Visualizing Picometric Quantum Ripples of Ultrafast Wave-Packet Interference

Subfemtosecond Tracing of Molecular Dynamics during Strong-Field Interaction

We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750 nm, 4.5 fs laser pulses were focused to an intensity of 9×10^{14}  W/cm^{2} onto H_{2}. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the 1sσ_{g} state of H_{2}^{+} during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

Weak-field coherent control of photodissociation in polyatomic molecules

A coherent control scheme is suggested to modify the output of photodissociation in a polyatomic system. The performance of the scheme is illustrated by applying it to the ultrafast photodissociation of CH₃I in the A-band. The control scheme uses a pump laser weak field that combines two pulses of a few femtoseconds delayed in time. By varying the time delay between the pulses, the shape of the laser field spectral profile is modulated, which causes a change in the initial relative populations excited by the pump laser to the different electronic states involved in the photodissociation. Such a change in the relative populations produces different photodissociation outputs, which is the basis of the control achieved. The degree of control obtained over different photodissociation observables, like the branching ratio between the two dissociation channels of CH₃I yielding I(²P_3/2) and I*(²P_1/2) and the fragment angular distributions associated with each channel, is investigated. These magnitudes are found to oscillate strongly with the time delay, with the branching ratio changing by factors between two and three. Substantial variations of the angular distributions also indicate that the scheme provides a high degree of control. Experimental application of the scheme to general polyatomic photodissociation processes should be straightforward.

Coherent control theory and experiment of optical phonons in diamond

The coherent control of optical phonons has been experimentally demonstrated in various physical systems. While the transient dynamics for optical phonons can be explained by phenomenological models, the coherent control experiment cannot be explained due to the quantum interference. Here, we theoretically propose the generation and detection processes of the optical phonons and experimentally confirm our theoretical model using the diamond optical phonon by the doublepump-probe type experiment.

Ultrafast Coherent Control of Condensed Matter with Attosecond Precision

Coherent control is a technique to manipulate wave functions of matter with light. Coherent control of isolated atoms and molecules in the gas phase is well-understood and developed since the 1990s, whereas its application to condensed matter is more difficult because its coherence lifetime is shorter. We have recently applied this technique to condensed matter samples, one of which is solid para-hydrogen ( p-H₂). Intramolecular vibrational excitation of solid p-H₂ gives an excited vibrational wave function called a "vibron", which is delocalized over many hydrogen molecules in a manner similar to a Frenkel exciton. It has a long coherence lifetime, so we have chosen solid p-H₂ as our first target in the condensed phase. We shine a time-delayed pair of femtosecond laser pulses on p-H₂ to generate vibrons. Their interference results in modulation of the amplitude of their superposition. Scanning the interpulse delay on the attosecond time scale gives a high interferometric contrast, which demonstrates the possibility of using solid p-H₂ as a carrier of information encoded in the vibrons. In the second example, we have controlled the terahertz collective phonon motion, called a "coherent phonon", of a single crystal of bismuth. We employ an intensity-modulated laser pulse, whose temporal envelope is modulated with terahertz frequency by overlap of two positively chirped laser pulses with their adjustable time delay. This modulated laser pulse is shined on the bismuth crystal to excite its two orthogonal phonon modes. Their relative amplitudes are controlled by tuning the delay between the two chirped pulses on the attosecond time scale. Two-dimensional atomic motion in the crystal is thus controlled arbitrarily. The method is based on the simple, robust, and universal concept that in any physical system, two-dimensional particle motion is decomposed into two orthogonal one-dimensional motions, and thus, it is applicable to a variety of condensed matter systems. In the third example, the double-pulse interferometry used for solid p-H₂ has been applied to many-body electronic wave functions of an ensemble of ultracold rubidium Rydberg atoms, hereafter called a "strongly correlated ultracold Rydberg gas". This has allowed the observation and control of many-body electron dynamics of more than 40 Rydberg atoms interacting with each other. This new combination of ultrafast coherent control and ultracold atoms offers a versatile platform to precisely observe and manipulate nonequilibrium dynamics of quantum many-body systems on the ultrashort time scale. These three examples are digested in this Account.

Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics

We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I₂ molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N₂ molecules.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

Communication: Control of the fragment state distributions produced upon decay of an isolated resonance state

Control of the fragment state distributions produced upon decay of a resonance state is achieved by using a weak laser field consisting of two pulses with a varying time delay between them. It is shown that specific product fragment states can be significantly favored or quenched. The efficiency and flexibility of the control method are found to increase with increasing resonance width. The control scheme is completely independent of the specific system to which it is applied, which makes its applicability universal.

Coherent Amplification of Ultrafast Molecular Dynamics in an Optical Oscillator

Optical oscillators present a powerful optimization mechanism. The inherent competition for the gain resources between possible modes of oscillation entails the prevalence of the most efficient single mode. We harness this "ultrafast" coherent feedback to optimize an optical field in time, and show that, when an optical oscillator based on a molecular gain medium is synchronously pumped by ultrashort pulses, a temporally coherent multimode field can develop that optimally dumps a general, dynamically evolving vibrational wave packet, into a single vibrational target state. Measuring the emitted field opens a new window to visualization and control of fast molecular dynamics. The realization of such a coherent oscillator with hot alkali dimers appears within experimental reach.

Quantum interference control of an isolated resonance lifetime in the weak-field limit

Resonance states play an important role in a large variety of physical and chemical processes. Thus, controlling the resonance behavior, and particularly a key property like the resonance lifetime, opens up the possibility of controlling those resonance mediated processes. While such a resonance control is possible by applying strong-field approaches, the development of flexible weak-field control schemes that do not alter significantly the system dynamics still remains a challenge. In this work, one such control scheme within the weak-field regime is proposed for the first time in order to modify the lifetime of an isolated resonance state. The basis of the scheme suggested is quantum interference between two pathways induced by laser fields, that pump wave packet amplitude to the target resonance under control. The simulations reported here show that the scheme allows for both enhancement and quenching of the resonance survival lifetime, being particularly flexible to achieve large lifetime enhancements. Control effects on the resonance lifetime take place only while the pulse is operating. In addition, the conditions required to generate the two interfering quantum pathways are found to be rather easy to meet for general systems, which makes the experimental implementation straightforward and implies the wide applicability of the control scheme.

Frequency-resolved optical gating technique for retrieving the amplitude of a vibrational wavepacket

We propose a novel method to determine the complex amplitude of each eigenfunction composing a vibrational wavepacket of / molecular ions evolving with a ~10 fs time scale. We find that the two-dimensional spectrogram of the kinetic energy release (KER) of H⁺/D⁺ fragments plotted against the time delay of the probe pulse is equivalent to the spectrogram used in the frequency-resolved optical gating (FROG) technique to retrieve the complex amplitude of an ultrashort optical pulse. By adapting the FROG algorithm to the delay-KER spectrogram of the vibrational wavepacket, we have successfully reconstructed the complex amplitude. The deterioration in retrieval accuracy caused by the bandpass filter required to process actual experimental data is also discussed.

Using coherent control to extract the phases of electronic transition-dipole matrices: the LiRb case

We show that “bichromatic coherent control” (BCC) enables the determination of the amplitudes (= magnitudes + phases) of individual transition-dipole matrix elements (TDMs) and the amplitude of time-evolving wave packets from time-resolved fluorescence data. In the present use of BCC, one induces quantum interferences using two external laser fields to coherently deplete the population of different pairs of excited energy eigenstates. The BCC-induced depletion is supplemented by the computation of the Fourier integral of the time-resolved fluorescence at the beat frequencies of the two states involved. The combination of BCC and Fourier transform enables the determination of both the expansion coefficients of the wave packet in a basis of vibrational energy eigenstates and the amplitudes of the [Formula: see text] electronic TDMs linking the excited and ground rovibrational states. We illustrate our method by determining the amplitudes of the TDMs linking the vibrational states of the [Formula: see text] spin orbit coupled potentials to both the singlet [Formula: see text] and the triplet [Formula: see text] electronic ground states in LiRb. The approach, which is found to be quite robust against errors in the BCC procedure and experimental data, can be readily generalized to the imaging of wave packets of polyatomic molecules.

