Pump–probe spectroscopy with phase-locked pulses in the condensed phase: decoherence and control of vibrational wavepackets

Wave packet dynamics and control in excited states of molecular nitrogen

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Simultaneous manipulation and observation of multiple ro-vibrational eigenstates in solid para-hydrogen

We have experimentally performed the coherent control of delocalized ro-vibrational wave packets (RVWs) of solid para-hydrogen (p-H₂) by the wave packet interferometry (WPI) combined with coherent anti-Stokes Raman scattering (CARS). RVWs of solid p-H₂ are delocalized in the crystal, and the wave function with wave vector k ∼ 0 is selectively excited via the stimulated Raman process. We have excited the RVW twice by a pair of femtosecond laser pulses with delay controlled by a stabilized Michelson interferometer. Using a broad-band laser pulse, multiple ro-vibrational states can be excited simultaneously. We have observed the time-dependent Ramsey fringe spectra as a function of the inter-pulse delay by a spectrally resolved CARS technique using a narrow-band probe pulse, resolving the different intermediate states. Due to the different fringe oscillation periods among those intermediate states, we can manipulate their amplitude ratio by tuning the inter-pulse delay on the sub-femtosecond time scale. The state-selective manipulation and detection of the CARS signal combined with the WPI is a general and efficient protocol for the control of the interference of multiple quantum states in various quantum systems.

Vibrational relaxation and dephasing of Rb2 attached to helium nanodroplets

The vibrational wave-packet dynamics of diatomic rubidium molecules (Rb(2)) in triplet states formed on the surface of superfluid helium nanodroplets is investigated both experimentally and theoretically. Detailed comparison of experimental femtosecond pump-probe spectra with dissipative quantum dynamics simulations reveals that vibrational relaxation is the main source of dephasing. The rate constant for vibrational relaxation in the first excited triplet state 1(3)Σ(g)+ is found to be constant γ ≈ 0.5 ns(-1) for the lowest vibrational levels v ≲ 15 and to increase sharply when exciting to higher energies.

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.

Tracing, amplifying, and steering chromophore-bath coherences by ultrashort pulse trains

With a train of 5 phase controlled ultrashort pulses, we enhance a coherent vibronic transition to exceed a dominant incoherent background. The interference in the chromophore generates a spectral comb which is adjusted to a progression of internal Br2 vibrations coupled to phonons of the surrounding Ar lattice. It steers the mode-specific phase evolution of the system. The trains are generated by straightforward programing of the spectral comb in a pulse shaper unit. Excitations involving several hundred degrees of freedom remain coherent on a picosecond time scale.

Valence transitions of Br2 in Ar matrices: interaction with the lattice and predissociation

Fluorescence spectra from v(')=0 of the B, A and A(') states of Br(2)Ar are presented for excitation wavelengths from 630 to 540 nm with high resolution, to evaluate isotopic splittings in emission and absorption. The observed progression of sharp zero phonon lines (ZPLs) from v(')=2 to v(')=19 in B excitation is used to derive spectroscopic constants. The ZPL broadening and the growing phonon sideband (PSB) contributions indicate an increase of matrix influence on the X-B transition with rising v('). Contributions of the PSB are parameterized with the Huang-Rhys coupling constant S, where S=1 near the potential minimum reflects the electron-phonon coupling and S=4 close to Franck-Condon maximum originates from vibrational coupling. The PSB spectral composition correlates with the matrix phonon density of states, and the ZPL broadens and shifts with temperature. Two crossings with repulsive states (between v(')=4-5 and v(')=7-9) leading to matrix induced predissociation and a third tentative one between v(')=14 and 15 are indicated by ZPL broadening, population flow, and spectral shifts. The crossing energies are close to gas phase and matrix calculations. The stepwise flow of intensity from B via repulsive states to A(') and, similarly, from the A continuum to A(') is discussed. Emission quantum efficiency of the B state decreases from near unity at v(')=0 to less than 10(-3) at v(')=19. Broadening of ZPL near crossings yields predissociation times of 5 and 2.5 ps corresponding to probabilities of 5% and 10% per round-trip for the two lowest crossings, respectively.

