Quantum Shot Noise Fluctuations in the flow of electrons can Signal the transition from particlelike to wavelike behavior and signify the nature of Charge transport in mesoscopic Systems.
'l*he noise is the was a saying of Rolf Landauer, l one of the founding fathers of mesoscopic physics. What he meant was that fluctuations in time of a measurement can be a source of Information that is not present in the time-averaged value. As figure l reminds us, some types of noise are more interesting than others. A physicist with access to sensitive ways of distinguishing the granularity in a signal may delight in the noise. Noise plays a uniquely informative role in the particle-wave duality. In 1909, Albert Einstein realized that electromagnetic fluctuations vary depending on whether the energy is carried by waves or by particles. The magnitude of energy fluctuations scales linearly with the mean energy for classical waves, but it scales with the square root of the mean energy for classical particles. Since a photon is neither a classical wave nor a classical particle, the linear and square-root contributions coexist. Typically, the square-root (particle) contribution dominates at optical frequencies and the linear (wave) contribution takes over at radio frequencies. If Isaac Newton could have measured noise as the time-dependent fluctuations from the mean intensity, he would have been able to settle his dispute with Christiaan Huygens on the corpuscular nature of light—without actually needing to observe an individual photon. Such is the power of noise. The diagnostic power of photon noise was further developed in the 1960s, when it was discovered that one can teil the difference between radiation from a laser and that from a black body on the basis of their fluctuating Signals: The wave contribution to the fluctuations is entirely absent for a laser; it is merely small for a black body. Noise measurements are now a routine technique in quantum optics, and Roy Glauber's quantum mechanical theory of photon statistics is textbook material. Because electrons share the particle—wave duality with photons, one might expect fluctuations in the electrical current to play a similar diagnostic role. Current fluctuations due to the discreteness of the electrical charge are known as shot noise. Although the first observations of shot noise date from work on vacuum tubes in the 1920s,
'l*he noise is the was a saying of Rolf Landauer, l one of the founding fathers of mesoscopic physics. What he meant was that fluctuations in time of a measurement can be a source of Information that is not present in the time-averaged value. As figure l reminds us, some types of noise are more interesting than others. A physicist with access to sensitive ways of distinguishing the granularity in a signal may delight in the noise. Noise plays a uniquely informative role in the particle-wave duality. In 1909, Albert Einstein realized that electromagnetic fluctuations vary depending on whether the energy is carried by waves or by particles. The magnitude of energy fluctuations scales linearly with the mean energy for classical waves, but it scales with the square root of the mean energy for classical particles. Since a photon is neither a classical wave nor a classical particle, the linear and square-root contributions coexist. Typically, the square-root (particle) contribution dominates at optical frequencies and the linear (wave) contribution takes over at radio frequencies. If Isaac Newton could have measured noise as the time-dependent fluctuations from the mean intensity, he would have been able to settle his dispute with Christiaan Huygens on the corpuscular nature of light—without actually needing to observe an individual photon. Such is the power of noise. The diagnostic power of photon noise was further developed in the 1960s, when it was discovered that one can teil the difference between radiation from a laser and that from a black body on the basis of their fluctuating Signals: The wave contribution to the fluctuations is entirely absent for a laser; it is merely small for a black body. Noise measurements are now a routine technique in quantum optics, and Roy Glauber's quantum mechanical theory of photon statistics is textbook material. Because electrons share the particle—wave duality with photons, one might expect fluctuations in the electrical current to play a similar diagnostic role. Current fluctuations due to the discreteness of the electrical charge are known as shot noise. Although the first observations of shot noise date from work on vacuum tubes in the 1920s,
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.
The experimental current measured in mesoscopic systems fluctuates around average values as a consequence of the wave‐particle nature of electrons. An alternative quantum noise approach, based on Bohm trajectories, is presented. This formalism directly deals with the wave and particle nature of electrons and provides an intuitive framework to study quantum noise. The approach allows the direct consideration of coulomb correlation among electrons. In fact, most of the numerical techniques used in classical Monte Carlo simulations of electron devices can be directly adapted to our approach. Simulated noise results for interacting electrons tunnelling through double barriers are presented in agreement with experimental results. The present approach opens a new path for studying electron transport and quantum noise in mesoscopic systems.
When light from a laser is fully absorbed by an ideal detector, the detected current exhibits a fluctuation called here ``photonic noise.'' The spectral density of Iintensity noiseR, defined as the difference of the photonic-noise spectral density and a term corresponding to the shot-noise level, is negative for sub-Poissonian statistics. The usefulness of the relative-intensity-noise concept is that it is independent of any linear attenuation. A simple circuit theory of intensity noise based only on energy conservation and the Nyquist formula (zero-point fluctuation) leads to expressions of the spectral densities that agree with quantum theory even for sub-Poissonian photon statistics. When the optical gain and loss are frequency independent, the circuit theory reduces to a corpuscular theory that keeps track of the time rates of change of electron and photon numbers treated as continuous variables. Consideration is given to laser diodes in which the rate of electron-photon conversion depends nonlinearly on both the carrier and photon densities. The cross-spectral density between electrical-voltage and relative photonic fluctuations is independent of internal or external optical losses. Standard rate equations are inaccurate in the case of gain compression. Very general yet simple formulas for intensity noise are applied to room-temperature GaAs laser diodes, using recently calculated optical parameters.
In classical optics light is considered as an electromagnetic wave, and its dynamical properties are described by the time dependence of amplitude and phase. If a light emerging from a source has random fluctuation of amplitude and phase, this light can be described by a proper ensemble from which the mean and the dispersion of the dynamical variables are calculated. On the other hand, the same light beam can be also considered as a stream of photons in quantum optics, and the wave-particle duality produces nonclassical results in some cases. It is our purpose to clarify the role of wave and particle nature of light and distinguish the classical and quantum effects via the characterization of the dynamical variables when the light goes through a beamsplitter.
Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.