Excitons and polaritons are fascinating quasiparticles in solid-state physics. Excitons form when electrons and holes bind together, influencing optical and electronic properties of materials. They come in different types and play crucial roles in various phenomena.

Polaritons result from strong coupling between photons and other excitations like excitons. They exhibit unique properties of both light and matter, enabling manipulation of light-matter interactions at the nanoscale. Polaritons have exciting applications in quantum technologies and optoelectronics.

Excitons

• Quasiparticles formed by the bound state of an electron and a hole in a solid, particularly in semiconductors and insulators
• Play a crucial role in the optical and electronic properties of materials, influencing absorption, emission, and energy transfer processes

Formation of excitons

• Occurs when a photon with sufficient energy excites an electron from the valence band to the conduction band, leaving behind a positively charged hole
• The attractive Coulomb force between the electron and hole binds them together, forming a hydrogen-like state (exciton)
• The formation process depends on factors such as the material's band structure, dielectric constant, and temperature

Frenkel vs Wannier-Mott excitons

• Frenkel excitons: tightly bound electron-hole pairs, typically found in materials with strong electron-hole interactions and low dielectric constants (organic semiconductors, molecular crystals)
• Wannier-Mott excitons: weakly bound electron-hole pairs, usually observed in materials with high dielectric constants and delocalized electronic states (inorganic semiconductors like GaAs, CdTe)
• The type of exciton formed depends on the material properties and the strength of the electron-hole interaction

Binding energy of excitons

• The energy required to dissociate an exciton into a free electron and a free hole
• Depends on factors such as the material's dielectric constant, effective masses of the electron and hole, and the exciton's spatial extent
• Higher binding energies indicate more stable excitons and stronger electron-hole interactions (Frenkel excitons), while lower binding energies suggest weaker interactions (Wannier-Mott excitons)

Exciton Bohr radius

• The average distance between the electron and hole in an exciton, analogous to the Bohr radius in a hydrogen atom
• Depends on the material's dielectric constant and the effective masses of the electron and hole
• Larger exciton Bohr radii are associated with Wannier-Mott excitons (typically tens of nanometers), while smaller radii are characteristic of Frenkel excitons (on the order of a lattice constant)

Exciton recombination

• The process by which an electron and a hole in an exciton recombine, releasing energy in the form of a photon (radiative recombination) or heat (non-radiative recombination)
• Radiative recombination is the basis for light emission in materials such as LEDs and quantum dots
• Non-radiative recombination occurs through various mechanisms, such as defect-assisted recombination or Auger recombination, and can limit the efficiency of optoelectronic devices

Exciton diffusion

• The movement of excitons through a material, driven by concentration gradients or applied electric fields
• Plays a crucial role in energy transfer processes, such as exciton migration to interfaces or defects
• The diffusion length, which is the average distance an exciton travels before recombining, depends on factors such as the exciton lifetime, mobility, and the material's structural and electronic properties

Exciton-phonon interactions

• The coupling between excitons and lattice vibrations (phonons) in a material
• Can lead to the formation of exciton-polaritons, quasiparticles that exhibit both excitonic and phononic properties
• Exciton-phonon interactions can influence exciton dynamics, such as relaxation, thermalization, and transport, and can be studied using techniques like Raman spectroscopy

Exciton fine structure

• The splitting of exciton energy levels due to various interactions, such as spin-orbit coupling, exchange interaction, or crystal field effects
• Can give rise to multiple exciton states with different energies and optical properties, such as bright and dark excitons
• The exciton fine structure can be probed using high-resolution spectroscopic techniques (photoluminescence excitation spectroscopy) and can provide insights into the underlying physics of excitons in materials

Excitons in quantum wells

• Quantum wells are thin semiconductor layers sandwiched between barrier layers with a larger bandgap, confining excitons in one dimension
• Confinement effects in quantum wells lead to modified exciton properties, such as increased binding energy, reduced Bohr radius, and discrete energy levels
• Quantum well excitons play a crucial role in optoelectronic devices (quantum well lasers, light-emitting diodes) and are used to study fundamental properties of excitons in reduced dimensions