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.

Quantum interference spectroscopy of rubidium-helium exciplexes formed on helium nanodroplets

Femtosecond multiphoton pump-probe photoionization is applied to helium nanodroplets doped with rubidium (Rb). The yield of Rb+ ions features pronounced quantum interference (QI) fringes demonstrating the coherence of a superposition of electronic states on a time scale of tens of picoseconds. Furthermore, we observe QI in the yield of formed RbHe exciplex molecules. The quantum interferogram allows us to determine the vibrational structure of these unstable molecules. From a sliced Fourier analysis one cannot only extract the population dynamics of vibrational states but also follow their energetic evolution during the RbHe formation.

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.

Semiclassical treatments for small-molecule dynamics in low-temperature crystals using fixed and adiabatic vibrational bases

Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculations of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Without resorting to a simple harmonic analysis, both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath. Both approaches expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intermolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude--but still perhaps coherent--motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials. Computational demands for propagation of the parameter equations of motion appear quite manageable for tens or hundreds of atoms and scale similarly with system size in the two cases. Because of the time-scale separation between intermolecular and lattice vibrations, the AVB/GB theory may in some instances require fewer vibrational basis states than the FVB/GB approach. Either framework should enable practical first-principles calculations of nonlinear optical signals from molecules in cryogenic matrices and their semiclassical interpretation in terms of electronic and vibrational decoherence and vibrational population relaxation, all within a pure-state description of the macroscopic many-body complex.

Toward Separation of Nuclear Spin Isomers with Coherent Light

We propose an approach for separating nuclear spin isomers with coherent light and illustrate it by numerical calculations using fulvene as a model system. The scheme employs the equivalence of torsion and interchange of equivalent H-atoms in a class of molecules of which fulvene is a simple example. The exchange symmetry couples with the rotational symmetry to produce a spatial distinction between the two photo-excited nuclear spin isomers, and wavepacket interferometry is applied to separate the species.

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.

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.

Cage motions induced by electronic and vibrational excitations: Cl2 in Ar

Femtosecond dynamics of molecular vibrations as well as cage motions in the B<--X transition of Cl2 in solid Ar have been investigated. We observed molecular vibrational wave-packet motion in experimental pump-probe spectra and an additional oscillation with a 500 fs period which is assigned to the zone-boundary phonon of the Ar crystal. The cage motion is impulsively driven by the B<--X transition due to the expansion of the electronic cloud of the chromophore. To clarify the underlying mechanism, we performed simulations based on the diatomics-in-molecules method which takes into account the different shapes of the Cl2 electronic wave function in the B and X states as well as the anisotropic interaction with the matrix. The simulation results show that Ar atom motion in the (100) plane is initiated by the electronic transition and that only those Ar atoms oscillate coherently with an approximately 500 fs period which are essentially decoupled from the molecular vibration. Their phase and time evolution are in good agreement with the experimentally observed oscillation, supporting the assignment as a displacive excitation of coherent phonons.

Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix

The intramolecular wave packet dynamics on the electronic B (3pi0) potential of Br2 in solid argon is induced and interrogated by femtosecond pump-probe spectroscopy. An effective potential of the chromophore in the solid is derived from the wave packet period for different excitation photon energies. Deep in the potential well, it is consistent with vibrational energies from wavelength-resolved spectra. It extends to higher energies, where the vibrational bands merge to a continuum, and even beyond the dissociation limit, thus quantifying the cage effect of the argon matrix. This advantage of pump-probe spectroscopy is related to a reduced contribution of homogeneous and inhomogeneous line broadenings. The vibrational energy relaxation rates are determined by a variation of the probe window spatial position via the probe quantum energy. A very large energy loss in the first excursion of the wave packet is observed near the dissociation limit. This strong interaction with the argon matrix is directly displayed in an experimental trajectory.