Real-time observation of vibrational revival in the fastest molecular system

Rudenko, Artem; Ergler, Th.; Feuerstein, B.; Zrost, K.; Schröter, C. D.; Moshammer, R.; Ullrich, J.

doi:10.1016/j.chemphys.2006.06.038

Cited by 56 publications

(27 citation statements)

References 55 publications

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“…This experiment is typical of the class of stroboscopic pumpprobe approaches that are widely used to investigate the temporal evolution of ultrafast processes 17 . Because such phenomena can be heavily obscured by timing uncertainty, the dataset used here represents a critical test of our data-analytic approach.…”

Section: Letter Researchmentioning

confidence: 99%

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Dynamics from noisy data with extreme timing uncertainty

Fung

Hanna

Vendrell

et al. 2016

Nature

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Imperfect knowledge of the times at which 'snapshots' of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron lasers, for example, the uncertainty-the so-called timing jitterbetween the arrival of an optical trigger ('pump') pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude 1 , marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty [2][3][4] . These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis [5][6][7] , that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty 1 . Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty.The fundamental premise of our approach is simple. A series of snapshots concatenated in the order of their inaccurate time stamps will contain some time-evolutionary information ('a weak arrow of time'), provided that the concatenation window spans a period comparable with, or longer than, the timing uncertainty associated with each individual snapshot. This realization leads one to consider a series of c-fold concatenated snapshots, formed by moving a c-frame-wide window over the raw dataset ordered according to the inaccurate time stamps. The dynamical history can then be extracted from the series of concatenated snapshots using techniques developed to extract signal from noise, such as singular-value decomposition (SVD) 8 . SVD determines a series of statistically significant modes, each consisting of a characteristic pattern (topogram) and its time evolution (chronogram). A topogram can be a characteristic image or spectrum, with the corresponding chronogram showing its change with time. For each mode, a singular value specifies the power contained in that mode 8 .Consider snapshots, such as images or spectra, that can be represented as vectors by using the pixel values of each snapshot as the components of a ve...

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Section: Letter Researchmentioning

confidence: 99%

“…In a minority of X-ray absorption events, a valence electron is ejected to produce + N 2 ions. Abrupt events are expected to launch vibrational 17,24,25 and/or charge 26 wave-packet dynamics. As shown in Fig.…”

Section: Letter Researchmentioning

confidence: 99%

Dynamics from noisy data with extreme timing uncertainty

Fung

Hanna

Vendrell

et al. 2016

Nature

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“…Elsewhere, similar methods have been used to consider the R dependence of wavepacket motion in H + 2 , where a molecular ADK formula was folded into the Coulomb projection and the intensity dependence taken into account [71]. Moreover, with higher pulse intensities the R dependence of the D + 2 wavepacket has been elucidated with excellent resolution across a larger range of R values [70] where the experimental energy spectrum has been converted to a map of the inferred internuclear separation as a function of pump-probe delay time.…”

Section: Modelling the Probe Pulse: Coulomb Explosionmentioning

confidence: 99%

Time-resolved studies of ultrafast wavepacket dynamics in hydrogen molecules

et al. 2010

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a b s t r a c tRecent advances in the study of quantum vibrations and rotations in the fundamental hydrogen molecules are reported. Using the deuterium molecules (D + 2 and D 2 ) as exemplars, the application of ultrafast femtosecond pump-probe experiments to study the creation and time-resolved imaging of coherent nuclear wavepackets is discussed. The ability to study the motion of these fundamental molecules in the time-domain is a notable milestone, made possible through the advent of ultrashort intense laser pulses with durations on sub-vibrational (and sub-rotational) timescales. Quantum wavepacket revivals are characterised for both vibrational and rotational degrees of freedom and quantum models are used to provide a detailed discussion of the underlying ultrafast physical dynamics for the specialist and non-specialist alike.

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“…Revivals have received considerable attention over the last decades [2]. Both experimental and theoretical progress was made in, among others, Rydberg atoms, molecular vibrational states, electric currents in graphene or Bose-Einstein condensates [3][4][5][6][7][8][9]. Recently, methods for isotope separation [10], number factorization [11] as well as for wave-packet control [12][13][14] have been put forward that are based on revival phenomena, and the presence of effective multi-body interactions in a system of ultracold bosonic atoms in a three-dimensional optical lattice was identified in time-resolved traces of quantum phase revivals [15].…”

Section: Introductionmentioning

confidence: 99%

Revival times at quantum phase transitions

Santos

Romera

2013

Phys. Rev. A

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The concept of quantum revivals is extended to many-body systems and the implications of traversing a quantum phase transition are explored. By analyzing two different models, the vibron model for the bending of polyatomic molecules and the Dicke model for a quantum radiation field interacting with a system of two-level atoms, we show evidence of revival behavior for wave packets centered around energy levels as low as the fundamental state. Away from criticality, revival times exhibit smooth, nonsingular behavior, and are proportional to the system size. Upon approaching a quantum critical point, they diverge as a power law and scale with the system size, although the scaling is no longer linear.

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Real-time observation of vibrational revival in the fastest molecular system

Cited by 56 publications

References 55 publications

Dynamics from noisy data with extreme timing uncertainty

Dynamics from noisy data with extreme timing uncertainty

Time-resolved studies of ultrafast wavepacket dynamics in hydrogen molecules

Revival times at quantum phase transitions

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