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Determining angle of arrival of radio frequency fields using subwavelength, amplitude-only measurements of standing waves in a Rydberg atom sensor

Published by National Institute of Standards and Technology | National Institute of Standards and Technology | Catalog Last Checked: August 03, 2026 at 03:52 AM | Dataset Last Updated: October 18, 2024
Deep subwavelength RF imaging with atomic Rydberg sensors has overcome fundamental limitations of traditionalantennas and enabled ultra-wideband detection of omni-directional time varying fields all in a compactform factor. However, in most applications, Rydberg sensors require the use of a secondary strong RF referencefield to serve as a phase reference. Here, we demonstrate a new type of Rydberg sensor for Angle-of-Arrival(AoA) sensing which utilizes subwavelength imaging of standing wave fields. By placing a metallic plate withinthe Rydberg cell, we can determine the AoA independent of the strength of incoming RF field and without requiringa secondary strong RF phase reference field. We perform precision AoA measurements with a roboticantenna positioning system for 4.2, 5.0, and 5.7 GHz signals and demonstrate a 1.7◦ polar angular resolutionfrom 0◦ to 60◦ AoA and 4.1◦ over all possible angles.

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Complete Metadata
@type dcat:Dataset
accessLevel public
accrualPeriodicity irregular
bureauCode 
[
  "006:55"
]
contactPoint 
{
  "fn": "Matt Simons",
  "hasEmail": "mailto:matthew.simons@nist.gov"
}
description Deep subwavelength RF imaging with atomic Rydberg sensors has overcome fundamental limitations of traditionalantennas and enabled ultra-wideband detection of omni-directional time varying fields all in a compactform factor. However, in most applications, Rydberg sensors require the use of a secondary strong RF referencefield to serve as a phase reference. Here, we demonstrate a new type of Rydberg sensor for Angle-of-Arrival(AoA) sensing which utilizes subwavelength imaging of standing wave fields. By placing a metallic plate withinthe Rydberg cell, we can determine the AoA independent of the strength of incoming RF field and without requiringa secondary strong RF phase reference field. We perform precision AoA measurements with a roboticantenna positioning system for 4.2, 5.0, and 5.7 GHz signals and demonstrate a 1.7◦ polar angular resolutionfrom 0◦ to 60◦ AoA and 4.1◦ over all possible angles.
distribution 
[
  {
    "title": "Fig 6a_6b_6c",
    "format": "csv 6 columns of data for 8 2D plots",
    "mediaType": "text/csv",
    "description": "(a) Probe absorption intensity in Beam A and Beam B vs detuning and vs theta for all 	combinations of probe and coupling laser polarizations. 	In the data file, linP = Linear Probe, linC = Linear Coupling, circP = Circular Probe,	 and circC = Circular coupling. 	(b-c) The data in these two plots is a subset of the data shown in (a). 	Format: Col A: Probe Polarization  (Type) 		Col B: Coupling Polarization (Type)		Col C: Angle : Theta (deg) 		Col D: Detuning (MHz)		Col E: Beam A probe absorption (Arb Units)		Col F: Beam B probe absorption (Arb Units)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig6a_6b_6c.csv"
  },
  {
    "title": "Fig 2b",
    "format": "csv, four columns of 1D data",
    "mediaType": "text/csv",
    "description": "E-fields in V/m along Beam A and B, E_A and E_B, respectively, and the ratio of the fields, EA/EB, as a function of theta in degrees, for fields polarized parallel to the plane of incidence.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2b.csv"
  },
  {
    "title": "Fig 2d",
    "format": "csv, 4 columns of 1D data",
    "mediaType": "text/csv",
    "description": "E-fields in V/m along Beam A and B, E_A and E_B, respectively, and the ratio of the fields, EA/EB, as a function of theta in degrees, for fields polarized perpendicular to the plane of incidence.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2d.csv"
  },
  {
    "title": "Fig 8d",
    "format": "csv 4 columns",
    "mediaType": "text/csv",
    "description": "Fraction in central peak, as a function of theta and for varying RF polarization, chi = 0, 45 and 90 degrees.		Format: Col A: Angle : Theta (deg)		Col B: Fraction Central Peak  Chi 0 (Unitless)		Col C: Fraction Central Peak  Chi 45 (Unitless)		Col D: Fraction Central Peak  Chi 90 (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig8d.csv"
  },
  {
    "title": "Fig 2f",
    "format": "csv, 11 columns of 1D data",
    "mediaType": "text/csv",
    "description": "Numerically determined average field strength in V/m along the length of the cell z in mm for various theta in degrees.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2f.csv"
  },
  {
    "title": "Fig 4b",