Polaritons

• Quasiparticles that arise from the strong coupling between photons and other excitations in a material, such as excitons, phonons, or plasmons
• Exhibit properties of both light and matter, allowing for the manipulation of light-matter interactions at the nanoscale

Coupling of excitons and photons

• When the energy exchange rate between an exciton and a photon exceeds their individual decay rates, strong coupling occurs, leading to the formation of exciton-polaritons
• The coupling strength depends on factors such as the exciton oscillator strength, the photon confinement, and the overlap between the exciton and photon wavefunctions
• Strong coupling results in the hybridization of exciton and photon states, giving rise to new eigenstates with mixed exciton-photon character

Cavity polaritons

• Polaritons that form in optical cavities, where photons are confined between two highly reflective mirrors
• The confinement enhances the interaction between excitons and photons, leading to strong coupling and the formation of cavity polaritons
• Cavity polaritons have been observed in various systems, such as semiconductor microcavities, plasmonic cavities, and organic microcavities

Polariton dispersion

• The relationship between the energy and momentum of polaritons, which exhibits a non-linear, anticrossing behavior near the exciton-photon resonance
• The polariton dispersion consists of two branches: the lower polariton branch (LPB) and the upper polariton branch (UPB), separated by the Rabi splitting
• The shape of the polariton dispersion depends on factors such as the exciton-photon detuning, the coupling strength, and the cavity properties

Upper vs lower polariton branches

• The upper polariton branch (UPB) is the higher-energy branch of the polariton dispersion, with a more photon-like character at large momenta
• The lower polariton branch (LPB) is the lower-energy branch, exhibiting a more exciton-like character at large momenta
• The relative contributions of the exciton and photon components to the UPB and LPB vary along the dispersion curve, with a 50-50 mixture at the anticrossing point

Rabi splitting

• The energy gap between the upper and lower polariton branches at the anticrossing point, where the exciton and photon energies are in resonance
• Represents the strength of the exciton-photon coupling and is proportional to the square root of the product of the exciton oscillator strength and the photon confinement
• Larger Rabi splittings indicate stronger coupling and more pronounced polariton effects, such as enhanced nonlinearities and faster dynamics

Polariton condensation

• The formation of a macroscopic coherent state of polaritons, akin to Bose-Einstein condensation in atomic systems
• Occurs when polaritons accumulate in the lowest-energy state of the lower polariton branch, driven by stimulated scattering and bosonic final-state stimulation
• Polariton condensates exhibit unique properties, such as superfluidity, vortex formation, and long-range coherence, making them promising for applications in quantum simulation and information processing

Polariton lasing

• The generation of coherent light emission from a polariton condensate, without the need for population inversion as in conventional lasers
• Relies on the stimulated scattering of polaritons into the lowest-energy state, leading to a buildup of a macroscopic coherent population
• Polariton lasers have the potential for low-threshold, high-efficiency operation and could enable novel applications in integrated photonics and quantum technologies

Polariton-polariton interactions

• The interactions between polaritons, mediated by their excitonic component, which can give rise to rich nonlinear phenomena
• Polariton-polariton interactions can be repulsive or attractive, depending on the spin configuration of the interacting polaritons and the material properties
• These interactions enable the realization of polariton-based quantum fluids, solitons, and quantum gates, as well as the study of many-body physics in solid-state systems

Polaritons in microcavities

• Microcavities are optical cavities with dimensions on the order of the wavelength of light, enabling strong confinement of photons and enhanced light-matter interactions
• Polaritons in microcavities have been extensively studied due to their unique properties, such as low effective mass, long coherence times, and strong nonlinearities
• Microcavity polaritons have been used to demonstrate various phenomena, such as polariton condensation, lasing, superfluidity, and quantum vortices, and are promising for applications in quantum simulation, sensing, and information processing

Applications of polaritons

• Polariton-based devices: polariton lasers, polariton light-emitting diodes, polariton transistors, and polariton-based sensors
• Quantum simulation: using polariton systems to simulate complex many-body phenomena, such as phase transitions, topological states, and quantum magnetism
• Quantum information processing: exploiting polariton-polariton interactions and coherence for implementing quantum gates, entanglement generation, and quantum algorithms
• Nonlinear optics: harnessing the strong nonlinearities of polaritons for efficient frequency conversion, all-optical switching, and signal processing