9.2 Heralded single-photon sources

Heralded single-photon sources are game-changers in quantum optics. They use spontaneous parametric down-conversion to generate single photons with high certainty. By detecting one photon, we can announce the presence of its twin, giving us on-demand single photons for quantum applications.

These sources are crucial for quantum communication, cryptography, and computing. They enable secure key distribution, quantum teleportation, and linear optical quantum computing. As we improve their efficiency and reliability, we're unlocking new possibilities in quantum technologies and pushing the boundaries of what's possible.

Heralded Single-Photon Sources

Concept and Working Principles

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• Heralded single-photon sources generate single photons with high certainty and control by exploiting spontaneous parametric down-conversion (SPDC)
• In SPDC, a high-energy pump photon interacts with a nonlinear crystal (beta-barium borate (BBO) or periodically poled potassium titanyl phosphate (PPKTP)) and spontaneously splits into two lower-energy photons called signal and idler photons
• Signal and idler photons are generated simultaneously and are correlated in time, energy, and polarization due to conservation of energy and momentum during SPDC
• Detecting the idler photon using a single-photon detector "heralds" the presence of its twin signal photon, announcing the signal photon's existence with high certainty
• Heralding allows for on-demand generation of single photons, as detecting the idler photon triggers the emission of the signal photon for various quantum applications
• Quality of the heralded single-photon source depends on the purity of the single-photon state, heralding efficiency, and suppression of multi-photon events

Experimental Setups and Components

• A typical setup consists of a pump laser, nonlinear crystal for SPDC, single-photon detectors, and optical components for filtering and manipulating photons
  • Pump laser (continuous-wave or pulsed) has a wavelength chosen to match phase-matching conditions of the nonlinear crystal for efficient SPDC
  • Nonlinear crystal is selected and engineered to optimize SPDC, considering crystal type, phase-matching conditions, and optical properties
  • Spectral filtering (interference filters or diffraction gratings) selects specific wavelengths of signal and idler photons to improve single-photon state purity and minimize background noise
  • Spatial filtering (coupling photons into single-mode optical fibers or using apertures) ensures spatial mode purity of the photons
  • Single-photon detectors (avalanche photodiodes (APDs) or superconducting nanowire single-photon detectors (SNSPDs)) detect the idler photon and herald the signal photon
  • Coincidence electronics (time-to-digital converters (TDCs) or field-programmable gate arrays (FPGAs)) record timing information of detected photons and identify coincidence events between signal and idler photons

Components of Heralded Sources

Pump Laser and Nonlinear Crystal

• Pump laser provides the high-energy photons necessary for SPDC
  • Wavelength is chosen to match phase-matching conditions of the nonlinear crystal for efficient down-conversion
  • Can be continuous-wave or pulsed, depending on the desired characteristics of the generated single photons
• Nonlinear crystal is the heart of the SPDC process, where the pump photon splits into signal and idler photons
  • Common crystals include beta-barium borate (BBO) and periodically poled potassium titanyl phosphate (PPKTP)
  • Crystal properties (type, phase-matching conditions, optical properties) are carefully engineered to optimize SPDC efficiency and photon characteristics

Filtering and Manipulation of Photons

• Spectral filtering improves the purity of the single-photon state and minimizes background noise
  • Narrowband filters (interference filters or diffraction gratings) select specific wavelengths of signal and idler photons
  • Ensures photons have well-defined spectral properties, which is crucial for their indistinguishability and suitability for quantum applications
• Spatial filtering ensures the spatial mode purity of the photons
  • Coupling photons into single-mode optical fibers or using apertures helps to define the spatial mode
  • Spatial mode purity is important for achieving high-visibility interference and efficient coupling to other quantum systems

Detection and Coincidence Electronics

• Single-photon detectors are used to detect the idler photon and herald the presence of the signal photon
  • Avalanche photodiodes (APDs) and superconducting nanowire single-photon detectors (SNSPDs) are common choices
  • Detectors should have high detection efficiency, low dark counts, and fast response times for efficient heralding
• Coincidence electronics record the timing information of detected photons and identify coincidence events between signal and idler photons
  • Time-to-digital converters (TDCs) or field-programmable gate arrays (FPGAs) are used for this purpose
  • Coincidence detection allows for the identification of true heralded single-photon events and the rejection of background noise and multi-photon events

