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Cambridge University Press eBooks

Macroscopic quantum jumps

Partha Ghose

Published Apr 29, 1999• 0 citations

Abstract

Introduction The quantum theory of atoms and molecules had its origin in the famous 1913 paper of Bohr [186] in which he suggested that the interaction of radiation and atoms occurred with the transition of an atom from one stationary internal state to another, accompanied by the emission or absorption of radiation of a frequency determined by the energy difference between these states. These transitions came to be known as ‘quantum jumps’. Since all experiments until the late 1970s used to be carried out with large ensembles of atoms and molecules, these jumps were masked and could not be directly observed; they were only inferred from spectroscopic data. In fact, with the advent of quantum mechanics they eventually came to be regarded as artefacts of Bohr's simple-minded semi-classical model. But with the availability of coherent light sources and single ions prepared in ion traps [187], [188], and optically cooled [189], [190], the issue has been reopened with the experimental demonstration of quantum jumps in single ions [191], [192], [193]. These experiments have also opened up the contentious issue of wave function collapse or reduction on measurement, as they can be regarded as making collapse visible on the oscilloscope screen [191]. Evidence of the discrete nature of quantum transitions in a single quantum system had been accumulating from the observation of photon anti-bunching in single-atom resonance fluorescence [194], the tunneling of single electrons in metal–oxide-–semiconductor junctions [195] and spin-flips of individual electrons in a Penning trap [196].

DOI: 10.1017/cbo9780511585784.009

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Introduction The quantum theory of atoms and molecules had its origin in the famous 1913 paper of Bohr [186] in which he suggested that the interaction of radiation and atoms occurred with the transition of an atom from one stationary internal state to another, accompanied by the emission or absorption of radiation of a frequency determined by the energy difference between these states. These transitions came to be known as ‘quantum jumps’. Since all experiments until the late 1970s used to be carried out with large ensembles of atoms and molecules, these jumps were masked and could not be directly observed; they were only inferred from spectroscopic data. In fact, with the advent of quantum mechanics they eventually came to be regarded as artefacts of Bohr's simple-minded semi-classical model. But with the availability of coherent light sources and single ions prepared in ion traps [187], [188], and optically cooled [189], [190], the issue has been reopened with the experimental demonstration of quantum jumps in single ions [191], [192], [193]. These experiments have also opened up the contentious issue of wave function collapse or reduction on measurement, as they can be regarded as making collapse visible on the oscilloscope screen [191]. Evidence of the discrete nature of quantum transitions in a single quantum system had been accumulating from the observation of photon anti-bunching in single-atom resonance fluorescence [194], the tunneling of single electrons in metal–oxide-–semiconductor junctions [195] and spin-flips of individual electrons in a Penning trap [196].

The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]

In 1913, when Bohr’s atom allowed electron jumps between discrete orbits, it was impossible to experiment on single atoms and study individually these jumps. Many people considered them not real, but something artificial for the explanation of the linear spectra of atoms. Especially Schrödinger rejected the image of negatively charged electrons orbiting around the nucleus and in particular their jumps from orbit to orbit. Finally, in 1986 single atoms (ions) laser cooled and confined in an electromagnetic trap gave the possibility to investigate experimentally electron jumps to and fro a metastable state. Recently, physicists experimenting on a macroscopic superconducting circuit with discrete quantum states analogous to a natural atom were able to halt and reverse quantum jumps mid-flight revealing very interesting details of them.

Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.

We have used stored ion methods to improve resolution and sensitivity in optical spectroscopy. Single atomic ions have been confined by electric and magnetic fields, cooled by laser radiation pressure to temperatures on the order of 1 mK, and probed spectroscopically with narrowband lasers. The absorption resonance of a single Hg + ion has been observed by a decrease in the transmitted light intensity. An ultraviolet transition in Hg + has been observed with a linewidth of only 30 kHz. Quantum jumps to and from metastable levels of Hg + have been observed and used to determine radiative decay rates and to infer the existence of photon antibunching. Quantum jumps have also been observed in single Mg + ions.

A number of experiments on trapped single ions or atoms have been performed in recent years [1,2,3,4]. Monitoring the intensity of scattered laser light off of such systems has shown abrupt changes that have been cited as evidence of between states of the scattered ion or atom . The existence of such jumps was required by Bohr in his theory of the atom. Bohr’s quantum jumps between atomic states [5] were the first form of quantum dynamics to be postulated. He assumed that an atom remained in an atomic eigenstate until it made an instantaneous jump to another state with the emission or absorption of a photon. Since these jumps do not appear to occur in solutions of the Schrodinger equation, something similar to Bohr's idea has been added as an extra postulate in modern quantum mechanics. Stochastic quantum jump equations [6], [7],[8]were introduced as a tool for simulating the dynamics of a dissipative system with a large Hilbert space and their links with quantum measurement the or were also noted [9],[10],[11],[12],[13].This measurement interpretation is generally known as quantum trajectory theory [14].By adding filter cavities as part of the apparatus, even the quantum jumps in the dressed state model can be interpreted as approximations to measurement-induced jumps [15]. The question arises whether an explanation of these jumps can be found to result from an Colombeau solution [16]-[18](Ψe(x, t;ħ))e of the Schrodinger equation alone without additional postulates. We found exact quasi-classical asymptotic of the quantum averages