    "format": "csv, 10 columns representing 6 2D plots",
    "mediaType": "text/csv",
    "description": "Probe absorption intensity across theta at f = 4.228, 5.044, and 5.711 GHz, for scanning coupling laser in Beam A, Beam B.	Format: Stack of 2d contourf plot data.		Col A: Angle: Theta  (degrees) 		Col B: Detuning for 4.228 GHz (MHz)                Col C: Beam A data for 4.228 GHz (Arb Units)		Col D: Beam B data for 4.228 GHz (Arb Units)		Col E: Detuning for 5.044 GHz (MHz)		Col F: Beam A data for 5.044 GHz (Arb Units)		Col G: Beam A data for 5.044 GHz (Arb Units)		Col H: Detuning for 5.711 GHz (MHz)		Col I: Beam A data for 5.711 GHz (Arb Units)		Col J: Beam A data for 5.711 GHz (Arb Units)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig4b.csv"
  },
  {
    "title": "Fig 8b",
    "format": "csv 8 columns",
    "mediaType": "text/csv",
    "description": "Probe absorption intensity in Beam A and Beam B vs detuning and vs theta for varying RF polarization, chi.	The data file columns include one column for each beam and chi=0, 45 and 90 degrees combination.		Format: Col A: Angle : Theta (deg)		Col B: Detuning (MHz)		Col C: BeamA_Chi0 (Arb Units)		Col D: BeamB_Chi0 (Arb Units) 		Col E: BeamA_Chi45 (Arb Units)		Col F: BeamB_Chi45 (Arb Units)		Col G: BeamA_Chi90 (Arb Units)		Col H: BeamB_Chi90 (Arb Units)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig8b.csv"
  },
  {
    "title": "Fig 4a",
    "format": "csv, 4 columns of 1D data",
    "mediaType": "text/csv",
    "description": "Probe transmission through PEC cell in arbitrary units vs. optical frequency detuning of coupling laser in MHz. Three traces are Beam A, Beam B, and the Reference cell. RF frequency was 5.044 GHz in the PEC cell.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig4a.csv"
  },
  {
    "title": "Fig 8c",
    "format": "csv 4 columns",
    "mediaType": "text/csv",
    "description": "Ratio : EA/EB, as a function of theta and for varying RF polarization, chi = 0, 45 and 90 degrees.		Format: Col A: Angle : Theta (deg)		Col B: Ratio EA/EB  Chi 0 (Unitless)		Col C: Ratio EA/EB  Chi 45 (Unitless)		Col D: Ratio EA/EB  Chi 90 (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig8c.csv"
  },
  {
    "title": "Fig 9c",
    "format": "csv 4 columns",
    "mediaType": "text/csv",
    "description": "Ratio of probe absorption heights of beam B and beam A (Ib/Ia)at zero detuning 	for varying theta and at f = 4.228, 5.044, and 5.711 GHz.		Format: Col A: Angle : Theta (deg)		Col B: Ib/Ia-4.228GHz (Unitless)		Col C: Ib/Ia-5.044GHz (Unitless)		Col D: Ib/Ia-5.711GHz (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig9c.csv"
  },
  {
    "title": "Fig 9b",
    "format": "csv 3 columns",
    "mediaType": "text/csv",
    "description": "Ratio, EA/EB, as a function of theta with and without an external conducting plate.		Format: Col A: Angle : Theta (deg)		Col B: EA/EB - Without Plate (Unitless)		Col C: EA/EB - With Plate (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig9b.csv"
  },
  {
    "title": "Fig 5b",
    "format": "csv 4 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The deviation in the AoA estimate from two repeat measurements, Deviation Run 2 and 3,	and the Total Uncertainty (k=1) from the error model in Figure 5a.	Format: Three linear plots data		Col A: Angle: Theta  (deg) 		Col B: Deviation Run 2 (deg)		Col C: Deviation Run 3 (deg)		Col D: Total Uncertainty (k=1) (deg)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig5b.csv"
  },
  {
    "title": "Fig 6f",
    "format": "csv 6 columns",
    "mediaType": "text/csv",
    "description": "The dipole moment transitions values are listed against the quantum numbers of the two states.	"Pi" polarized probe, coupling and RF fields.		Format: Col A: Quantum Number F1  (unitless)		Col B: Quantum Number mF1 (unitless)		Col C: Quantum Number F2  (unitless)		Col D: Quantum Number mF2 (unitless)		Col E: Polarization q (unitless)		Col F: Dipole Moment (ea_0)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig6f.csv"
  },
  {
    "title": "Fig 6g",
    "format": "csv 6 columns",
    "mediaType": "text/csv",
    "description": "The dipole moment transitions values are listed against the quantum numbers of the two states.        "Sigma" polarized probe, coupling with "Pi" polarized RF fields.		Format: Col A: Quantum Number F1  (unitless)		Col B: Quantum Number mF1 (unitless)		Col C: Quantum Number F2  (unitless)		Col D: Quantum Number mF2 (unitless)		Col E: Polarization q (unitless)		Col F: Dipole Moment (ea_0)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig6g.csv"
  },
  {
    "title": "Fig 2a",
    "format": "csv, 2D plot with 3 columns",
    "mediaType": "text/csv",