Performance Metrics for Sources

Single-Photon Purity and Heralding Efficiency

• Heralding efficiency measures the probability of detecting a signal photon given the detection of its corresponding idler photon
  • High heralding efficiencies are desirable for efficient and reliable single-photon generation
  • Heralding efficiency is affected by factors such as detector efficiency, optical losses, and mode-matching between signal and idler photons
• Second-order correlation function, g^(2)(0), quantifies the degree of single-photon purity
  • g^(2)(0) < 0.5 indicates a strong single-photon character, with g^(2)(0) = 0 representing an ideal single-photon state
  • Measured using a Hanbury Brown and Twiss (HBT) interferometer, which consists of a beam splitter and two single-photon detectors

Indistinguishability and Spectral Properties

• Indistinguishability of generated single photons is assessed through Hong-Ou-Mandel (HOM) interference experiments
  • Two indistinguishable photons entering a beam splitter exhibit bunching behavior, resulting in a characteristic HOM dip
  • Visibility of the HOM dip quantifies the degree of indistinguishability, with higher visibility indicating better indistinguishability
• Spectral purity and bandwidth of the generated single photons are crucial for their suitability in quantum applications
  • Narrow spectral bandwidth is often desired for efficient interaction with atomic systems or for achieving high-visibility interference
  • Spectral purity can be characterized using single-photon spectrometers or by measuring the joint spectral intensity (JSI) of the signal and idler photons

Photon Generation Rate and Efficiency

• Photon generation rate determines the speed and scalability of quantum protocols relying on single photons
  • Higher generation rates allow for faster quantum operations and more efficient quantum communication and computation
  • Generation rate is influenced by factors such as pump power, nonlinear crystal properties, and collection efficiency of the photons
• Overall efficiency of the heralded single-photon source takes into account the losses in the entire system
  • Includes losses from SPDC, filtering, coupling, and detection stages
  • High overall efficiency is important for practical applications, as it directly impacts the success probability of quantum protocols and the scalability of quantum systems

Applications of Heralded Sources

Quantum Communication and Cryptography

• Heralded single-photon sources are a key enabling technology for quantum communication and cryptography protocols
  • Quantum key distribution (QKD) uses single photons to generate secure cryptographic keys, ensuring security through quantum mechanics principles
  • Quantum teleportation allows transfer of quantum information between distant locations using entanglement and classical communication, with single photons serving as quantum information carriers
  • Quantum repeaters, essential for extending the range of quantum communication networks, rely on heralded single-photon sources for generating and distributing entanglement between distant nodes
• Development of efficient and reliable heralded single-photon sources is crucial for practical implementation and widespread adoption of quantum communication and cryptography technologies
  • Enables secure and long-distance quantum networks
  • Paves the way for quantum-enhanced security and privacy in various applications (secure communication, sensitive data transmission, online transactions)

Quantum Computing and Metrology

• Linear optical quantum computing (LOQC) relies on heralded single-photon sources for realizing quantum gates and circuits
  • Single photons serve as qubits, the fundamental building blocks of quantum information processing
  • Quality and scalability of single-photon sources directly impact the performance and feasibility of LOQC systems
  • Heralded sources enable the generation of high-purity and indistinguishable single photons, which are essential for achieving high-fidelity quantum operations and error correction
• Quantum metrology and sensing applications exploit the non-classical properties of single photons for enhanced precision and sensitivity
  • Single photons can be used as probes in quantum imaging, spectroscopy, and interferometry
  • Heralded single-photon sources provide well-defined and controllable photon states, enabling advanced quantum metrology techniques (quantum illumination, quantum phase estimation)
• Advancement of heralded single-photon sources is key to unlocking the potential of quantum computing and metrology
  • Enables the development of scalable and fault-tolerant quantum computers
  • Enhances the capabilities of quantum sensors for various applications (biomedical imaging, material characterization, fundamental physics research)