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arXiv:1910.13878

Considerations regarding one-photon phase control

Cyrille Lavigne, Paul W. Brumer

Published Oct 30, 2019• 2 citations
arXivHTMLPDF

Abstract

The dynamics of a system interacting with an ultrashort pulse is known to depend on the phase content of said pulse. For linear absorption, phase control is possible over time-varying quantities, such as the population of metastable states, but not over time-independent quantities, such as the population of steady states. We derive here a strict upper bound for phase control that interpolates between these two cases --- the bound quantifies the approach to the steady state and resulting loss of one-photon phase control based on physical timescales. Significantly, this bound is violated by a number of numerical and experimental investigations. A careful analysis of the physical conditions underlying this result exposes multiphoton effects as a mechanism for these experiments.

DOI
10.48550/arxiv.1910.13878

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The dynamics of a system interacting with an ultrashort pulse is known to depend on the phase content of said pulse. For linear absorption, phase control is possible over time-varying quantities, such as the population of metastable states, but not over time-independent quantities, such as the population of steady states. We derive here a strict upper bound for phase control that interpolates between these two cases --- the bound quantifies the approach to the steady state and resulting loss of one-photon phase control based on physical timescales. Significantly, this bound is violated by a number of numerical and experimental investigations. A careful analysis of the physical conditions underlying this result exposes multiphoton effects as a mechanism for these experiments.
Single-photon pulses cannot be generated on demand, due to incompatible requirements of positive frequencies and positive times. Resulting states therefore contain small probabilities for multiphotons. We derive upper and lower bounds for the maximum fidelity of realizable states that approximate single-photon pulses. The bounds have implications for ultrafast optics; the maximum fidelity is low for pulses with few cycles or close to the onset, but increases rapidly as the pulse envelope varies more slowly. We also demonstrate strictly localized states that are close to single photons.
Exact single photons cannot be generated on demand due to their infinite tails. To quantify how close realizable optical states can be to some target single photon in one dimension, we argue that there are two natural but incompatible ways to specify the target state. Either it can be expressed as a photon with a chosen positive-frequency spectrum, or it can be described as an (unphysical) photon in a chosen positive-time pulse. The results show that for sufficiently short target pulses, the closest realizable states contain substantial multiphoton components. Upper and lower bounds for the maximum fidelity are derived and are expressed as functions of the size of the target state's tail, for negative time or negative frequency, respectively. We also generalize the bounds to arbitrary photon-number states.
Coherent control schemes are interference-based procedures for the control of quantum mechanical systems informed by a careful analysis of the physical conditions on interference. In this thesis, the coherent control approach is applied to experimental phase control in the condensed phase. Specifically, coherent control schemes are proposed as mechanisms for experimental manifestations of phase interference. First, a simulation of a ``black box'' feedback control experiment using realistic pulse shaping is shown to automatically find a specific, previously devised coherent control scheme. Qualitative features of experiments performed in this way are reproduced. Second, an analysis of interference in one-photon phase control yields an upper bound on the duration of phase effects. One-photon phase control was previously shown to be possible only over the transient (as opposed to steady-state) value of observables. The bound described here quantifies this statement and provide a rigorous definition of ``transient'' control. We propose that phase control beyond this bound, as reported in a number of weak-field experimental and computational studies, is the result of previously unaccounted for multiphoton effects. Third, we analyze a recent experiment showing phase control of the macroscopic current emanating from living brain cells photostimulated by two-photon absorption. We propose mechanisms for the phase dependence of the current that operate over fifteen orders of magnitude in time, from the femtosecond dynamics of light-matter interactions to the macroscopic dynamics of neuron current. Significantly, coherent control is extended to the case of systems repeatedly interacting with pulses of light; we show that macroscopic control is obtained, in this case, from the multi-pulse accumulation of small phase effects. Research into multiphoton control led to the development of a novel algorithm to compute higher order perturbation theory integrals, presented in the final chapter of this thesis. The Fourier-Laplace Inversion of the Perturbation Theory (FLIPT) method is a highly efficient, numerically exact, ``black box'' integration algorithm. The FLIPT method exploits the specific structure of the multidimensional perturbation theory integrals to obtain an exponential improvement in performance over standard quadrature.
Mechanisms and optimal experimental conditions in coherent control still intensely stimulate debates. In this work, a phase-only control mechanism in an open quantum system is investigated experimentally and numerically. Several parameterizations for femtosecond pulse shaping (combination of chirp and multipulses) are exploited in transient absorption of a prototype organic molecule to control population and vibrational coherence in ground and excited states. Experimental results are further numerically simulated and corroborated with a four-level density-matrix model, which reveals a phase-only control mechanism based on the interaction between the tailored phase of the excitation pulse and the induced transient absorption. In spite of performing experiment and numerical simulations in the linear regime of excitation, the control effect amplitude depends non-linearly on the excitation energy and is explained as a pump-dump control mechanism. No evidence of single-photon control is observed with the model. Moreover, our results also show that the control effect on the population and vibrational coherence is highly dependent on the spectral detuning of the excitation spectrum. Contrary to the popular belief in coherent control experiments, spectrally resonant tailored excitation will lead to the control of the excited state only for very specific conditions.
We consider the coherent population trapping effect with a train of ultrashort pulses in a $\ensuremath{\Lambda}$-type system with two bound states and a continuum replacing the upper state. Population transfer to the continuum can be totally suppressed provided that the splitting between the bound states is a multiple of the pulse repetition rate. Compared to the traditional case with only two laser fields coupling the bound states to the continuum, CPT with a pulse train allows one to avoid incoherent population losses due to interaction of the fields with ``wrong'' transitions, which results in only partial suppression of ionization. A method of suppression of excited-state absorption of pumping radiation in laser crystals, with pumping in the form of the pulse train, is proposed. As a particular example pumping dynamics of a Ti3+:YAlO3{\mathrm{Ti}}^{3+}:{\mathrm{YAlO}}_{3}Ti3+:YAlO3​ crystal using this technique is numerically analyzed.