Recent experiments have found abrupt changes in the intensity of laser light scattered off single ions and atoms. These abrupt changes have been interpreted as resulting from Bohr's ``quantum jumps'' of the ion or atom from one state to another. In Bohr's description, such quantum jumps are not predicted by the Schr\"odinger equation and are introduced by additional postulates into quantum theory. We consider here an alternative explanation of these experiments using only properties of solutions of the Schr\"odinger equation and avoiding Bohr's added postulate.
Recent experiments have found abrupt changes in the intensity of laser light scattered off single ions and atoms. These abrupt changes have been interpreted as resulting from Bohr's ``quantum jumps'' of the ion or atom from one state to another. In Bohr's description, such quantum jumps are not predicted by the Schr"odinger equation and are introduced by additional postulates into quantum theory. We consider here an alternative explanation of these experiments using only properties of solutions of the Schr"odinger equation and avoiding Bohr's added postulate.
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
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.
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 apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies. However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space. In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.
If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved. E. Schrödinger Introduction I have borrowed the title of a characteristic paper by Schrödinger (Schrödinger, 1952). In it he contrasts the smooth evolution of the Schrödinger wavefunction with the erratic behaviour of the picture by which the wavefunction is usually supplemented, or ‘interpreted’, in the minds of most physicists. He objects in particular to the notion of ‘stationary states’, and above all to ‘quantum jumping’ between those states. He regards these concepts as hangovers from the old Bohr quantum theory, of 1913, and entirely unmotivated by anything in the mathematics of the new theory of 1926. He would like to regard the wavefunction itself as the complete picture, and completely determined by the Schrödinger equation, and so evolving smoothly without ‘quantum jumps’. Nor would he have ‘particles’ in the picture. At an early stage, he had tried to replace ‘particles’ by wavepackets (Schrödinger, 1926). But wavepackets diffuse. And the paper of 1952 ends, rather lamely, with the admission that Schrödinger does not see how, for the present, to account for particle tracks in track chambers … nor, more generally, for the definiteness, the particularity, of the world of experience, as compared with the indefiniteness, the waviness, of the wavefunction. It is the problem that he had had (Schrödinger, 1935 a ) with his cat. He thought that she could not be both dead and alive.
We have recorded the laser-excited resonance fluorescence of one to three Ba+ ions and observed Bohr's "quantum jumps" when an ion decayed to the metastable 2D25 state, suddenly quenching its fluorescence. Most of the jumps mark Raman-Stokes scattering from the 2S21 and 2D23 levels.