Theory of the Energy Variance in a Quantum Bit

TL;DR

This paper introduces a new quantum operator for energy variance, linking it to high-frequency oscillations and quantum jumps, providing a novel theoretical framework for understanding energy fluctuations in qubits.

Contribution

It defines the energy variance operator in quantum mechanics and connects it to high-frequency oscillations and quantum jump phenomena, offering new insights into quantum energy fluctuations.

Findings

Energy variance operator corresponds to high-frequency oscillations.

The theory explains the duration of quantum jumps.

Validation through experimental quantum jump data.

Abstract

We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the energy about the mean value of this latter. We show by use of an exact Hamiltonian description that this standard deviation is due to the high-frequeny energy oscillations which are usually discarded in the rotating wave aproximation. We check the present theory by recovering the duration of an abrupt quantum jump that has been described in a recent experiment.