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arXiv:1312.2932 · The Journal of Chemical Physics

Transient quantum coherent response to a partially coherent radiation field

Zaheen S. Sadeq, Paul Brumer

Published Feb 19, 2014• 18 citations
arXivHTMLPDF

Abstract

The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level V system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in the long time limit, with rates dictated by the adjacent level spacings and the coherence time of the light, and via a mechanism that is distinctly different from traditional decoherence. These two excitation scenarios are also explored for a minimal "toy" model of the electronic levels in pigment protein complex PC645 by both a collisionally broadened CW laser and by a noisy pulse, where unexpectedly long transient coherence times are observed and explained. The significance of environmentally induced decoherence is noted.

DOI
10.1063/1.4864759

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The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level V system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in the long time limit, with rates dictated by the adjacent level spacings and the coherence time of the light, and via a mechanism that is distinctly different from traditional decoherence. These two excitation scenarios are also explored for a minimal "toy" model of the electronic levels in pigment protein complex PC645 by both a collisionally broadened CW laser and by a noisy pulse, where unexpectedly long transient coherence times are observed and explained. The significance of environmentally induced decoherence is noted.
We investigate quantum coherences between excited states induced on quantum systems upon excitation by partially coherent radiation sources. Attempts at rejuvenating coherences using noisy sources are also explored. This work is most relevant to studies of photo-excitation of light harvesting systems under natural conditions as well as to quantum optical experiments using partially coherent lasers. The transient coherent response of a model VVV system upon irradiation by various models of incoherent light is explored and it was found that it was possible to induce transient excited state coherences upon excitation. These excited state coherences eventually become a small fraction of population and the system reaches a mixed state. Lastly, we critique an existing literature model of excitation by noisy laser and we show that the coherence observed in that scenario is artificial. We propose an alternative using a physical model of noisy excitation.
We analyze a model where a closed VVV system is excited by two uncorrelated partially coherent fields. We use a collisionally broadened cw laser, which is a good model for an experimentally realizable partially coherent field, and show that it is possible to generate excited-state coherences even if the two fields are uncorrelated. This transient coherence can be increased if splitting between the excited states is reduced relative to the radiation coherence time ${\ensuremath{\tau}}_{d}$. For small excited-state splitting, one can use this scheme to generate a long-lived coherent response in the system.
We present a theoretical study of noise-induced quantum coherences in a model three-level VVV-type system interacting with incoherent radiation, an important prototype for a wide range of physical systems ranging from trapped ions to biomolecules and quantum dots. By solving the quantum optical equations of motion, we obtain analytic expressions for the noise-induced coherences and show that they exhibit an oscillating behavior in the limit of large excited level spacing $\mathrm{\ensuremath{\Delta}}$ ($\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}\ensuremath{\gg}1$, where $\ensuremath{\gamma}$ is the radiative decay width). Most remarkably, we find that in the opposite limit of small level spacing $\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}\ensuremath{\ll}1$, appropriate for large molecules, (a) the coherences can survive for an extremely long time $\ensuremath{\tau}=(2/\ensuremath{\gamma})(\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}{)}^{\ensuremath{-}2}$ before eventually decaying to zero, and (b) coherences at short times can be substantial. We further show that the long-lived coherences can survive environmental relaxation and decoherence, suggesting implications to the design of quantum heat engines and to incoherent light excitation of biological systems.
The time-dependent spectrum of the light scattered by a collisionally damped two-level atom weakly excited off resonance by a partially coherent laser field is evaluated. Both the collisional and the laser noise are treated as classical Markovian, Gaussian processes while, in addition, the atom is assumed to experience damping and fluctuations that are due to its coupling to an unspecified exterior reservoir. The scattered-field spectra are determined both at steady state and at times following the abrupt turn off of the laser field (the delayed spectrum). The distinct contributions to these spectra arising from the various noise sources as well as the finite bandwidth of the detecting interferometer are investigated in each case. Where appropriate, comparisons are made with related work of Saari [ Light Scattering in Solids ( Plenum, New York, 1979)]. A general inequality is also found that must be satisfied by the longitudinal and the transverse decay rates induced by the exterior reservoir. Finally, the inverse detuning of the laser is found to provide a limit on the time in which the undressing of the atom could be observed to occur following the turn off of the laser.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
Abstract The interplay of coherence and decoherence is played out in a three-level quantum system, in which the third level is incoherently coupled to the second one which itself is in coherent interaction with the first level. The study is based on a stochastic scenario in which the coherent, unitary evolution of the system is randomly interrupted by a Poisson-driven pulse sequence. In the absence of an external pulse, the system undergoes coherent, unitary evolution restricted to the subspace spanned by the first level (level 1) and the second level (level 2). The application of a pulse induces transitions between the second and the third level (level 3), thereby introducing non-unitary effects that perturb the otherwise isolated two-level dynamics. The pulses are assumed to have infinitesimal duration, with strengths modeled as random variables that are uncorrelated across different pulses. A representative model for the stochastically-averaged transition (super)operator mimicking the dynamics induced by the application of pulses allows for an analytical derivation of the matrix elements of the averaged density operator, especially, the element pertaining to the first level. When the system is initially in level 1, we obtain in particular the temporal behavior of the stay-put probability, that is, the probability P 1 ( t ) that the system is still in level 1 at time t. As a function of time, the quantity P 1 ( t ) exhibits a coherence-to-decoherence crossover behavior. At short times t ≪ 1 / λ , where λ is the average frequency at which pulses are applied to the system, coherent dynamics dominate. Consequently, P 1 ( t ) displays pronounced Rabi-like oscillations. At long times t ≫ 1 / λ , decoherence effects prevail, leading to an exponential decay of the form P 1 ( t ) − 1 / 3 ∼ exp ⁡ ( − λ t ) . The results are relevant in the context of well-established Rabi oscillations, applicable to molecular beams and magnetic resonance experiments, as well as in more contemporary frameworks including quantum information processing, quantum resetting protocols, and the theory of quantum trajectories.