This paper asks an experimental question about photon absorption and emission in a two-state electronic system where the incident frequency of exciting light is below the mean frequency of the emission line but still within the line width. Since it is well known that the absorption spectrum and the emission spectrum are identical [1]-[3], then quantum mechanics as well as astronomical observations say that excitations will still occur. Once a quantum state excites, then it is expected to decay back with a typical time constant and the usual emission spectrum. The problem is that the mean frequency of that emission spectrum will then be higher than the frequency of the exciting photon, suggesting that more energy is emitted than being received on average. A search of quantum mechanical references finds no discussion of this issue, so this paper considers the options available to resolve this inconsistency, including an experiment.
This paper asks an experimental question about photon absorption and emission in a two-state electronic system where the incident frequency of exciting light is below the mean frequency of the emission line but still within the line width. Since it is well known that the absorption spectrum and the emission spectrum are identical [1]-[3], then quantum mechanics as well as astronomical observations say that excitations will still occur. Once a quantum state excites, then it is expected to decay back with a typical time constant and the usual emission spectrum. The problem is that the mean frequency of that emission spectrum will then be higher than the frequency of the exciting photon, suggesting that more energy is emitted than being received on average. A search of quantum mechanical references finds no discussion of this issue, so this paper considers the options available to resolve this inconsistency, including an experiment.
A complete solution of the time-dependent Schrodinger equation for the overall absorption-emission process is presented for a particular model system possessing an excited state manifold of (nearly) uniformly spaced molecular eigenstates with a lorentzian distribution of transition moment. Results for both narrow and broad band excitation are derived, and it is shown that the fluorescence quantum yield is essentially the same for both broad band and narrow band excitations. It is argued that the lifetime of the incident photon state is important in determining the presence or absence of structure in the absorption spectrum and, consequently, that the absorption spectrum observed depends upon both the optical density of the sample and the intensity of the incident light.
Light emission occurs as a result of interaction between light and matter. Let us assume a two-level atom with levels 1 (ground state) and 2 (excited state). The energies of the ground and excited states are E 1 and E 2 , respectively, and the energy difference is therefore given by the difference ΔE 12 =E 2 −E 1 . When light with photons of energy equal to this difference is absorbed by the atomic or molecular system, an electron will be excited from level 1 to level 2. The energy of the photons is given by ΔE 12 =E 12 =hν 12 (h is Planck's constant and 1→2 is the frequency of light resulting from the level 1→2 transition). This energy is absorbed by an atom or a molecule that has energy levels, separated by ΔE, where these energy levels are the ground and the excited states. This kind of “quantum jump” of an electron between two states occurs in atomic systems between electronic levels; it can be extended to molecular systems, where vibrational and translational energy levels participate in the quantum jump. The interaction between light and matter involves the transition of electrons between different states. This interaction results in the absorption of photons (stimulated absorption) as well as spontaneous and stimulated emission. These processes can be described using Einstein's A and B coefficients, as will be described in the next paragraphs.
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.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
Backward, turn backward, O time in your flight. Make me a child again, just for tonight. –Elizabeth Akers Allen Since the time of Kirchhoff it has been known that, when light is passed through an atomic gas, those wavelengths are observed that would be emitted if the gas were incandescent. If the gas is sufficiently cold, then the wavelengths observed are limited to ground-state transitions. As the temperature of the sample is elevated, wavelengths corresponding to transitions between excited states become absorbing, and balances between emission and absorption occur. The study of the central wavelengths of emission lines or absorption notches is known as first-order spectroscopy, and it provides information on the energy-level structure of the atom. The study of the shape of these lines in frequency space is known as second-order spectroscopy, and provides information on the lifetime of the level and the collision rates and temperature of the gas. Thus, whereas first-order spectroscopy shows that emission and absorption measurements yield the same central wavelengths, second-order spectroscopy shows that the natural linewidth for emission and absorption are both specified by the level lifetime, and that the intensity of emission and absorption features both involve the linestrength factor (through the emission transition probability rate and the absorption oscillator strength). The connection between the lifetime and the linewidth can be made plausible by a simple semiclassical model. When an electron is excited to a specific orbit in an atom, its binding energy is established through the exchange of virtual photons with the effective central core. If the perturbations that eventually cause the electron to make a transition from that orbit are weak, the meanlife will be long.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.