Quantum electrodynamics predicts identity of incident and emitted photons in stimulated emission. This fundamental law is important to test experimentally. In this work stimulated emission in GaAs semiconductor amplifier was investigated and positive frequency shift of the amplified beam was detected. In relative units this frequency shift was found equal $Δν/ν= (+1.7 \pm 0.2)\cdot10^{-18}$. This indicates violation of the photon energy conservation in stimulated emission.
Quantum electrodynamics predicts identity of incident and emitted photons in stimulated emission. This fundamental law is important to test experimentally. In this work stimulated emission in GaAs semiconductor amplifier was investigated and positive frequency shift of the amplified beam was detected. In relative units this frequency shift was found equal Δν/ν=(+1.7±0.2)⋅10−18. This indicates violation of the photon energy conservation in stimulated emission.
Stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. Hence, the two outgoing photons are identical. In a waveguide or free space, this intuition is typically found through Fermi's Golden rule, however, this does not properly account for the wave-like nature of the photons. Here, I present an exact solution to stimulated emission from a quantum two-level atom that properly accounts for the incoming and outgoing electromagnetic modes. This result is valid over a huge range of incident photon numbers. For a single incident photon, it shows how the photon must properly mode match the two-level system to cause stimulated emission. For a Fock state drive with large photon number, the exact solution shows how a two-level system Rabi oscillates with the traveling Fock mode as it passes by. I additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two-level system's state factorizes with the electromagnetic field's coherent state. Recent advances in superconducting circuits make them an ideal platform to test these predictions.
The laser linewidth manifests the spectral coherence of a lasing resonator mode. It is of fundamental importance, theoretically as much as practically. For more than half a century we have been told that the laser linewidth is a result of quantum fluctuations due to spontaneous emission, which induce amplitude and phase fluctuations, whereas stimulated emission occurs in phase with the incident field. Unfortunately, in such a scenario each emission process would violate the law of energy conservation. We show that a (spontaneous or stimulated) emission process occurs 90 degrees in lead of the incident field, converts one atomic excitation into one photon in the lasing mode and, therefore, conserves the energy, whereas the mentioned fluctuations are the result of vacuum energy and occur at an orders-of-magnitude faster time scale than an emission process.
In the literature one finds several conflicting accounts of the phase difference of stimulated and spontaneous emission, as well as absorption, with respect to an existing (triggering) electromagnetic field. One of these approaches proposes that stimulated emission and absorption occur in phase and out of phase with their driving field, respectively, whereas spontaneous emission occurs under an arbitrary phase difference with respect to an existing field. It has served as a basis for explaining quantum-mechanically the laser linewidth, its narrowing by a factor of 2 around the laser threshold, as well as its broadening due to amplitude–phase coupling, resulting in Henry’s α-factor. Assuming the validity of Maxwell’s equations, all three processes would, thus, violate the law of energy conservation. In semi-classical approaches, we investigate stimulated emission in a Fabry–Perot resonator, analyze the Lorentz oscillator model, apply the Kramers–Kronig relations to the complex susceptibility, understand the summation of quantized electric fields, and quantitatively interpret emission and absorption in the amplitude–phase diagram. In all cases, we derive that the phase of stimulated emission is 90° in lead of the driving field, and the phase of absorption lags 90° behind the transmitted field. Also spontaneous emission must obey energy conservation, hence it occurs with 90° phase in lead of an existing field. These semi-classical findings agree with recent experimental investigations regarding the interaction of attosecond pulses with an atom, thereby questioning the physical explanation of the laser linewidth and its narrowing or broadening.
Introduction When an electromagnetic wave propagates through amedium stimulated emissions increase the intensity of the wave, while absorptions diminish it. The overall intensity will increase if the number of stimulated emissions can be made larger than the number of absorptions. If we can create such a situation then we have built an amplifier that operates through the mechanism of stimulated emission. This laser amplifier , in common with electronic amplifiers, has useful gain only over a particular frequency bandwidth. Its operating frequency range will be determined by the lineshape of the transition, and we expect the frequency width of its useful operating range to be of the same order as the width of the lineshape. It is very important to consider how this frequencywidth is related to the various mechanisms by which transitions between different energy states of a particle are smeared out over a range of frequencies. This line broadening affects in a fundamental way not only the frequency bandwidth of the amplifier, but also its gain. A laser amplifier can be turned into an oscillator by supplying an appropriate amount of positive feedback. The level of oscillation will stabilize because the amplifier saturates. Laser amplifiers fall into two categories, which saturate in different ways. A homogeneously broadened amplifier consists of a number of amplifying particles that are essentially equivalent, whereas an inhomogeneously broadened amplifier contains amplifying particles with a distribution of amplification characteristics. Homogeneous line broadening All energy states, except the lowest energy state of a particle (the ground state) cover a range of possible energies.
The coherence and directional properties of stimulated and spontaneous emission can be understood without a knowledge of quantum electrodynamics. This paper presents a semiclassical description of the interaction between a free atom and a weak optical field under conditions of either a stimulated emission or a stimulated absorption resonance. It is shown that, under certain conditions, the stimulated or spontaneous radiation fields emitted from a sample of atoms will propagate in the same direction as the incident beam, will be coherent with the incident beam, and will have the correct phase to provide amplification or attenuation.
We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherent-state photon pulse. We provide an analytical result when a short π pulse is incident, which shows that the atoms emit photons coherently into the output pulse, which remains a coherent state in the short pulse limit. An incident pulse is amplified in a phase-preserving manner, where noise is added almost entirely in the phase direction in phase space. This property improves the ratio of the intensity signal to noise after the amplification for sufficiently short pulses. This is a unique feature different from general phase-preserving linear amplifiers, where the signal-to-noise ratio deteriorates in the amplification process. We also discuss the dependence of the photon-emission probability on pulse parameters, such as the pulse area and the duration.