👀Quantum Optics Unit 9 – Single–Photon Sources and Detectors

Key Concepts and Principles

• Single-photon sources emit light as individual photons rather than classical electromagnetic waves
• Single-photon detectors can resolve the arrival of individual photons with high temporal resolution
• Photon antibunching is a key signature of single-photon emission demonstrated by a dip in the second-order correlation function $g^{(2)}(\tau)$ at zero time delay $\tau=0$
• Heralded single-photon sources use spontaneous parametric down-conversion (SPDC) to generate correlated photon pairs, where detection of one photon heralds the presence of its twin
  • SPDC involves a nonlinear crystal (beta barium borate) pumped by a laser to create entangled photon pairs
• On-demand single-photon sources, such as quantum dots or color centers in diamond, can emit single photons at predetermined times
• Single-photon detectors exploit various physical processes (photoelectric effect, avalanche multiplication) to convert individual photons into measurable electrical signals
• Quantum efficiency, dark count rate, dead time, and timing jitter are key performance metrics for single-photon detectors
• Single-photon technology enables fundamental tests of quantum mechanics (Bell's inequality) and practical applications in quantum information processing

Single-Photon Sources: Types and Mechanisms

• Heralded single-photon sources based on SPDC are widely used due to their room-temperature operation and compatibility with optical fibers
  • Type-I SPDC produces photon pairs with parallel polarizations, while type-II SPDC generates orthogonally polarized pairs
• Parametric down-conversion can be achieved in bulk crystals, waveguides, or periodically poled structures for increased efficiency and compact design
• Quantum dots are semiconductor nanostructures that confine excitons (electron-hole pairs) in three dimensions, acting as artificial atoms
  • InAs/GaAs self-assembled quantum dots are commonly used for single-photon emission in the near-infrared range
  • Electrically driven quantum dot single-photon sources enable on-demand operation and integration with electronic circuits
• Nitrogen-vacancy (NV) centers in diamond are atomic-scale defects that can emit single photons at room temperature
  • NV centers consist of a substitutional nitrogen atom adjacent to a vacancy in the diamond lattice
  • Optically detected magnetic resonance (ODMR) techniques allow for spin-selective readout and manipulation of NV centers
• Trapped atoms (rubidium) or ions (calcium) can serve as single-photon sources with long coherence times and high indistinguishability
• Molecules (dibenzoterrylene) and carbon nanotubes have also been explored as room-temperature single-photon emitters

Single-Photon Detectors: Technologies and Methods

• Photomultiplier tubes (PMTs) are vacuum devices that convert photons into electrons via the photoelectric effect and multiply them through secondary emission
  • PMTs offer large active areas and low dark counts but have limited quantum efficiency and timing resolution
• Single-photon avalanche diodes (SPADs) are reverse-biased p-n junctions operated above the breakdown voltage in Geiger mode
  • SPADs provide high quantum efficiency, low timing jitter, and compact size but suffer from afterpulsing and require active quenching circuits
• Superconducting nanowire single-photon detectors (SNSPDs) consist of thin (a few nanometers) superconducting films (niobium nitride) patterned into meandering nanowires
  • SNSPDs offer high quantum efficiency, low dark counts, and excellent timing resolution but require cryogenic cooling (2-4 K)
• Transition edge sensors (TESs) are superconducting devices biased at the transition between the superconducting and normal states
  • TESs can resolve the number of photons in a pulse (photon-number resolution) but have slower response times compared to SPADs or SNSPDs
• Up-conversion single-photon detectors use a nonlinear crystal (periodically poled lithium niobate) to convert near-infrared photons to visible wavelengths detectable by silicon SPADs
• Quantum dot optically gated field-effect transistors (QDOGFETs) are promising for room-temperature single-photon detection in the infrared range

Quantum Properties and Statistics

• Single photons exhibit quantum properties such as superposition, entanglement, and indistinguishability
• Photon statistics can be characterized by the Fock state representation, where $|n\rangle$ denotes a state with a definite number of photons $n$
• Coherent states $|\alpha\rangle$ are quantum analogs of classical electromagnetic waves with Poissonian photon number distribution
  • Coherent states have equal uncertainties in the quadrature amplitudes (position and momentum) and maintain their shape under time evolution
• Squeezed states have reduced uncertainty in one quadrature at the expense of increased uncertainty in the other, useful for precision measurements
• Photon bunching (super-Poissonian statistics) occurs for thermal light sources, while photon antibunching (sub-Poissonian statistics) is a hallmark of single-photon emission
• The degree of second-order coherence $g^{(2)}(0)$ quantifies the deviation from Poissonian statistics, with $g^{(2)}(0)<1$ indicating antibunching
• Hong-Ou-Mandel (HOM) interference is a two-photon interference effect demonstrating the indistinguishability of single photons
  • In HOM interference, two indistinguishable single photons incident on a beam splitter always exit together (bunching), resulting in a dip in coincidence counts

