The Einstein A and B coefficients

2021 ◽  
pp. 228-240
Author(s):  
Geoffrey Brooker
Keyword(s):  
Spontaneous Emission ◽  
Line Profile ◽  
Quantum Electrodynamics ◽  
Detailed Balance ◽  
Stimulated Emission ◽  
Spectral Lineshape ◽  
Single Field ◽  
Atomic States ◽  
B Coefficients ◽  
Lineshape Function

The Einstein A and B coefficients for atom–photon reactions are defined: they describe absorption, stimulated emission, and spontaneous emission. We calculate B and consequently find A by the Einstein trick. The procedure is validated by application of detailed balance. Separating out frequencies permits introduction of the spectral lineshape function (normalized line profile). A reformulation describes transitions involving single atomic states and single field modes. This points to a link with quantum electrodynamics.

Spontaneous emission of radiation

2021 ◽  
pp. 417-454
Author(s):  
Geoffrey Brooker
Keyword(s):  
Spontaneous Emission ◽  
Line Profile ◽  
High Frequency ◽  
Quantum Electrodynamics ◽  
Golden Rule ◽  
Dipole Emission ◽  
Radiation Induced ◽  
Rule Number ◽  
Spectral Line Profile ◽  
Elliptically Polarized

“Spontaneous emission of radiation” calculates the rate of spontaneous electric-dipole emission of a photon by an excited atom or molecule. The calculation proceeds by using basic quantum mechanics (i.e. not using the short cuts of Chapter 19); it uses quantum electrodynamics but is not, on that account, particularly difficult. A 2p–1s transition in hydrogen is used as exemplar; the radiation is elliptically polarized. The spectral line profile (lineshape function) is approximately Lorentzian, but has a high-frequency cut-off, needed to prevent the power radiated from diverging. A radiation-induced frequency shift is negligible. The width of the line profile agrees with the Einstein A-coefficient. A high-frequency cut-off is shown to apply similarly in the derivation of Golden Rule Number Two.

scholarly journals Amplified Spontaneous Emission and Optical Gain in Organic Single Crystal Quinquethiophene

Crystals ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 609 ◽  
Author(s):  
Muhammad Zeb ◽  
Muhammad Tahir ◽  
Fida Muhammad ◽  
Suhana Mohd Said ◽  
Mohd Faizul Mohd Sabri ◽  
...  
Keyword(s):  
Single Crystal ◽  
Spontaneous Emission ◽  
Threshold Energy ◽  
Pump Energy ◽  
Optical Gain ◽  
Amplified Spontaneous Emission ◽  
Stimulated Emission ◽  
Excitation Wavelength ◽  
Optical Amplification ◽  
Organic Single Crystal

In this paper, we report optical characteristics of an organic single crystal oligomer 5,5⁗-diphenyl-2,2′:5′,2″:5″,2‴:5‴,2⁗-quinquethiophene (P5T). P5T crystal is a thiophene/phenylene co-oligomer that possesses better charge mobility as well as photoluminescence quantum efficiency (PLQE) as compared to other organic materials. Stimulated emission in P5T is investigated via amplified spontaneous emission (ASE) measurements within broad pump energies ranging from 35.26 to 163.34 µJ/cm2. An Nd-YAG femtosecond-tunable pulsed laser is used as a pump energy source for the ASE measurements of P5T crystals at an excitation wavelength of 445 nm. The ASE spectra exhibit optical amplification in P5T crystals at a 625 nm peak wavelength with a lower threshold energy density (Eth) ≈ 52.64 μJ/cm2. P5T also demonstrates higher optical gain with a value of 72 cm−1, that is calculated by using the variable stripe-length method. The value of PLQE is measured to be 68.24% for P5T. This study proposes potential applications of P5T single crystals in organic solid state lasers, photodetectors, and optical amplifiers.

SCHEME FOR CONCENTRATION OF UNKNOWN ENTANGLED ATOMIC STATES

2008 ◽  
Vol 22 (16) ◽  
pp. 1567-1571 ◽  
Author(s):  
YAN-LIN LIAO ◽  
YAN ZHAO
Keyword(s):  
Quantum Electrodynamics ◽  
Thermal Field ◽  
Cavity Quantum Electrodynamics ◽  
Driving Field ◽  
Cavity Decay ◽  
Atomic States

We proposed a physical scheme to concentrate unknown non-maximally entangled atomic states via cavity quantum electrodynamics (QED) techniques. In this scheme, the unique advantage is that the effects of the cavity decay and thermal field have been eliminated by using a classical driving field. The discussion indicates that it can be realized by current technologies.

scholarly journals Ultrafast stimulated emission microscopy of single nanocrystals

Science ◽  
2019 ◽  
Vol 366 (6470) ◽  
pp. 1240-1243 ◽  
Author(s):  
Lukasz Piatkowski ◽  
Nicolò Accanto ◽  
Gaëtan Calbris ◽  
Sotirios Christodoulou ◽  
Iwan Moreels ◽  
...  
Keyword(s):  
Excited State ◽  
Spontaneous Emission ◽  
Single Molecule ◽  
Room Temperature ◽  
Direct Detection ◽  
Excited State Absorption ◽  
Stimulated Emission ◽  
Detection Capability ◽  
Emission Signal ◽  
Carrier Population

Single-molecule detection is a powerful method used to distinguish different species and follow time trajectories within the ensemble average. However, such detection capability requires efficient emitters and is prone to photobleaching, and the slow, nanosecond spontaneous emission process only reports on the lowest excited state. We demonstrate direct detection of stimulated emission from individual colloidal nanocrystals at room temperature while simultaneously recording the depleted spontaneous emission, enabling us to trace the carrier population through the entire photocycle. By capturing the femtosecond evolution of the stimulated emission signal, together with the nanosecond fluorescence, we can disentangle the ultrafast charge trajectories in the excited state and determine the populations that experience stimulated emission, spontaneous emission, and excited-state absorption processes.

An Introduction to Quantum Optics and Quantum Fluctuations

2019 ◽  
Author(s):  
Peter W. Milonni
Keyword(s):  
Quantum Optics ◽  
Spontaneous Emission ◽  
Quantum Electrodynamics ◽  
Planck Equation ◽  
Quantum Fluctuations ◽  
Van Der Waals Interactions ◽  
Vacuum Field ◽  
Langevin Equations ◽  
Uncertainty Relations ◽  
Point Energy

This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.

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