Molecular quantum dynamics in a thermal system: Fractional wave packet revivals probed by random-phase fluorescence interferometry

Compacting the density matrix in quantum dynamics: Singular value decomposition of the surprisal and the dominant constraints for anharmonic systems

We introduce a practical method for compacting the time evolution of the quantum state of a closed physical system. The density matrix is specified as a function of a few time-independent observables where their coefficients are time-dependent. The key mathematical step is the vectorization of the surprisal, the logarithm of the density matrix, at each time point of interest. The time span used depends on the required spectral resolution. The entire course of the system evolution is represented as a matrix where each column is the vectorized surprisal at the given time point. Using the singular value decomposition (SVD) of this matrix, we generate realistic approximations for the time-independent observables and their respective time-dependent coefficients. This allows for a simplification of the algebraic procedure for determining the dominant constraints (the time-independent observables) in the sense of the maximal entropy approach. A non-stationary coherent initial state of a Morse oscillator is used to introduce the approach. We derive the analytical exact expression for the surprisal as a function of time, and this offers a benchmark for comparison with the accurate but approximate SVD results. We discuss two examples of a Morse potential of different anharmonicities, H₂ and I₂ molecules. We further demonstrate the approach for a two-coupled electronic state problem, the well-studied non-radiative decay of pyrazine from its bright state. Five constraints are found to be enough to capture the ultrafast electronic population exchange and to recover the dynamics of the wave packet in both electronic states.

A proposed new scheme for vibronically resolved time-dependent photoelectron spectroscopy: pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes)

We propose a new scheme for time-resolved photoelectron spectroscopy denoted as pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes). This scheme is comprised of two femtosecond laser (pump) pulses under cw illumination (probe). By changing the time-delay between pump and repump lasers one can manipulate the populations of vibronic levels in electronic excited states. The cw laser acts on for a long time and establishes resonance between excited states and the continuum photo-ionized states. Sharp spectra can be obtained from the resonance condition [formula: see text]. The intensities in the spectra are sensitive to the time-delay between the pump-repump pulses, but only depend on the populations of excited states, not the phase relations (coherence). As a result, each time-delayed snapshot spectrum is a weighted sum of so-called fingerprints, where a fingerprint is the vibrationally resolved photoelectron spectrum for a single vibronic excited state. The latter information can potentially be simulated reliably using vibronic models and wave packet propagation methods. In the easiest application of the experiment, different time-delays produce different spectra, for a single molecular system. This wealth of experimental data can be fitted to an, ideally small, set of theoretical fingerprints by adjusting the populations as fitting parameters. This technique might be able to distinguish between closely related molecular species. Adopting a different viewpoint, the proposed scheme can also be employed to monitor the time-dependent dynamics by changing the phase relationship between the pump and repump laser that can be viewed as a "control mechanism" employed in wave packet interferometry. Simplifications arise as the change in the spectra is due to the changing populations, not because of the coherence. In this paper, we outline the ideas behind the scheme and illustrate the ideas theoretically using simple model systems.

Wave packet interferometry with attosecond precision and picometric structure

Wave packet (WP) interferometry is applied to the vibrational WPs of the iodine molecule. Interference fringes of quantum waves weave highly regular space-time images called "quantum carpets." The structure of the carpet has picometre and femtosecond resolutions, and changes drastically depending on the amplitudes and phases of the vibrational eigenstates composing the WP. In this review, we focus on the situation where quantum carpets are created by two counter-propagating nuclear vibrational WPs. Such WPs can be prepared with either a single or double femtosecond (fs) laser pulse. In the single pulse scheme, the relevant situation appears around the half revival time. Similar situations can be generated with a pair of fs laser pulses whose relative phase is stabilized on the attosecond time scale. In the latter case we can design the quantum carpet by controlling the timing between the phase-locked pulses. We demonstrate this carpet design and visualize the designed carpets by the fs pump-probe measurements, tuning the probe wavelength to resolve the WP density-distribution along the internuclear axis with ~3 pm spatial resolution and ~100 fs temporal resolution.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Actively tailored spatiotemporal images of quantum interference on the picometer and femtosecond scales

Interference fringes of quantum waves weave highly regular space-time images, which could be seen in various wave systems such as wave packets in atoms and molecules, Bose-Einstein condensates, and fermions in a box potential. We have experimentally designed and visualized spatiotemporal images of dynamical quantum interferences of two counterpropagating nuclear wave packets in the iodine molecule; the wave packets are generated with a pair of femtosecond laser pulses whose relative phase is locked within the attosecond time scale. The design of the image has picometer and femtosecond resolutions, and changes drastically as we change the relative phase of the laser pulses, providing a direct spatiotemporal control of quantum interferences.

Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation

Two-dimensional electronic coherence spectroscopy (ECS) is an important method to study the coupling between distinct optical modes of a material system. Such studies often involve excitation using a sequence of phased ultrashort laser pulses. In conventional approaches, the delays between pulse temporal envelopes must be precisely monitored or maintained. Here, we introduce a new experimental scheme for phase-selective nonlinear ECS, which combines acousto-optic phase modulation with ultrashort laser excitation to produce intensity modulated nonlinear fluorescence signals. We isolate specific nonlinear signal contributions by synchronous detection, with respect to appropriately constructed references. Our method effectively decouples the relative temporal phases from the pulse envelopes of a collinear train of four sequential pulses. We thus achieve a robust and high signal-to-noise scheme for phase-selective ECS to investigate the resonant nonlinear optical response of photoluminescent systems. We demonstrate the validity of our method using a model quantum three-level system-atomic Rb vapor. Moreover, we show how our measurements determine the resonant complex-valued third-order susceptibility.

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.

Identifying wave-packet fractional revivals by means of information entropy

Wave-packet fractional revivals is a relevant feature in the long time-scale evolution of a wide range of physical systems, including atoms, molecules, and nonlinear systems. We show that the sum of information entropies in both position and momentum conjugate spaces is an indicator of fractional revivals by analyzing three different model systems: (i) the infinite square well, (ii) a particle bouncing vertically against a wall in a gravitational field, and (iii) the vibrational dynamics of hydrogen iodide molecules. This description in terms of information entropies complements the usual one in terms of the autocorrelation function.

Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.

Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.

Real-time observation of phase-controlled molecular wave-packet interference

The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.

Correlation of femtosecond wave packets and fluorescence interference in a conjugated polymer: Towards the measurement of site homogeneous dephasing

Probing electronic femtosecond (fs) coherence among segmental sites that are congested by static and dynamic site disorder and subject to structural relaxation is a big, experimental challenge in the study of photophysics of poly(p-phenylenevinylene). In this work, fs-wave-packet fluorescence interferometry experiments are presented that measure macroscopic coherent kernels and their phase-relaxation in the low-temperature, bottom-state regime of the density-of-states below the migrational threshold energy where downhill site-to-site transfer is marginal. By using freely propagating and tunable 70 fs excitation/probing pulses and employing narrow-band spectral filtering of wave packets, fluorescence interferograms with strongly damped beatings can be observed. The coherences formally follow the in-phase superpositions of two site-optical free-induction-decays and originate from distinct pairs of coherent doorway-states, different in energy and space, each of them being targeted, by two discrete quantum-arrival-states 1(alpha) and 1(beta), via independent, isoenergetic 0-->1 fluorescence transitions. The coherent transients are explained as site-to-site polarization beatings, caused by the interference of two fluorescence correlation signals. The numerical analysis of the damping regime, based upon second-order perturbational solutions, reveals the lower limit value of homogeneous dephasing in the range from T(2) approximately 100 fs to T(2) approximately 200 fs depending on the site-excitation energy of the bottom-states. The experiments enable to look into the formation of the relaxed state as a special molecular process of electron-phonon coupling and hence open-up a quite new perspective in the puzzle of multichromophore optical dynamics and structural relaxation in conjugated polymers.

High-precision molecular wave-packet interferometry with HgAr dimers

Molecular wave-packet (WP) interferometry has been demonstrated in the A electronic state of the HgAr van der Waals complex with two time-delayed UV fs pulses at 254 nm. The interferograms of three vibrational levels in the WP's display almost 100% fringe contrast as a function of the interpulse delay tau, which is tuned with sub-10 as stability and resolution. It is clearly observed that the three interferograms show their dephasing and rephasing within a single vibrational period, allowing us to prepare arbitrary relative populations of the three levels by adjusting a single parameter tau.