Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0407187

The "Forgotten" Process : the emission stimulated by matter waves

Philippe Tourrenc, Marie-Christine Angonin, Peter Wolf

Published Jul 23, 2004• 1 citation
arXivHTMLPDF

Abstract

In a famous paper where he introduces the A and B coefficients, Einstein considered that atomic decays of excited atoms can be stimulated by light waves. Here we consider that atomic decays can also be stimulated by atomic waves. It is however necessary to change the Maxwell-Boltzmann statistics of thermal equilibrium into Bose-Einstein statistics and to introduce a coefficient C which complements the list of the coefficients introduced by Einstein. Stimulated emission of light can be considered as the first step towards the laser. Similarly, stimulated production of matter waves can be considered as the basic phenomenon for an atom-laser. Most of the results that we obtain here are not new. However, the method that we use remains very close to elementary classical physics and emphasizes the symmetry between electromagnetic and matter waves from various points of view.

DOI
10.48550/arxiv.quant-ph/0407187

Related papers

STIMULATED EMISSION AND DIPOLE OSCILLATORS

Murray, Iii Sargent

The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis­ sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.

CRC Press eBooks•Mar 5, 2018•1 citation

Spontaneous emission

P. van der Straten, Harold J. Metcalf

Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.

Cambridge University Press eBooks•Dec 31, 2015•0 citations

Elements of Light-Matter Interaction

Yehoshua Y. Kalisky

This chapter briefly explains several concepts pertaining to the interaction between light and matter. Basic concepts such as Einstein coefficients, which describe the spontaneous emission and the stimulated absorption, as well as the classical and quantum mechanical description of absorption and emission processes are explained. More-detailed descriptions of various emission and absorption models can be found in several textbooks, such as those by Yariv, Siegman, and Miloni and Eberly.

SPIE eBooks•Jul 31, 2014•0 citations

Radiative Transitions between Discrete Quantum States

Greg J. Tallents

Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.

Cambridge University Press eBooks•Feb 20, 2018•0 citations

ANALISIS LENGKAP TEORI EMISI TERANGSANG EINSTEIN (COMPLETE ANALYSIS OF EINSTEIN'S THEORY ON STIMULATED EMISSION)

Muslim Fakhruddin

ABSTRACT\nUsing Brownian's motion, Maxwell-Boltzmann' s molecular energy distribution, bohr postulates and Einstein's theory on quantum theory of photon radiation due to the interaction between photons and atoms/molecules accuring at thermal equilibrium, the Einstein's theory on stimulated emission by an exited moving atomic ensemble has been investigated. The modified spectral energy density p of the inducing photons appearing in the plank's law of black body radiation with an additional drag coefficient 7L which accommodates recoil effect of atoms/ molecules when the inducing photons hit them has been derived giving the form\nB":\thv\t\tand .[R„ R,1hv° [1\t1 dln(p) \nB\np(v) =\te v \t\nC2\t3 d In( v)\ne\t—B:\nB:\nThe modification steps which have been done based on momentum equilibrium, have improved the Einstein's theory on stimulated emission semiclassically.\n\nKeywords : stimulated, momentum-equilibrium, black body radiation, drag coefficient, photon spectral energy.

Teknosains•Jan 1, 2001•0 citations

Fermi–Dirac and Bose–Einstein distributions and the interaction of light with matter

Robert N. Zitter, Robert C. Hilborn

Einstein’s treatment of stimulated emission, spontaneous emission, and absorption yields the Planck distribution law for photons if the ‘‘atoms’’ with which the photons interact are described by the Boltzmann distribution. We show that the Planck law is also obtained when the photons interact with matter that is described by either Fermi–Dirac or Bose–Einstein distributions.

American Journal of Physics•Jun 1, 1987•5 citations
In a famous paper where he introduces the A and B coefficients, Einstein considered that atomic decays of excited atoms can be stimulated by light waves. Here we consider that atomic decays can also be stimulated by atomic waves. It is however necessary to change the Maxwell-Boltzmann statistics of thermal equilibrium into Bose-Einstein statistics and to introduce a coefficient C which complements the list of the coefficients introduced by Einstein. Stimulated emission of light can be considered as the first step towards the laser. Similarly, stimulated production of matter waves can be considered as the basic phenomenon for an atom-laser. Most of the results that we obtain here are not new. However, the method that we use remains very close to elementary classical physics and emphasizes the symmetry between electromagnetic and matter waves from various points of view.
The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis­ sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
ABSTRACT\nUsing Brownian's motion, Maxwell-Boltzmann' s molecular energy distribution, bohr postulates and Einstein's theory on quantum theory of photon radiation due to the interaction between photons and atoms/molecules accuring at thermal equilibrium, the Einstein's theory on stimulated emission by an exited moving atomic ensemble has been investigated. The modified spectral energy density p of the inducing photons appearing in the plank's law of black body radiation with an additional drag coefficient 7L which accommodates recoil effect of atoms/ molecules when the inducing photons hit them has been derived giving the form\nB":\thv\t\tand .[R„ R,1hv° [1\t1 dln(p) \nB\np(v) =\te v \t\nC2\t3 d In( v)\ne\t—B:\nB:\nThe modification steps which have been done based on momentum equilibrium, have improved the Einstein's theory on stimulated emission semiclassically.\n\nKeywords : stimulated, momentum-equilibrium, black body radiation, drag coefficient, photon spectral energy.