Photon Number Resolution (PNR)

Photon number resolution (PNR) is a measurement technique that determines the number of photons detected in a single optical event. It employs highly sensitive single-photon detectors in combination with signal-processing methods to distinguish between events involving one, two, or several photons. Unlike purely binary on/off detection schemes, PNR provides discrete photon-number statistics, offering insight into the probabilistic nature of light generation and quantum interactions. Depending on the experimental realization, PNR can be implemented using different approaches that extract photon-number information either directly from detector signals or through multi-channel detection strategies.

The method plays a key role in photonic quantum computing and quantum communication, enabling detailed studies of photon-number distributions, photon correlations, antibunching, and non-classical light sources.

PNR is realized by analyzing the detector response to individual photon events using high-precision timing electronics. By resolving variations in signal timing, shape, and spatial position or detection channel, information about the number of contributing photons can be extracted.

PNR Approaches

In practice, PNR can be realized using two main approaches: intrinsic PNR and multiplexed PNR. Intrinsic PNR relies on detectors whose response directly reflects the number of absorbed photons within a single detection event. The detector signal itself carries photon-number information, which can be extracted through detailed signal analysis. Multiplexed PNR, also referred to as pseudo-PNR, distributes incoming photons across multiple detection channels. The photon number is then inferred from the number of coincident detection events. This can be implemented using spatial multiplexing with detector arrays or temporal multiplexing by separating photon arrivals in time.

Detector Technologies for PNR

Different detector technologies enable PNR with distinct advantages and limitations.

• Transition-Edge Sensors (TESs) provide true photon-number and energy resolution by measuring the deposited energy with high precision, but typically still exhibit longer recovery times, which limit their maximum count rates.
• Superconducting Nanowire Single-Photon Detectors (SNSPDs) offer excellent timing performance and high count-rate capability. While not inherently energy-resolving, their pulse shapes can be analyzed to extract photon-number information, although the number of distinguishable photon levels is typically limited compared to TES-based systems.
• SPAD and SiPM arrays enable multiplexed PNR by distributing photons across many channels. Their main advantage is room-temperature operation, while limitations include reduced detection efficiency and higher dark count rates compared to superconducting detectors.

The choice of detector depends on the required balance between timing resolution, count rate, and photon-number discrimination capability.

Signal Analysis in Intrinsic PNR

In intrinsic PNR, photon-number information is extracted from the detailed temporal or amplitude characteristics of the detector signal. Using SNSPDs as an example, the absorption of multiple photons within the nanowire leads to a larger initial normal-conducting region and a faster redistribution of the bias current. As a result, the electrical response of the detector changes in a photon-number-dependent way, affecting both the onset and evolution of the output pulse.

Key observables include:

• Slew rate (rising edge): The slope of the rising edge increases with photon number, as multiple absorbed photons lead to a faster formation and expansion of the resistive region. This results in a steeper signal onset, which can be evaluated using precise timing electronics to discriminate between different photon-number events.
• Pulse width: Multi-photon events often produce broader electrical pulses, as the detector remains in a resistive state for a longer time. This is commonly quantified using the time-over-threshold (ToT), providing a robust parameter that is less sensitive to amplitude fluctuations.
• Amplitude: The signal amplitude can increase with photon number due to stronger redistribution of the bias current. While this parameter can be affected by noise and readout bandwidth, it still provides useful complementary information when combined with timing-based observables.
• Timing relative to a synchronization pulse: Under pulsed excitation, the effective detection timing can shift depending on photon number. Multi-photon absorption can lead to earlier trigger conditions, resulting in measurable timing differences relative to a sync signal. This is particularly efficient when using PicoQuant’s T3 mode, where photon arrival times are recorded relative to the excitation cycle, enabling compact data representation and high-throughput analysis of photon-number-dependent timing shifts.

By combining these observables, photon-number-dependent signatures can be separated more robustly than with a single parameter alone. In particular, correlating multiple signal features enables reliable photon-number discrimination even under high count-rate conditions.

Photon number resolution is particularly valuable in applications where the exact number of detected photons carries meaningful information. This includes the characterization of light sources, for example to distinguish true single-photon emission from multi-photon contributions, as well as quantum information protocols, such as photon-number-based encoding schemes or the verification of multi-photon states used in quantum communication and photonic quantum computing. In addition, PNR plays an important role in the calibration and performance evaluation of single-photon detectors, enabling a deeper understanding of detector response under varying signal conditions.

Photon-number-resolving measurements often rely on multi-dimensional representations of detector signals. A particularly powerful method is the use of two-dimensional histograms, where different timing parameters of the same pulse are analyzed simultaneously. For example, the arrival times of the rising and falling edges relative to a synchronization signal can be recorded and plotted against each other. This reveals distinct clusters corresponding to different photon numbers, allowing direct visual discrimination of one-, two-, and multi-photon events.

Such representations also expose systematic effects at high count rates. In particular, incomplete detector recovery can lead to shifted or duplicated clusters. By transforming the data, for example into a time-over-threshold representation, and applying appropriate corrections, these effects can be compensated, enabling robust photon-number classification even under demanding conditions.

These analysis methods allow efficient gating and classification of photon-number-dependent events and form the basis for real-time PNR evaluation.