Experimental Setups and Techniques

• Hanbury Brown and Twiss (HBT) interferometer is used to measure the second-order correlation function $g^{(2)}(\tau)$ and demonstrate photon antibunching
  • HBT setup consists of a beam splitter and two single-photon detectors connected to a time-correlated single-photon counting (TCSPC) module
• Confocal microscopy is employed to isolate single quantum emitters (quantum dots, NV centers) and collect their fluorescence
  • Confocal setup uses a high numerical aperture objective lens, a pinhole to reject out-of-focus light, and a single-photon detector (SPAD or SNSPD)
• Microcavities (photonic crystals, micropillars) can be used to enhance the emission rate and directionality of single-photon sources through the Purcell effect
• Quantum state tomography allows for the reconstruction of the density matrix of a single-photon state using a series of projective measurements
• Quantum key distribution (QKD) protocols, such as BB84, rely on single-photon sources and detectors to establish secure communication channels
  • In BB84, Alice encodes bits in the polarization states of single photons, and Bob measures them in randomly chosen bases to detect eavesdropping
• Quantum teleportation and entanglement swapping experiments require the generation and detection of entangled photon pairs using SPDC sources and coincidence measurements

Applications in Quantum Information

• Quantum cryptography: Single-photon sources and detectors enable secure communication protocols (BB84) resistant to eavesdropping
  • Decoy state protocols improve the security and practicality of QKD systems by mitigating photon-number-splitting attacks
• Quantum computing: Single photons can serve as qubits in photonic quantum computers, with linear optical elements (beam splitters, phase shifters) performing quantum gates
  • Knill, Laflamme, and Milburn (KLM) scheme proposed a scalable approach to photonic quantum computing using linear optics and measurement-induced nonlinearities
• Quantum simulation: Single photons can simulate the behavior of complex quantum systems, such as boson sampling or quantum walks
  • Boson sampling involves sending single photons through a linear optical network and measuring their output distribution to solve classically intractable problems
• Quantum metrology: Single-photon states can enhance the precision of optical measurements beyond the classical shot noise limit
  • N00N states, consisting of a superposition of $N$ photons in two modes, can achieve Heisenberg-limited phase sensitivity scaling as $1/N$
• Quantum imaging: Single-photon detectors enable low-light imaging techniques, such as ghost imaging or quantum illumination, which exploit the spatial and temporal correlations of entangled photon pairs
• Quantum networks: Single-photon sources and detectors are essential components for the realization of quantum repeaters and long-distance entanglement distribution in quantum networks

Challenges and Limitations

• Scalability: Increasing the complexity and integration of single-photon devices while maintaining their quantum properties is a significant challenge
  • Solid-state sources (quantum dots, NV centers) offer the potential for scalable fabrication but suffer from inhomogeneous broadening and decoherence
• Efficiency: The generation and detection efficiencies of single photons are limited by various factors, such as collection optics, detector quantum efficiency, and coupling losses
  • Photon loss is a major obstacle for the realization of large-scale photonic quantum computers and long-distance quantum communication
• Indistinguishability: Generating indistinguishable single photons with identical spectral, temporal, and spatial properties is crucial for quantum interference and entanglement
  • Resonant excitation and cavity coupling can improve the indistinguishability of single-photon sources, but at the cost of increased experimental complexity
• Wavelength compatibility: Integrating single-photon sources and detectors with existing telecommunication infrastructure (1550 nm) is desirable for practical quantum communication
  • Frequency conversion techniques, such as difference frequency generation or four-wave mixing, can bridge the wavelength gap between visible single-photon sources and telecom wavelengths
• Dark counts and background noise: Single-photon detectors are sensitive to unwanted signals, such as thermal dark counts or stray light, which can limit their performance
  • Cryogenic cooling, time-gating, and spatial filtering can help reduce the impact of dark counts and background noise on single-photon measurements
• Timing jitter: The temporal resolution of single-photon detectors is limited by timing jitter, which can degrade the fidelity of quantum operations and measurements
  • Low-jitter detectors, such as SNSPDs or fast SPADs, are essential for applications requiring precise timing information, such as quantum clock synchronization or time-bin encoding

Future Directions and Research

• Deterministic single-photon sources: Developing on-demand sources with near-unity efficiency and indistinguishability is a key goal for scalable photonic quantum technologies
  • Quantum dot-cavity systems and coherent control techniques are promising approaches to achieve deterministic single-photon generation
• Integrated quantum photonics: Miniaturization and integration of single-photon devices on photonic chips can enable complex quantum circuits and reduce losses
  • Silicon, silicon nitride, and III-V semiconductor platforms are being explored for the realization of integrated single-photon sources, detectors, and quantum gates
• Hybrid quantum systems: Interfacing single photons with other quantum systems, such as atoms, ions, or superconducting qubits, can combine the advantages of different platforms
  • Cavity quantum electrodynamics (CQED) techniques allow for strong coupling between single photons and matter qubits, enabling efficient quantum interfaces and memories
• Satellite-based quantum communication: Extending quantum networks to global scales requires the development of space-compatible single-photon sources and detectors
  • Satellite-based QKD and entanglement distribution have been demonstrated, paving the way for a worldwide quantum internet
• Machine learning for single-photon technologies: Applying machine learning algorithms to the design, optimization, and characterization of single-photon devices can accelerate their development
  • Deep learning can be used to enhance the performance of single-photon detectors, predict the properties of single-photon sources, or optimize quantum error correction codes
• Quantum-enhanced sensing and imaging: Exploiting the sensitivity of single-photon measurements can lead to novel sensing and imaging techniques with improved resolution and specificity
  • Quantum ghost imaging, sub-shot-noise spectroscopy, and single-photon lidar are examples of emerging quantum-enhanced sensing applications