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arXiv:1511.02069 · Physical Review A

Excited-to-excited-state scattering using weak measurements

U. Satya Sainadh, Andal Narayanan

Published Nov 30, 2015• 0 citations
arXivHTMLPDF

Abstract

Weak measurements are a subset of measurement processes in quantum mechanics wherein the system, which is being measured, interacts very weakly with the measuring apparatus. Measurement values of observables undergoing a weak interaction and their amplification are concepts that have sharpened our understanding of interaction processes in quantum mechanics. Recent experiments show that naturally occurring processes such as resonance fluorescence from excited states of an atom can exhibit weak value amplification effect. In this paper we theoretically analyze the process of elastic resonance fluorescence from a $\mathsf{V}$-type three-level atomic system, using the well-known Weiskopff-Wigner (WW) theory of spontaneous emission. Within this theory we show that a weak interaction regime can be identified and for suitable choices of initial and final excited states the mean scattering time between these states show an amplification effect during interaction with the vacuum bath modes of the electromagnetic field. We thus show that a system-bath interaction can show weak value amplification. Using our theory we reproduce the published experimental results carried out in such a system. More importantly, our theory can calculate scattering time scales in elastic resonance scattering between multiple excited states of a single atom or between common excited state configurations of interacting multiatom systems.

DOI
10.1103/physreva.92.052123

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Weak measurements are a subset of measurement processes in quantum mechanics wherein the system, which is being measured, interacts very weakly with the measuring apparatus. Measurement values of observables undergoing a weak interaction and their amplification are concepts that have sharpened our understanding of interaction processes in quantum mechanics. Recent experiments show that naturally occurring processes such as resonance fluorescence from excited states of an atom can exhibit weak value amplification effect. In this paper we theoretically analyze the process of elastic resonance fluorescence from a V\mathsf{V}V-type three-level atomic system, using the well-known Weiskopff-Wigner (WW) theory of spontaneous emission. Within this theory we show that a weak interaction regime can be identified and for suitable choices of initial and final excited states the mean scattering time between these states show an amplification effect during interaction with the vacuum bath modes of the electromagnetic field. We thus show that a system-bath interaction can show weak value amplification. Using our theory we reproduce the published experimental results carried out in such a system. More importantly, our theory can calculate scattering time scales in elastic resonance scattering between multiple excited states of a single atom or between common excited state configurations of interacting multiatom systems.
The concept of weak measurement and associated weak value amplification has sharpened our understanding of the measurement process in quantum mechanics. Recent experiments show that elastic scattering events in resonance fluorescence experiments can exhibit weak value amplification effect, by post-selecting a particular measurement outcome. In this article, we theoretically analyse the physics behind this amplification process. We show that, in general, weak interaction and the associated weak value amplification in resonance fluorescence can be derived from the wellknown theory of spontaneous emission put forth by Wigner and Weiskopff. Using this theory we show that in the elastic scattering regime of resonance fluorescence, weak value amplification helps in segregating rare events. To our knowledge, weak value amplification has not been applied earlier in the time domain as a potential tool to study rare events.
The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.
A measurement of an observable A performed on a quantum system that is initially prepared in a state ρi, followed by a probabilistic procedure that leaves the system in a final state ρf, a process often referred as state postselection (or filtering process), can yield, on average, anomalous measurement results, i.e., values that may exceed the eigenvalue range of the observable being measured or be complex numbers. There is, therefore, an amplification effect of the average measurement result, i.e., the effect of the system on the measurement device is increased. When the coupling between the system and the measurement device satisfies some weakness conditions, the amplification effect occurs due to the weak value of the operator A. In this article, the amplification effect due to the postselection process is reviewed, and theoretical proposals and experiments published in the recent literature on the field are commented on. The emphasis is made on interactions occurring in optical nonlinear media and opto-mechanical and spin-mechanical systems, in which the amplification of number operators takes place.
The notions of weak measurement, weak value, and two-state-vector formalism provide a new quantum-theoretical frame for extracting additional information from a system in the limit of small disturbances to its state. Here, we provide an application to the case of two-body scattering with one body weakly interacting with an environment. The direct connection to real scattering experiments is pointed out by making contact with the field of impulsive incoherent neutron scattering from molecules and condensed systems. In particular, we predict a new quantum effect in neutron-atom collisions, namely an observable momentum transfer deficit; or equivalently, a reduction of effective mass below that of the free scattering atom. Two corroborative experimental findings are shortly presented. Implications for current and further experiments are mentioned. An interpretation of this effect and the associated experimental results within conventional theory is currently unavailable. Quanta 2016; 5: 61–84.
We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.