Quantum Mechanical Limit Research Articles

Quantized Hall effect yields e2/h to a part per million

Several recent experiments investigating the Hall effect in its quantummechanical limit have made it clear that Nature is providing us with a fundamental unit of resistance. The extraordinary accuracy with which these experiments appear to be obeying the naive theoretical expression for the quantized Hall resistance is at once promising and puzzling.

Design of a resonant gravitational-wave detector with quantum-limited sensitivity

It is shown that aresonant transducer is indispensable in a wide range of experimental conditions in order to accomplish optimum matching between a cryogenic antenna and a low-noise amplifier. Noise characteristics of a d.c. SQUID are analyzed and an improved design of a point contact d.c. SQUID is described. Conditions for transducer matching and detectability of a gravitational-wave signal are derived for a system employing a d.c. SQUID. It appears that a d.c. SQUID operating at the quantum-limited sensitivity could be realized in our proposed design and matched to a massive aluminum antenna cooled to 0.05 K by using a resonant superconducting inductive transducer. Presently achievable detector parameters are shown to be sufficient to allow a detection sensitivity corresponding to a resolution of a few photons in the antenna, the ultimate quantum-mechanical limit derived for an antenna instrumented with a linear-motion detector.

Ultimate sensitivity limit of a resonant gravitational wave antenna using a linear motion detector

The sensitivity of a resonant-mass gravitational radiation antenna coupled to a motion detector with given noise properties is calculated in detail. It is shown that the quantum-mechanical limit of linear amplifier performance implies an important restriction on the sensitivity for any system using a linear motion detector. For a signal frequency ${\ensuremath{\omega}}_{a}$, this fundamental limit requires that the gravitational radiation pulse be capable of driving the antenna from rest to an energy level exceeding $2\ensuremath{\hbar}{\ensuremath{\omega}}_{a}$.

Electron interactions and quantum plasma physics

The ‘quantum electrodynamics’ of the scattering of radiation from a fully ionized, interacting plasma is to be considered.The plasma particle interaction must properly be treated quantum mechanically when the electron plasma wave phonon energies are comparable to or greater than the mean random electron energies and/or when the phonon momenta are of the order of magnitude or greater than the average electron momenta in the plasma.In these two circumstances or either one of them, the plasma particle inter action must be treated in a quantum mechanical manner. The ‘solid-state’ plasma recently discussed by D.E.McCumber is an example of a quantum plasma.Whether a classical or a quantum plasma is considered, the collective properties, as well as the single-particle properties, need to be considered. The collective properties of the plasma become important when it interacts with a radiation field in the case where the electron plasma frequency, ωp, is of the same order of magnitude, or exceeds, the operating radiation frequency ω, i.e. ωp≥ω.A criterion to distinguish the properties of a plasma as to whether it is classical or quantum mechanical in nature can be defined in terms of three fundamental lengths of the electron gas. These definitions hold for a one-component plasma. They are: the classical length βe2, the Debye screening length and the thermal de Broglie wavelength defined as 1/kT. From these three quantities, we can define two dimensionless parameters. They are the classical parameter and the quantum parameter δ=λ/λD which is a measure of the quantum effects. For a quantum plasma δ>1 and in the classical limit (h = 0),δ=0, Λ<1.When we take into account the collective behaviour characterized by the plasma oscillations, screening effects are an automatic aspect of the electron plasma gas.It is hoped that the present review article will provide the background material for general understanding of the field and easy access to the current literature. It is also hoped that the present discussion will establish greater interest in this subject.As an example of a calculation of plasma properties, a calculation of the generalized dielectric constant for both a low-density plasma in the classical limit and a high-density plasma in the quantum mechanical limit is performed and compared in a suitable manner.