    "description": "The field E in V/m at a normalized distance, z/wavelength RF, as a function of incoming angle-of-arrival (AoA), theta in degrees, for an incident 1.0 V/m E-field incident on an infinite conducting plane polarized parallel to the plane of incidence.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2a.csv"
  },
  {
    "title": "Fig 2c",
    "format": "csv, 2D data in 3 columns",
    "mediaType": "text/csv",
    "description": "The field E in V/m at a normalized distance, z/wavelength RF, as a function of incoming angle-of-arrival (AoA), theta in degrees, for an incident 1.0 V/m E-field incident on an infinite conducting plane polarized perpendicular to the plane of incidence.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2c.csv"
  },
  {
    "title": "Fig 2g",
    "format": "csv, 8 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The field ratio, EA/EB, vs. theta in degrees, for various frequencies in GHz.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig2g.csv"
  },
  {
    "title": "Fig 6d",
    "format": "csv 4 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The fraction of the probe absorption profile which does not split, 	i.e., the percentage area in the central peak, is given for differing optical 	polarizations and angle. 	The polarization abbreviations are the same as in Figure 6a.	Format: Col A: Probe Polarization  (Type) 		Col B: Coupling Polarization (Type)		Col C: Angle : Theta (deg) 		Col D: Fraction in Central Peak - Beam A (Arb Units)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig6d.csv"
  },
  {
    "title": "Fig 1b",
    "format": "csv, four columns",
    "mediaType": "text/csv",
    "description": "The measured ratio, E_A/E_B, as a function of theta in degrees at f = 4.228, 5.044, and 5.711 GHz.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig1b.csv"
  },
  {
    "title": "Fig 6e",
    "format": "csv 6 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The ratio, EA/EB, for different polarizations compared to that of the simulation result.	Format: Col A: Angle : Theta (deg)		Col B: EA/EB - Linear Probe: Linear Coupling (Unitless)		Col C: EA/EB - Linear Probe: Circular Coupling (Unitless)		Col D: EA/EB - Circular Probe: Linear Coupling (Unitless)		Col E: EA/EB - Circular Probe: Circular Coupling (Unitless)		Col F: EA/EB - Simulation (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig6e.csv"
  },
  {
    "title": "Fig 7a_7b",
    "format": "csv 4 columns",
    "mediaType": "text/csv",
    "description": "The ratio, EA/EB, for simulated and measured values for varying 	azimuthal angle, phi, and polar angle, theta.	Format: Col A: Angle : Theta (deg)		Col B: Angle : Phi (deg)		Col C: Simulated Ratio EA/EB (Unitless)		Col D: Measured Ratio EA/EB (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig7a_7b.csv"
  },
  {
    "title": "Fig 4c",
    "format": "csv 6 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The ratio, E_A/E_B, as a function of theta in degrees at f = 4.228, 5.044, and 5.711 GHz.	Format: Six linear plots data		Col A: Angle: Theta (degrees) 		Col B: Experimental Ratio for 4.228 GHz (Unitless)                Col C: Simulation Ratio for 4.228 GHz (Unitless)		Col D: Experimental Ratio for 5.044 GHz (Unitless)                Col E: Simulation Ratio for 5.044 GHz (Unitless)		Col F: Experimental Ratio for 5.711 GHz (Unitless)                Col G: Simulation Ratio for 5.711 GHz (Unitless)",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig4c.csv"
  },
  {
    "title": "Fig 5a",
    "format": "csv 4 columns of 1D data",
    "mediaType": "text/csv",
    "description": "The standard deviation of the ratio E_A/ E_B for the components of the error model.	Format: Three linear plots data		Col A: Angle: Theta (degrees) 		Col B: Standard deviation from repeat measurements (deg)		Col C: Standard error of the peak location fitting (deg)		Col D: Type B analysis for the deviation in the ratio due to beam displacements	",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Fig5a.csv"
  },
  {
    "title": "README",
    "format": "txt",
    "mediaType": "text/plain",
    "description": "readme info for files",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-3609/Read_Me.txt"
  }
]
identifier ark:/88434/mds2-3609
issued 2025-05-16
keyword 
[
  "Rydberg atoms",
  "atomic physics",
  "electric field",
  "fields strength",
  "receivers",
  "volts/meter"
]
landingPage https://data.nist.gov/od/id/mds2-3609
language 
[
  "en"
]
license https://www.nist.gov/open/license
modified 2024-10-18 00:00:00
programCode 
[
  "006:045"
]
publisher 
{
  "name": "National Institute of Standards and Technology",
  "@type": "org:Organization"
}
theme 
[
  "Electronics:Electromagnetics",
  "Physics:Atomic, molecular, and quantum"
]
title Determining angle of arrival of radio frequency fields using subwavelength, amplitude-only measurements of standing waves in a Rydberg atom sensor

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