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Using ultrafast pump–probe spectroscopy, we observe quantum beats between rovibrational states located on the uncoupled bound G 1 Π g + and F 1 Σ g + electronic curves of Li 2 . From a pure launch state ( A 1 Σ u + v A , J A = 11 , 28 ) , a wave packet is prepared using the output from a visible ultrafast optical parametric amplifier and is photoionized by an 800 nm ultrafast pulse. As the OPA wavelength is scanned, a vibrational progression of rotational quantum beats on the G curve is observed. At energies around 35 000 cm −1 , in addition to rotational beats on the G curve, vibrational, rotational, and electronic beating between the G and F curves is observed.

Optical phase manipulation of nonresonant frequencies is investigated as a method of achieving optimal population transfer during resonant impulsive stimulated Raman scattering. Wave packets containing quantum beats between an initially prepared rovibrational level in the A(1Σu+) electronic state of Li2 and states populated via a resonance-enhanced rotational Raman process are created using a shaped ultrafast pulse centered near 800 nm. Study of these wave packets allows a quantitative comparison of population transfer as a function of applied phases in the ultrafast pulse. Two cases are explored to determine the ability to enhance population transfer: one with a wide state spacing [A(νA=11, JA=28)-A(11,30) at 50.1 cm−1] and one with a narrow spacing [A(11,8)-A(11,10) at 16.6 cm−1]. In both cases, several different phase masks are applied to the wave packet preparation pulse to enhance the population transferred to the newly formed state of interest. One phase mask involves the application of a −90° phase...

Using feedback and an evolutionary algorithm (EA), the weak field pump–probe photoionization signal at a single time delay is optimized in Li2. A single launch state is prepared via excitation with a cw laser, from which a pump pulse excites a superposition of two rotational states on an excited electronic potential energy curve: E 1Σg+(vE=9, JE=27 and 29). The EA modifies the phase pattern versus wavelength of the ultrafast pump pulses using a pulse shaper with a 128 pixel liquid crystal spatial light modulator. Limitations of frequency resolution for the pulse shaper create an effective temporal window in which pulses can be shaped. Optimization of the photoionization signal at pump–probe time delays outside of this temporal pulse shaping window involves phase shifts of only the two frequencies resonant with the transition of the wave packet states, effectively introducing a phase shift in the wave packet recurrences. For pump–probe time delays inside the pulse shaping window, optimization of the photoionization shows the influence of not only resonant but also nonresonant wavelengths. In this regime, the phase shift of wave packet recurrences as well as the time-dependent wave packet amplitude coefficients are optimized. First order time dependent perturbation theory is used to explain the mechanism by which the photoionization is maximized. These experiments are the first to use an optimization routine as a tool to identify a variety of simultaneous mechanisms that underlie the maximization of a process.

State-selective phase control of rotational Li2 wave packets, prepared simultaneously in the E(1∑g+) electronic state by one photon absorption and the A(1∑u+) electronic state by resonant impulsive stimulated Raman scattering, is demonstrated. Following the initial population of a rovibrational launch state on the A electronic potential energy curve with a cw laser, a single sub-picosecond wave packet preparation pulse centered near 800 nm simultaneously creates a two-state rotational wave packet in the E state (νE=18, JE=23 and 25) and a three-state rotational wave packet in the A state (νA=15, JA=22, 24, and 26). A temporally delayed 800 nm probe pulse subsequently ionizes both electronic components of the wave packet to allow measurement of the time-dependent coherence in these two electronic states. Via phase manipulation of resonant transition frequencies contained within the preparation pulse, the phases of the E(18,25) and A(15,26) quantum states are either varied concurrently or individually controlled, whereas the phases of the other rovibronic states of the wave packet are in all cases held essentially constant. This phase manipulation is shown to be more complex than a simple additive effect involving the phases applied to the resonant frequencies. These experimental results are compared with the predictions of second order time-dependent perturbation theory. Although systematic discrepancies exist, most likely due to an additional phase introduced during the two-photon probe process, once these differences are accounted for, good agreement is found between experiment and perturbation theory.

Time shifting (up to a global arbitrary phase) the dynamics of molecular wave packets, i.e, |Ψ(t)〉→|Ψ(t−tshift)〉, is demonstrated using a high degree of state selective coherent phase control with shaped femtosecond laser pulses. The benchmark system for the present work is the lithium dimer molecule. The phase-tailored Li2 wave packets are composed of several rovibrational states of the electronic E 1 Σ g + shelf state excited from a single rovibrational level (selected using a cw laser) of the A 1 Σ u + state. The time-shifting operation has implications for the experimental implementation of coherent control, as well as for the use of the control ability to study coherent configurations and dynamics that otherwise would be difficult (sometimes impossible) to access experimentally. This is due, for example, to dephasing and/or depopulation of the wave packet in combination with long recurrence times. One such inaccessible coherent configuration of the present Li2 wave packets corresponds to the global maximum of their ionization yield (as probed in the present experiment).

An ultrafast pulse shaping scheme is presented that transiently modifies a two-state superposition on the E {sup 1}{sigma}{sub g}{sup +} curve of the lithium dimer. At short time delays, the wave-function amplitude of one of the states is forced to undergo a sign change, while the sign of the second state is programmed to remain static, analogous to the operation of a quantum-computational Z gate. This is observed as a {pi} phase shift in the time-dependent wave-packet signal for pump-probe delays

State-selective phase control over rotational wave packets in two Li2 electronic states using tailored femtosecond pulses is demonstrated. A shaped preparation pulse simultaneously creates wave packets in the A and E electronic states, which are probed using a second time-delayed pulse. This allows independent phase control of selected rotational wave packet components in both electronic states.bl]References

Ultrafast pulse shapes are used to control simultaneously the optimal population transfer coefficients and rotational wave-packet quantum interferences in the E 1 Σ + g state of Li 2 (v E =9, J E =27 and 29). By dividing the spectral bandwidth of the ultrafast pulses into multiple "control domains" centered on each resonant wavelength, the population transfer coefficients can be manipulated independently of the wave-packet interferences to maximize the Li 2 photoionization yield at arbitrary short pump-probe time delays. To investigate the population transfer coefficients with and without wave-packet interferences, respectively, the pump polarization is set to be either parallel to or at the magic angle (∼55°) relative to the probe polarization. A comparison is made between phases that are symmetric and antisymmetric about the resonances. The effects of resonant and nonresonant frequencies are separately established and quantified. It is estimated that up to 90% of the possible nonresonant Rabi oscillations can be brought into phase simultaneously for each rovibrational state in the wave packet, while at the same time a constant phase offset added to one of the control domains establishes the phase of the wave-packet interference.

Linearly chirped femtosecond laser pulses are used to excite ro-vibrational wave packets in lithium dimers from a single well-prepared launch state. Two-photon resonant Raman transitions excite a manifold of rotational states in a coherent superposition. Excitation with positively chirped laser pulses is shown to enhance a quantum beat involving states with lower rotational quantum numbers, whereas negatively chirped pulses enhance a quantum beat between states with higher rotational quantum numbers, thus steering the rotational coherences to higher or lower rotational states. Time-dependent perturbation theory calculations verify the magnitudes and directions of the enhancement as a function of the applied chirp. The quantitative calculations and experimental results demonstrate that excitation with chirped pulses is an effective method for enhancing specific rotational coherences involving higher or lower rotational states.