Quantum Dot Single-Photon Source for Fiber-Based Quantum Key Distribution

A Quantum Mechanics Engineering Problem (Quantum Photonics)

Problem Statement

A quantum photonics company is developing an integrated single-photon source based on InAs/GaAs semiconductor quantum dots embedded in a micropillar cavity for deployment in metropolitan quantum key distribution (QKD) networks. The device must emit single photons on-demand at telecom wavelengths with high purity and indistinguishability while operating within the constraints of real-world quantum communication systems.

Device Specifications (based on state-of-the-art quantum dot sources)

Quantum Dot System:

Material: InAs self-assembled quantum dots in GaAs matrix
Dot dimensions: ~20 nm diameter, ~5 nm height (typical self-assembled dots)
Confinement potential: ~300 meV (electron ground state)
Emission wavelength target: $\lambda = 1310\ \mathrm{nm}$ or $1550\ \mathrm{nm}$ (telecom O-band or C-band)
Operating temperature: $T = 4\ \mathrm{K}$ (liquid helium or closed-cycle cryostat)

Cavity Parameters (micropillar resonator):

Cavity type: Distributed Bragg reflector (DBR) micropillar
Pillar diameter: $d = 2.0\ \mu\mathrm{m}$
Cavity mode volume: $V_{\mathrm{cav}} \approx 2(\lambda/n)^3$ where $n = 3.5$ (GaAs refractive index)
Top mirror reflectivity: $R_{\mathrm{top}} = 99.5\%$
Bottom mirror reflectivity: $R_{\mathrm{bottom}} = 99.9\%$
Quality factor: $Q = 10{,}000$ (typical for high-performance micropillars)

Physical Constants:

Planck constant: $\hbar = 1.055 \times 10^{-34}\ \mathrm{J \cdot s}$
Speed of light: $c = 3 \times 10^8\ \mathrm{m/s}$
Boltzmann constant: $k_B = 1.381 \times 10^{-23}\ \mathrm{J/K}$
Electron mass: $m_e = 9.109 \times 10^{-31}\ \mathrm{kg}$
Effective electron mass in InAs: $m^* = 0.023\ m_e$

QKD System Requirements (ITU-T standards and commercial targets):

Target secure key rate: $K_{\mathrm{secure}} \ge 1\ \mathrm{kbit/s}$ over metropolitan distances
Fiber link distance: $L = 50\ \mathrm{km}$ (standard single-mode fiber)
Fiber attenuation: $\alpha = 0.2\ \mathrm{dB/km}$ at $1550\ \mathrm{nm}$
Required single-photon purity: $g^{(2)}(0) < 0.1$ (multi-photon probability $< 10\%$ )
Required photon indistinguishability: $I > 0.90$ (visibility in Hong-Ou-Mandel interference)
Quantum bit error rate (QBER) budget: $< 11\%$ for BB84 protocol security

Questions

What are the discrete energy levels of the electron in the quantum dot confinement potential, and what emission wavelength does the ground-to-first-excited transition produce? Does this match the telecom wavelength requirement?
What Purcell factor is achieved by the micropillar cavity, and how much does it enhance the spontaneous emission rate compared to bulk semiconductor?
What is the radiative lifetime of the excited state with and without the cavity, and what repetition rate (photons per second) can the source achieve?
What are the primary decoherence mechanisms (phonon coupling, spectral diffusion) at 4 K, and what coherence time $T_2$ limits photon indistinguishability?
What is the total system efficiency (from dot excitation to fiber-coupled photon detection), and what source brightness is required to achieve 1 kbit/s secure key rate over 50 km?
Does the thermal occupation of the excited state at 4 K create significant background noise, and what operating temperature is required to suppress thermal population to $< 1\%$ ?

Analytical Reasoning

Before mathematical formulation, we must understand the quantum mechanics and engineering physics:

Quantum Confinement and Discrete Energy Levels

A quantum dot confines electrons and holes in all three spatial dimensions, creating atom-like discrete energy states. The confinement arises from the potential difference between the InAs dot and surrounding GaAs barrier material. For a simple model, treat the dot as a 3D quantum box or parabolic potential well.

The energy quantization fundamentally distinguishes quantum dots from bulk semiconductors (continuous bands) and enables single-photon emission: when an excited electron-hole pair (exciton) recombines, exactly one photon is emitted at a wavelength determined by the energy level spacing.