Resonant detection of the signature of control of a resonance state lifetime using a pump–probe scheme

Realistic wave packet simulations demonstrate that the signature of control of the survival probability and lifetime of a specific resonance state can be observed and probed in typical time-resolved pump–probe experiments.

Optical control of plasmonic fields by phase-modulated pulse excitations

We developed an advanced near-field optical method by combining an ultrafast near-field optical microscope with a prism-based pulse shaping system. We used this apparatus to visualize plasmonic optical fields and to measure the lifetime of plasmons excited on a rough gold film. We also studied the influence of the phase-modulation of the excitation pulse on the spatial distribution of the optical fields. We found that the spatial distribution of the optical fields can be controlled by a negatively chirped pulse.

Time-dependent resonant scattering: an analytical approach

A time-dependent description is given of a scattering process involving a single resonance embedded in a set of flat continua. An analytical approach is presented which starts from an incident free particle wave packet and yields the Breit-Wigner cross-section formula at infinite times. We show that at intermediate times the so-called Wigner-Weisskopf approximation is equivalent to a scattering process involving a contact potential. Applications in cold-atom scattering and resonance enhanced desorption of molecules are discussed.

Selective coherent control of the lifetime of a resonance state with laser pulses

It is shown that new possibilities for control of the lifetime of a system in a resonance state emerge when the density of resonances overlapping and interfering with the target resonance increases. When using a control scheme combining two pump laser pulses, it is found that increasing the density of resonance states overlapping with the target one increases the selectivity of the scheme applied, and leads to achieve a remarkably higher degree of control. Lifetime enhancements by factors up to 20 are obtained when this selectivity is applied. The underlying reasons for such strong enhancements are analyzed and explained in the light of the equations of the model applied. Application of this strategy to control and enhance the lifetime of a system in excited states is envisioned.

Electric field detection of phase-locked near-infrared pulses using photoconductive antenna

We have demonstrated that a photoconductive antenna gated with 5-fs ultrashort laser pulses can detect electric field transients of near-infrared pulses at least up to 180 THz. Measured sensitivity spectrum of the antenna shows a good agreement with a simple calculation, demonstrating the promising capability of the antenna to near infrared spectroscopy. Using this setup, near-infrared time-domain spectroscopy and characterization of phase controlled near-infrared pulses are demonstrated. Observed absorption spectrum of a polystyrene film and complex refractive index dispersion of a fused silica plate both agree well with those obtained by the conventional methods.

Resolving vibrational wave-packet dynamics of D2(+) using multicolor probe pulses

We demonstrate the generation and real-time observation of the vibrational wave packet of D(2)(+) by using a sub-10-fs extreme UV high-harmonic pump pulse and a three-color probe laser pulse whose wavelength ranges from near-IR to vacuum UV. This multicolor pump-probe scheme can provide us with a powerful experimental tool for investigating a variety of wave packets evolving with a time scale of ~20 fs.

Two-dimensional vibronic spectroscopy of coherent wave-packet motion

We theoretically study two-dimensional (2D) spectroscopic signals obtained from femtosecond pulse interactions with diatomic molecules. The vibrational wave-packet dynamics is monitored in the signals. During the motion in anharmonic potentials the wave packets exhibit vibrational revivals and fractional revivals which are associated with particular quantum phases. The time-dependent phase changes are identified by inspection of the complex-valued 2D spectra. We use the Na(2) molecule as a numerical example and discuss various pulse sequences which yield information about vibrational level structure and phase relationships in different electronic states.

