Strong-field atomic phase matching

Charge oscillation controlled molecular excitation

The direct manipulation of charge oscillations has emerged as a new perspective in chemical reaction control. Here, we demonstrate, in a joint experimental and theoretical study, that the electron dynamics of a molecule is efficiently steered by controlling the interplay of a driving femtosecond laser pulse with the photoinduced charge oscillation. These oscillations have a typical Bohr period of around 1 fs for valence electrons; therefore, control has to be exerted on a shorter time scale. Specifically, we show how precision pulse shaping is used to manipulate the coupled electron and nuclear dynamics in order to address different bound electronic target states in a molecule. We present a strong-field coherent control mechanism which is understood in terms of a simple classical picture and at the same time verified by solving the time-dependent Schrödinger equation. This mechanism is universally applicable and opens a wide spectrum of applications in the reaction control of complex systems.

An extremely robust strong-field control of atomic coherence

We propose and analyze a scheme for adiabatic creation of maximum coherence of 0.5 with a controllable phase between a ground state and the excited state in a model Λ-structured atom using two short laser pulses. One of the pulses has constant carrier frequency quasi-resonant with transition between an initially empty ground and the excite states. The frequency of the second pulse is swept through the resonance with the adjacent transition between the initially populated ground state and the common excited state of the atom. We demonstrate high degree of robustness of the scheme against variation of parameters of the laser radiation in relatively broad region of values. The proposed scheme may find practical applications in the field of multi-photon ionization, high-order harmonics and Raman sideband generation, as well as in nonlinear wave mixing in coherently prepared media.

Weak-field multiphoton femtosecond coherent control in the single-cycle regime

Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.

Strong-field quantum control of 2 + 1 photon absorption of atomic sodium

We demonstrate ultrafast coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level system that models optical interactions with sodium atoms, we control the quantum interference of sequential 2 + 1 photons and direct three-photon transitions. Dynamic change in energy levels predicts an enormous enhancement of |7p>-state excitation in the strong-field regime by a negatively chirped pulse. In addition, the |4s>-state excitation is enhanced symmetrically by nonzero linear chirp rates given as a function of laser peak intensity and laser detuning. Experiments performed by ultrafast shaped-pulse excitation of ground-state atomic sodium verifies the various strong-field contributions to |3s>-|7p> and |3s>-|4s> transitions. The result suggests that for systems of molecular level understanding adiabatic control approach with analytically shaped pulses becomes a more direct control than feedback-loop black-box approaches.

Two-photon coherent control of femtosecond photoassociation

Photoassociation with short laser pulses has been proposed as a technique to create ultracold ground state molecules. A broad-band excitation seems the natural choice to drive the series of excitation and deexcitation steps required to form a molecule in its vibronic ground state from two scattering atoms. First attempts at femtosecond photoassociation were, however, hampered by the requirement to eliminate the atomic excitation leading to trap depletion. On the other hand, molecular levels very close to the atomic transition are to be excited. The broad bandwidth of a femtosecond laser then appears to be rather an obstacle. To overcome the ostensible conflict of driving a narrow transition by a broad-band laser, we suggest a two-photon photoassociation scheme. In the weak-field regime, a spectral phase pattern can be employed to eliminate the atomic line. When the excitation is carried out by more than one photon, different pathways in the field can be interfered constructively or destructively. In the strong-field regime, a temporal phase can be applied to control dynamic Stark shifts. The atomic transition is suppressed by choosing a phase which keeps the levels out of resonance. We derive analytical solutions for atomic two-photon dark states in both the weak-field and strong-field regime. Two-photon excitation may thus pave the way toward coherent control of photoassociation. Ultimately, the success of such a scheme will depend on the details of the excited electronic states and transition dipole moments. We explore the possibility of two-photon femtosecond photoassociation for alkali and alkaline-earth metal dimers and present a detailed study for the example of calcium.

Characterization of transient molecular vibration excited with shaped femtosecond pulses

We study vibrational dynamics of molecules interacting with spectrally shaped broadband laser pulses. After performing a single measurement based on cross-correlation frequency resolved optical gating of molecular vibration, complete evolution of the complex-valued quantum coherence between the vibrational states is reconstructed with variable time and frequency resolution. The ability to change the resolution in the analysis of the transient molecular dynamics without repeating the experiment or changing experimental parameters is useful in designing and understanding various schemes of controlling quantum states of molecules.

Strong-field two-photon absorption in atomic cesium: an analytical control approach

We have considered an analytical control of two-photon absorption process of atoms in the strong-field interaction regime. The experiment was performed on gaseous cesium atoms strongly interacting with a shaped laser-pulse from a femtosecond laser amplifier and a programmable pulse-shaper. When this shaped laser-pulse transfers the atomic population from the 6s ground state to the 8s excited state, we have found that both positively- and negatively-chirped laser pulses, compared with a Gaussian pulse, enhance this excitation in the strong-field regime of laser-atom interaction. This unusual phenomena is explained because the temporal shape of the laser intensity compensates the effect of dynamic Stark shift for the two-photon resonant condition to be optimally maintained. We provide analytic calculations using the strong-field phase matching, which show good agreement with the experiment.

Robust photon locking

We experimentally demonstrate a strong-field coherent control mechanism that combines the advantages of photon locking (PL) and rapid adiabatic passage (RAP). Unlike earlier implementations of PL and RAP by pulse sequences or chirped pulses, we use shaped pulses generated by phase modulation of the spectrum of a femtosecond laser pulse with a generalized phase discontinuity. The novel control scenario is characterized by a high degree of robustness achieved via adiabatic preparation of a state of maximum coherence. Subsequent phase control allows for efficient switching among different target states. We investigate both properties by photoelectron spectroscopy on potassium atoms interacting with the intense shaped light field.

NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation

Shaped near-infrared (NIR) femtosecond pulses are used for the first time to control the generation of coherent deep-ultraviolet (UV) radiation in an atomic resonance-mediated (2+1) three-photon excitation. The broadband excitation coherently involves pathways that are on resonance with the intermediate resonance state as well as pathways that are near resonance with it. Experimental and theoretical results are presented for phase controlling the total emitted UV yield in atomic sodium. Depending on the NIR spectrum of the excitation pulse, the coherent UV emission is either predominantly due to a single excited real state that is accessed resonantly or due to a manifold of virtual states. The former leads to a narrowband UV emission, while the latter leads to a broadband UV radiation. Basic phase control is exercised in both cases, with excellent agreement between experiments and calculations. The tunability is over an order-of-magnitude UV-yield range.

Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses

We demonstrate strong-field population inversion in a three-level system with single and multiphoton coupling between levels using a single shaped ultrafast laser pulse. Our interpretation of the pulse shape dependence illustrates the difference between sequential population transfer and adiabatic rapid passage in three-level systems with multiphoton coupling between levels.

Multichannel selective femtosecond coherent control based on symmetry properties

We present and implement a new scheme for extended multichannel selective femtosecond coherent control based on symmetry properties of the excitation channels. Here, an atomic nonresonant two-photon absorption channel is coherently incorporated in a resonance-mediated (2+1) three-photon absorption channel. By proper pulse shaping, utilizing the invariance of the two-photon absorption to specific phase transformations of the pulse, the three-photon absorption is tuned independently over an order-of-magnitude yield range for any possible two-photon absorption yield. Noticeable is a set of "two-photon dark pulses" inducing widely tunable three-photon absorption.

Population transfer between two quantum states by piecewise chirping of femtosecond pulses: theory and experiment

We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.

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.