Cavity Quantum Electrodynamics (Cavity QED)

When the quantum dot is embedded in an optical microcavity, the local electromagnetic density of states is modified. If the dot emission wavelength matches the cavity resonance (spectral matching) and the dot is positioned at a cavity field antinode (spatial matching), the Purcell effect enhances spontaneous emission:

F_P = \frac{3}{4\pi^2}\left(\frac{\lambda}{n}\right)^3\frac{Q}{V_{\mathrm{cav}}}

This enhancement:

Increases emission rate (shorter radiative lifetime → higher repetition rate)
Channels emission into the cavity mode (higher collection efficiency)
Improves single-photon purity by suppressing emission into other modes

Single-Photon Purity and $g^{(2)}(0)$

The second-order correlation function $g^{(2)}(0)$ quantifies single-photon character:

g^{(2)}(0) = \frac{\langle n(t)n(t)\rangle}{\langle n(t)\rangle^2}

For perfect single-photon emission, $g^{(2)}(0) = 0$ (photon anti-bunching). For coherent light (laser), $g^{(2)}(0) = 1$ . For thermal light, $g^{(2)}(0) = 2$ .

Quantum dots can achieve $g^{(2)}(0) < 0.01$ experimentally, far better than attenuated lasers where Poissonian statistics limit multi-photon probability.

Photon Indistinguishability and Decoherence

For quantum interference applications (QKD, quantum computing), photons must be indistinguishable: identical in frequency, timing, polarization, and spatial mode. Indistinguishability $I$ is measured via Hong-Ou-Mandel (HOM) two-photon interference:

I = 1 - \frac{C_{\mathrm{HOM}}}{C_{\mathrm{classical}}}

where $C$ is the coincidence rate. Perfect indistinguishability ( $I = 1$ ) requires:

Transform-limited emission: Fourier-limited linewidth $\Delta\nu = 1/(2\pi T_1)$
No spectral diffusion: Charge noise and nuclear spin fluctuations cause random frequency shifts
Coherence time constraint: $T_2 \ge T_1$ (homogeneous broadening only)

Real quantum dots suffer from:

Phonon coupling at finite temperature → pure dephasing (reduces $T_2$ )
Charge noise from nearby trapped charges → spectral wandering
Nuclear spin bath (Overhauser effect) → hyperfine-induced dephasing

Fiber Transmission and System Efficiency

The overall probability that an emitted photon reaches a detector after 50 km fiber is:

\eta_{\mathrm{total}} = \eta_{\mathrm{extraction}} \times \eta_{\mathrm{coupling}} \times \eta_{\mathrm{fiber}} \times \eta_{\mathrm{detector}}

where:

$\eta_{\mathrm{extraction}}$ : photon escape from device into collection optics (~50% for micropillars)
$\eta_{\mathrm{coupling}}$ : coupling into single-mode fiber (~30–50%)
$\eta_{\mathrm{fiber}}$ : transmission through fiber $= 10^{-\alpha L/10}$
$\eta_{\mathrm{detector}}$ : detector quantum efficiency (~70–90% for SNSPDs at telecom wavelengths)

Secure Key Rate in QKD

For the BB84 protocol, the secure key rate is approximately:

K_{\mathrm{secure}} \approx R_{\mathrm{photon}} \times \eta_{\mathrm{total}} \times [1 - h(\mathrm{QBER})]

where $R_{\mathrm{photon}}$ is the source rate, and $h(\mathrm{QBER})$ is the binary entropy function accounting for error correction overhead. For QBER $< 11\%$ , positive secure key generation is possible.

Mathematical Formulation and Resolution

Step 1 — Quantum Dot Energy Levels and Emission Wavelength

Model: Treat the quantum dot as a 3D parabolic confinement potential:

V(\vec{r}) = \frac{1}{2}m^*\omega_0^2(x^2 + y^2 + z^2)

The Schrödinger equation gives harmonic oscillator energy levels:

E_{n_x,n_y,n_z} = \hbar\omega_0\left(n_x + n_y + n_z + \frac{3}{2}\right)

where $n_x, n_y, n_z = 0, 1, 2, \ldots$

Ground state (0,0,0):

E_0 = \frac{3}{2}\hbar\omega_0

First excited state (1,0,0) or equivalent:

E_1 = \frac{5}{2}\hbar\omega_0

Transition energy:

\Delta E = E_1 - E_0 = \hbar\omega_0

Estimate $\omega_0$ from confinement:

For a dot with lateral size $L \approx 20\ \mathrm{nm}$ , the confinement energy scale is:

\hbar\omega_0 \approx \frac{\hbar^2}{m^*L^2}

Calculation:

\hbar\omega_0 = \frac{(1.055 \times 10^{-34})^2}{0.023 \times 9.109 \times 10^{-31} \times (20 \times 10^{-9})^2}

= \frac{1.113 \times 10^{-68}}{0.023 \times 9.109 \times 10^{-31} \times 4 \times 10^{-16}}

= \frac{1.113 \times 10^{-68}}{8.38 \times 10^{-48}} = 1.33 \times 10^{-21}\ \mathrm{J}

Converting to eV:

\hbar\omega_0 = \frac{1.33 \times 10^{-21}}{1.602 \times 10^{-19}} = 0.0083\ \mathrm{eV} = 8.3\ \mathrm{meV}

However, real InAs quantum dots have stronger confinement and include the material bandgap. The typical emission wavelength is determined by:

E_{\mathrm{photon}} = E_{\mathrm{gap,InAs}} + E_{\mathrm{confinement,e}} + E_{\mathrm{confinement,h}}

For InAs dots in GaAs:

InAs bandgap: ~0.35 eV (bulk)
Confinement shifts: ~100–300 meV (combined electron and hole)
Typical emission energy: 0.9–1.0 eV → $\lambda \approx 1300$ – $1380\ \mathrm{nm}$

For telecom C-band (1550 nm = 0.8 eV), quantum dots require:

Larger size (weaker confinement)
Strain engineering
Alternative materials (InAs/InP or InGaAs)

\boxed{\lambda \approx 1310\ \mathrm{nm}\ \mathrm{(O-band\ telecom)}}

Conclusion: Standard InAs/GaAs dots naturally emit near 1310 nm (O-band), matching one telecom window. Reaching 1550 nm requires materials engineering but is achievable with InAs/InP or InGaAs/GaAs systems.

Step 2 — Purcell Factor and Emission Enhancement

Cavity mode volume at $\lambda = 1310\ \mathrm{nm}$ :

V_{\mathrm{cav}} = 2\left(\frac{\lambda}{n}\right)^3 = 2\left(\frac{1310 \times 10^{-9}}{3.5}\right)^3

= 2 \times (3.743 \times 10^{-7})^3 = 2 \times 5.248 \times 10^{-20} = 1.050 \times 10^{-19}\ \mathrm{m}^3

Purcell factor:

F_P = \frac{3}{4\pi^2}\left(\frac{\lambda}{n}\right)^3\frac{Q}{V_{\mathrm{cav}}}

F_P = \frac{3}{4\pi^2} \times \frac{Q \times (\lambda/n)^3}{V_{\mathrm{cav}}}

Since $V_{\mathrm{cav}} = 2(\lambda/n)^3$ :

F_P = \frac{3}{4\pi^2} \times \frac{Q}{2} = \frac{3Q}{8\pi^2}

F_P = \frac{3 \times 10{,}000}{8 \times 9.8696} = \frac{30{,}000}{78.957} = 380

\boxed{F_P \approx 380}

Conclusion: The micropillar cavity provides a Purcell enhancement factor of ~380, dramatically increasing the spontaneous emission rate into the cavity mode.

Step 3 — Radiative Lifetime and Repetition Rate

Bulk semiconductor radiative lifetime:

For InAs quantum dots in bulk GaAs, typical spontaneous emission lifetime:

\tau_{\mathrm{bulk}} \approx 1\ \mathrm{ns}

Cavity-enhanced lifetime:

\tau_{\mathrm{cav}} = \frac{\tau_{\mathrm{bulk}}}{F_P} = \frac{1\ \mathrm{ns}}{380} = 2.63\ \mathrm{ps}

Wait—this is unrealistically fast. The issue is that not all emission couples to the cavity mode. The effective Purcell factor considering mode matching ( $\beta$ -factor):

\tau_{\mathrm{eff}} = \frac{\tau_{\mathrm{bulk}}}{1 + \beta(F_P - 1)}

For well-aligned quantum dots in micropillars, $\beta \approx 0.5$ – $0.8$ (50–80% of emission into cavity mode).

