HBT Correlation

Calculate normalized zero-delay HBT second-order correlation.

Description

Zero-delay HBT normalization compares coincidence rate with the accidental-rate scale from two singles rates and a coincidence window.

Zero-delay HBT normalization compares coincidence rate with the accidental-rate scale from two singles rates and a coincidence window. Window convention matters to the normalization.^[1]

Calculate normalized zero-delay HBT second-order correlation.

When to use HBT Correlation

Use this tool to calculate normalized zero-delay HBT second-order correlation.

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.

How to use HBT Correlation and understand its results

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
Enter coincidenceRatePerSecond, firstSinglesRatePerSecond, secondSinglesRatePerSecond, coincidenceWindowSeconds using the field table and calculation rules, then run the tool.
Read g2Zero. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
coincidenceRatePerSecond	Coincidence rate (1/s)	number; minimum: 0	Required
firstSinglesRatePerSecond	First singles rate (1/s)	number; minimum: 0	Required
secondSinglesRatePerSecond	Second singles rate (1/s)	number; minimum: 0	Required
coincidenceWindowSeconds	Coincidence window (s)	number; minimum: 0	Required

Enter nonnegative coincidence rate and positive singles rates/window. Return normalized g2.

g2(0)=coincidenceRate/(singles1×singles2×window)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
g2Zero	Second-order correlation g²(0)	number; minimum: 0

json

{
  "input": {
    "coincidenceRatePerSecond": 100,
    "firstSinglesRatePerSecond": 100000,
    "secondSinglesRatePerSecond": 100000,
    "coincidenceWindowSeconds": 1e-8
  },
  "output": {
    "g2Zero": 1
  }
}

Limitations and assumptions

No histogram, dark-count correction, detector dead time, timing calibration or photon-state certification is supplied.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use SPDC Heralded Rate: Estimate detected SPDC coincidence, singles, and heralding rates from supplied efficiencies. For a complementary task, use Homodyne Quadrature Statistics: Calculate mean and population variance for shot-noise-normalized homodyne quadratures.

References

HBT Correlation — tool.io

Similar or alternative tools

SPDC Heralded Rate
Estimate detected SPDC coincidence, singles, and heralding rates from supplied efficiencies.
Homodyne Quadrature Statistics
Calculate mean and population variance for shot-noise-normalized homodyne quadratures.