Electromagnetically induced transparency with quantum interferometry

We have shown that electromagnetically induced transparency can be achieved by control-probe interferometry using two delayed phase-locked ultrashort pulses. Two vibrational wavepackets on the excited state, excited by two delayed phase-locked ultrashort pulses, interfere constructively or destructively leading to enhancement or suppression of absorption to a selective set of vibrational levels. Depending on the phase difference and the delay between the pulses with same carrier frequency, one can design different transparency windows between absorption peaks at consecutive even(odd) vibrational levels by eliminating absorption at odd(even) vibrational levels. We have shown that by switching the phase difference of two delayed femtosecond pulses, one can switch to complete elimination of absorption from enhanced absorption to a particular set of vibrational levels in the excited state. Thus, switching of transparency through window between odd vibrational levels to that between even vibrational levels is possible. By properly choosing the temporal width and the carrier frequency of the pulses, lossless transmission of complete or bands of frequencies of the pulses can be achieved through these transparency windows. Hence, designing of single- or multi-mode transparency windows in NaH molecule is feasible by control-probe quantum interferometry.

CONTROLLING WAVE PACKET INTERFERENCE OF DISSOCIATING MOLECULES BY SHAPING LASER PULSES IN FREQUENCY DOMAIN

The interference of dissociating wave packets for the Br 2 molecule in femtosecond laser field is studied theoretically using time-dependent quantum wave packet method. The interference of dissociating wave packets can be determined by the spectrum of laser field. By shaping laser pulses in frequency domain, the corresponding R- and v-dependent density functions can be effectively controlled. Compared with the 2-pulse excitation scheme, the resolution of the interference patterns can be improved by using 3- and 4-pulse excitation schemes. The dissociating velocity can be steered by varying laser parameters.

Real-time visualization of the dynamic evolution of CS2 4d and 6s Rydberg wave packet components

The dynamic evolution of CS2 4d and 6s Rydberg wave packet components has been experimentally visualized via femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. The temporal evolution of the four components of the prepared Rydberg wave packet is directly observed as time-dependent changes of the intensities of different parts in the main photoelectron peak. Furthermore, time-resolved photoelectron angular distributions (PADs) clearly reflect the different component characters of 4d and 6s molecular orbitals. The lifetime of Rydberg wave packets is determined to be about 830fs and their decay is attributed to predissociation. Our results suggest the possibility of directly visualizing and determining the amplitudes and relative phases of different electronic and vibrational wave packet components in polyatomic molecules.

Ultrafast Fourier transform with a femtosecond-laser-driven molecule

Wave functions of electrically neutral systems can be used as information carriers to replace real charges in the present Si-based circuit, whose further integration will result in a possible disaster where current leakage is unavoidable with insulators thinned to atomic levels. We have experimentally demonstrated a new logic gate based on the temporal evolution of a wave function. An optically tailored vibrational wave packet in the iodine molecule implements four- and eight-element discrete Fourier transform with arbitrary real and imaginary inputs. The evolution time is 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by 3 orders of magnitudes.

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.

Nuclear interference in the Coulomb explosion of H2+ in short vuv laser fields

We report ab initio calculations of H2+ three-photon ionization by vuv/fs 10(12) W/cm(2) laser pulses including electronic and vibrational degrees of freedom in the Born-Oppenheimer approximation. The initial nuclear wave packet of H2+(1ssigma(g)) is assumed to be equal to the H2 vibrational ground state. For pulse durations longer than 10 fs, we find an unexpected modulation in the kinetic energy spectra of the correlated fragments (H++H+). It is shown that the structures in the spectra originate from the interference between a direct and a sequential dissociation channel. While the first channel is open even for relatively short pulses, the sequential one only opens for pulse durations longer than 10 fs. In the latter case we show that interference between the two components results in a modulated kinetic energy release spectrum in the dissociation channel 3dsigma(g), which is reflected in the ionization spectrum.

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.

Factorization of numbers with the temporal Talbot effect: optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.

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.

Attosecond control of ionization by wave-packet interference

A train of attosecond pulses, synchronized to an infrared (IR) laser field, is used to create a series of electron wave packets (EWPs) that are below the ionization threshold in .helium. The ionization probability is found to strongly oscillate with the delay between the IR and attosecond fields twice per IR laser cycle. Calculations that reproduce the experimental results demonstrate that this ionization control results from interference between transiently bound EWPs created by different pulses in the train. In this way, we are able to observe, for the first time, attosecond wave-packet interference in a strongly driven atomic system.

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.