Using $\beta = 0.7$ :

\tau_{\mathrm{eff}} = \frac{1\ \mathrm{ns}}{1 + 0.7 \times (380 - 1)} = \frac{1\ \mathrm{ns}}{1 + 265.3} = \frac{1\ \mathrm{ns}}{266.3} = 3.75\ \mathrm{ps}

\boxed{\tau_{\mathrm{eff}} \approx 3.75\ \mathrm{ps}}

This is still very fast. However, the practical repetition rate is limited by the excitation scheme:

Resonant excitation: Limited by laser pulse repetition (~80 MHz = 12.5 ns period)
Non-resonant pumping: Carrier capture time ~100 ps + excited state lifetime

Practical repetition rate: 100 MHz to 1 GHz (1–10 ns period)

Using conservative 200 MHz repetition rate:

R_{\mathrm{photon}} = 200 \times 10^6\ \mathrm{photons/s}

\boxed{R_{\mathrm{photon}} = 200\ \mathrm{MHz}}

Step 4 — Decoherence and Photon Indistinguishability

Transform-limited linewidth:

\Delta\nu_{\mathrm{lifetime}} = \frac{1}{2\pi\tau_{\mathrm{eff}}} = \frac{1}{2\pi \times 3.75 \times 10^{-12}} = 42.5\ \mathrm{GHz}

Pure dephasing from phonon coupling:

At $T = 4\ \mathrm{K}$ , acoustic phonon interactions cause pure dephasing. The dephasing rate follows:

\Gamma_{\mathrm{phonon}}(T) \approx \Gamma_0\left(\frac{T}{T_0}\right)^3

For InAs dots, typical values: $\Gamma_0 \approx 1\ \mu\mathrm{eV}$ , $T_0 \approx 10\ \mathrm{K}$

\Gamma_{\mathrm{phonon}}(4\ \mathrm{K}) \approx 1\ \mu\mathrm{eV} \times \left(\frac{4}{10}\right)^3 = 1 \times 0.064 = 0.064\ \mu\mathrm{eV}

Converting to time:

T_2^{\mathrm{phonon}} = \frac{\hbar}{\Gamma_{\mathrm{phonon}}} = \frac{1.055 \times 10^{-34}}{0.064 \times 1.602 \times 10^{-25}} = \frac{1.055 \times 10^{-34}}{1.025 \times 10^{-26}} = 1.03 \times 10^{-8}\ \mathrm{s} = 10.3\ \mathrm{ns}

Total dephasing time:

\frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_2^{\mathrm{phonon}}}

Since $T_1 \approx \tau_{\mathrm{eff}} = 3.75\ \mathrm{ps} \ll T_2^{\mathrm{phonon}}$ :

\frac{1}{T_2} \approx \frac{1}{2 \times 3.75 \times 10^{-12}} = 1.33 \times 10^{11}\ \mathrm{s}^{-1}

T_2 \approx 7.5\ \mathrm{ps}

\boxed{T_2 \approx 7.5\ \mathrm{ps}}

Indistinguishability:

For Fourier-limited emission ( $T_2 = 2T_1$ ):

I_{\max} \approx 1

For $T_2 \approx 2T_1$ (minimal phonon coupling at 4 K):

I \approx 0.90\text{–}0.95

\boxed{I > 0.90}

Conclusion: At $T = 4\ \mathrm{K}$ , phonon dephasing is minimal and photon indistinguishability $I > 0.90$ is achievable, meeting the requirement.

Step 5 — System Efficiency and Required Source Brightness

Total transmission efficiency:

Extraction efficiency (micropillar): $\eta_{\mathrm{extraction}} = 0.50$
Fiber coupling: $\eta_{\mathrm{coupling}} = 0.40$
Fiber transmission (50 km at 0.2 dB/km):

\alpha_{\mathrm{total}} = 0.2 \times 50 = 10\ \mathrm{dB}

\eta_{\mathrm{fiber}} = 10^{-10/10} = 10^{-1} = 0.1

Detector efficiency: $\eta_{\mathrm{detector}} = 0.80$ (superconducting nanowire single-photon detector)

Total efficiency:

\eta_{\mathrm{total}} = 0.50 \times 0.40 \times 0.1 \times 0.80 = 0.016 = 1.6\%

\boxed{\eta_{\mathrm{total}} = 1.6\%}

Secure key rate calculation:

For BB84 with QBER = 5%, the efficiency factor is approximately:

f_{\mathrm{QKD}} \approx 0.5 \times [1 - h(0.05)] \approx 0.5 \times 0.71 = 0.355

Required detected photon rate for 1 kbit/s:

R_{\mathrm{detected}} = \frac{K_{\mathrm{secure}}}{f_{\mathrm{QKD}}} = \frac{1000\ \mathrm{bit/s}}{0.355} = 2817\ \mathrm{photons/s}

Required source rate:

R_{\mathrm{source}} = \frac{R_{\mathrm{detected}}}{\eta_{\mathrm{total}}} = \frac{2817}{0.016} = 176{,}000\ \mathrm{photons/s} = 176\ \mathrm{kHz}

\boxed{R_{\mathrm{source}} = 176\ \mathrm{kHz}}

Comparison with capability:

Our source can operate at 200 MHz = 200,000 kHz, which is 1000× higher than required. This provides substantial margin for:

Higher key rates
Longer distances
System losses
Protocol overhead

Conclusion: The quantum dot source easily meets the brightness requirement. The system is fiber-loss-limited, not source-limited.

Step 6 — Thermal Population and Operating Temperature

Thermal occupation of excited state:

The probability of thermal excitation from ground to excited state:

P_{\mathrm{thermal}} = \frac{e^{-\Delta E/k_B T}}{1 + e^{-\Delta E/k_B T}} \approx e^{-\Delta E/k_B T}\quad \text{(for $\Delta E \gg k_B T$)}

Transition energy: $\Delta E = 0.95\ \mathrm{eV}$ (for $\lambda = 1310\ \mathrm{nm}$ )

\Delta E = \frac{hc}{\lambda} = \frac{1.24\ \mathrm{eV \cdot \mu m}}{1.31\ \mu\mathrm{m}} = 0.946\ \mathrm{eV}

At $T = 4\ \mathrm{K}$ :

k_B T = 1.381 \times 10^{-23} \times 4 = 5.524 \times 10^{-23}\ \mathrm{J} = 0.345\ \mathrm{meV}

\frac{\Delta E}{k_B T} = \frac{0.946\ \mathrm{eV}}{0.345 \times 10^{-3}\ \mathrm{eV}} = 2742

P_{\mathrm{thermal}} = e^{-2742} \approx 10^{-1191}

This is astronomically small—thermal population is completely negligible.

For 1% thermal population:

0.01 = e^{-\Delta E/k_B T}

\ln(0.01) = -4.605 = -\frac{\Delta E}{k_B T}

T = \frac{\Delta E}{4.605k_B} = \frac{0.946 \times 1.602 \times 10^{-19}}{4.605 \times 1.381 \times 10^{-23}} = \frac{1.515 \times 10^{-19}}{6.359 \times 10^{-23}} = 2383\ \mathrm{K}

\boxed{T_{\mathrm{required}} = 2383\ \mathrm{K}\ \mathrm{for}\ 1\%\ \mathrm{thermal\ population}}

Conclusion: At $T = 4\ \mathrm{K}$ , thermal population is negligible ( $< 10^{-1000}$ ). Even at room temperature (300 K), thermal population would be only ~ $10^{-16}$ . Operating at 4 K is primarily for reducing phonon dephasing to maintain indistinguishability, not for suppressing thermal occupation.

Conclusions

This comprehensive quantum mechanics analysis reveals the fundamental physics and practical engineering considerations for quantum dot single-photon sources:

Energy Quantization and Wavelength Matching: The 3D quantum confinement in InAs/GaAs dots creates discrete energy levels with typical ground-to-excited-state transitions producing $\lambda \approx 1310\ \mathrm{nm}$ (O-band telecom), naturally compatible with fiber networks. Reaching 1550 nm (C-band) requires materials engineering (InAs/InP or strain-tuned InGaAs), demonstrating how quantum mechanics directly constrains device design.
Cavity QED and Purcell Enhancement: The micropillar cavity with $Q = 10{,}000$ provides a Purcell factor of ~380, reducing the radiative lifetime from ~1 ns to ~3.75 ps (considering mode-matching efficiency $\beta \approx 0.7$ ). This enhancement is critical for achieving high brightness and channeling emission into a well-defined spatial mode for efficient fiber coupling.
Repetition Rate Limitation: Despite the ultra-short radiative lifetime, the practical repetition rate is limited to 100 MHz - 1 GHz by excitation mechanisms (laser repetition, carrier capture dynamics). Our conservative estimate of 200 MHz provides 200 million photons/s, far exceeding QKD requirements.
Decoherence and Indistinguishability: At $T = 4\ \mathrm{K}$ , phonon-induced pure dephasing is minimal ( $T_2^{\mathrm{phonon}} \approx 10\ \mathrm{ns}$ ), yielding a total coherence time $T_2 \approx 2T_1 \approx 7.5\ \mathrm{ps}$ that approaches the transform limit. This enables photon indistinguishability $I > 0.90$ , meeting quantum interference requirements for QKD and photonic quantum computing.
System Efficiency and Source Performance: The end-to-end efficiency of $\eta_{\mathrm{total}} = 1.6\%$ (dominated by 50 km fiber loss of 10 dB) requires a source rate of only 176 kHz to achieve 1 kbit/s secure key rate. The quantum dot source operating at 200 MHz exceeds this by 1000-fold, confirming that metropolitan QKD is fiber-loss-limited, not source-limited. This margin enables:
- Longer reach (100+ km with improved detectors)
- Higher key rates (10+ kbit/s)
- Robustness against system losses
Thermal Population Negligibility: At the operating temperature of $T = 4\ \mathrm{K}$ , thermal population of the excited state is $< 10^{-1000}$ , completely negligible. Even at room temperature (300 K), thermal occupation would be only ~ $10^{-16}$ . Cryogenic operation is required primarily to suppress phonon scattering that degrades photon indistinguishability, not to prevent thermal noise.

Engineering Implications (Design Takeaways)

Quantum confinement engineering is critical: The dot size, composition, and strain state directly determine the emission wavelength through quantum mechanics. Achieving telecom wavelengths requires precise control over these nanoscale parameters.
Cavity design trades off Q-factor, mode volume, and bandwidth: Higher Q increases Purcell enhancement but narrows the resonance, requiring sub-nanometer spectral alignment between dot and cavity. Real devices use temperature tuning or electric-field Stark shifts for alignment.
Cryogenic operation is non-negotiable for high-performance sources: Room-temperature quantum dots suffer severe phonon dephasing ( $T_2 \ll T_1$ ) that destroys indistinguishability. The 4 K operating temperature is an engineering burden (cost, complexity, maintenance) that fundamentally limits deployment.
Single-photon purity ( $g^{(2)}(0) < 0.1$ ) versus indistinguishability ( $I > 0.9$ ) require different optimizations: Purity benefits from strong Purcell enhancement and fast lifetime, while indistinguishability requires minimizing dephasing. The optimal design balances both.
The transition from lab to field deployment faces practical challenges: Fiber coupling efficiency (~40%), long-term wavelength stability, vibration sensitivity, and scalable cryogenics are active areas of development. Commercial quantum dot sources are emerging but not yet widespread.

Quantum Dot Single-Photon Source for Fiber-Based Quantum Key Distribution

Key Concepts

Quantum Dot Single-Photon Source for Fiber-Based Quantum Key Distribution

Problem Statement

Device Specifications (based on state-of-the-art quantum dot sources)

Questions

Analytical Reasoning

Quantum Confinement and Discrete Energy Levels

Cavity Quantum Electrodynamics (Cavity QED)

Single-Photon Purity and g(2)(0)g^{(2)}(0)g(2)(0)

Photon Indistinguishability and Decoherence

Fiber Transmission and System Efficiency

Secure Key Rate in QKD

Mathematical Formulation and Resolution

Step 1 — Quantum Dot Energy Levels and Emission Wavelength

Step 2 — Purcell Factor and Emission Enhancement

Step 3 — Radiative Lifetime and Repetition Rate

Step 4 — Decoherence and Photon Indistinguishability

Step 5 — System Efficiency and Required Source Brightness

Step 6 — Thermal Population and Operating Temperature

Conclusions

Engineering Implications (Design Takeaways)

Single-Photon Purity and $g^{(2)}(0)$