantum sensors (NV centers, trapped ions) for high-spatial-resolution magnetic microscopy and quantum information processing.
  • Materials Science and Nanotechnology:
    • Magnetic Force Microscopy (MFM) and characterization of magnetic materials using micro-SQUIDs and NV centers, particularly for studying thin films and nanoscale devices.
  • Geophysics and Security:
    • High-sensitivity detection of magnetic anomalies using fluxgates (PAFG) and GMR/EMR sensors for geological surveys, mineral exploration, and unexploded ordnance detection.
  • Fundamental Physics:
    • Precision measurements using BECs and low-noise OPMs to search for exotic physics, including tests of fundamental symmetries and searches for dark matter.
View Original Abstract

The energy resolution per bandwidth $E_R$ is a figure of merit that combines the field resolution, bandwidth or duration of the measurement, and size of the sensed region. Several different dc magnetometer technologies approach $E_R = \hbar$, while to date none has surpassed this level. This suggests a technology-spanning quantum limit, a suggestion that is strengthened by model-based calculations for nitrogen-vacancy centres in diamond, for superconducting quantum interference device (SQUID) sensors, and for some optically-pumped alkali-vapor magnetometers, all of which predict a quantum limit close to $E_R = \hbar$. Here we review what is known about energy resolution limits, with the aim to understand when and how $E_R$ is limited by quantum effects. We include a survey of reported sensitivity versus size of the sensed region for more than twenty magnetometer technologies, review the known model-based quantum limits, and critically assess possible sources for a technology-spanning limit, including zero-point fluctuations, magnetic self-interaction, and quantum speed limits. Finally, we describe sensing approaches that appear to be unconstrained by any of the known limits, and thus are candidates to surpass $E_R = \hbar$.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - Optical Magnetometry

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