Quantum jumps, superpositions, and the continuous evolution of quantum states

Abstract

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.

Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

“…Temporarily neglecting again any diagonal elements of H 1 (which do not cause transitions) and ⟨1|H 1 |3⟩ because its detuning is large, the differential equations, eq 5, for three states excited by a monochromatic field at the two-photon resonance frequency (meaning 2ω = ω 21 + ω 32 , see Figure 5) are where we have used the RWA and the following notation: H (1) 12 = ℏV 1 e i(ωt+γ) , H (1) 23 = ℏV 2 e i(ωt+γ) , H (1) 21 = H (1) 12 *, H (1) 32 = H (1) 23 *, and δ = ω − ω 21 = ω 32 − ω. These equations yield the following solutions if a 1 (0) = 1…”

“…We will concentrate on the solution and clarification of the dynamics described by eq and await experiments to confirm or refute the results. Electron shelving experiments, − for example, involve single atoms and cannot easily be described using optical Bloch equations and density matrices of ensembles.…”

“… 3 observed absorption and emission in an artificial “atom” engineered using superconducting qubits and documented dynamics that appeared to be more deterministic. According to Dick, 1 resolution of the controversy in favor of jumps requires quantization of the field and appropriate asymptotic scattering states. However, both these experiments and their theoretical interpretation require spontaneous and well as stimulated emission.…”

“…Whether transitions between atomic-level quantum states occur as rapid, random “quantum jumps” or as continuously evolving dynamics has been intensely disputed. A review by Dick summarizes recent arguments. Experimental evidence of jumps using shelved-electron detection has accumulated since the 1980s .…”

Quantum jump simulation in three-level systems using photonic Gaussian modes

“…Another important source of noise is the fundamental process called quantum jump, where a quantum system evolves stochastically in an abrupt unpredictable operation. Quantum jump is an essential topic in the interpretation of quantum dynamics [22] and has been part of the historical debates about the quantum mechanics fundamentals [23]. This stochastic process, first proposed by Niels Bohr [24], has been observed in a single ion [25], molecule [26], electron in a trap [27], photon in a cavity [28], and in artificial atoms [29].…”