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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Measuring a single quantum trajectory

Dirk Bouwmeester, Gerard Nienhuis

Published Feb 1, 1996• 6 citations
Publisher

Abstract

We propose an experiment on single two-level atoms (or ions) which would demonstrate the physical significance of quantum trajectory descriptions for spontaneous decay. We predict that the experiment will reveal the reality of neoclassical decay of the atomic inversion before the emission of a photon.
DOI
10.1088/1355-5111/8/1/020

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We apply two quantum-trajectory methods to a decaying system of NNN two-level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the tanh\mathrm{tanh}tanh-like decay of the inversion for large NNN. This tanh\mathrm{tanh}tanh behavior is also found for the jump-free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emission. However, we find that this behavior of superfluorescence is governed by the jump statistics. The jump-free evolution of the Dicke system displays other atypical behavior. We find that the energy of the system can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffusion method to the system, we find that the trajectories keep the system in a spin coherent state, which confirms the picture of superfluorescence for single trajectories as a toppling needle point. This enables us to write an approximate analytic expression for the decay of the energy for any NNN. Finally, we discuss the calculation of two-time correlation functions per trajectory and as an illustration we calculate the single-trajectory spectra. In the quantum-jump method, these single-trajectory spectra do not correspond to intuition, which we ascribe to the incompatibility of photon counting and spectral measurement.
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Abstract We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach to this type of problem by considering a Kolmogorov equation for the probability distribution of the atomic state, which takes into account first the deterministic evolution of this state under the effect of the incoming laser beam and second the random emission of photons during the spontaneous decay of the excited state(s) to the ground state. This approach yields solvable equations in the two level atom case. For the three level atom case we set the problem and clearly define its frame. The results obtained are valid in both opposite limits of rare and frequent spontaneous decay, compared to the period of the optical Rabi oscillations due to the interaction between resonant excitation and atomic levels. Our analysis gives access to various statistical properties of the fluorescence light, including one showing that its fluctuations in time are not invariants under time reversal. This result makes evident the fundamentally irreversible character of quantum measurements, represented here by the emission of photons of fluorescence.