We develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.

We present a reference-free robust method for the nondestructive imaging of complex time-evolving molecular wave functions using as input the time-resolved fluorescence signal. The method is based on expanding the evolving wave function in a set of bound stationary states and determining the set of complex expansion coefficients by calculating a series of Fourier integrals of the signal. As illustrated for the A1∑ u + electronic state of Na2, the method faithfully reconstructs the time-dependent complex wave function of the nuclear motion. Moreover, using perturbation theory to connect the excitation pulse and the material expansion coefficients, our method is used to determine the electromagnetic field of the excitation pulse, thus providing a simple technique for pulse characterization that obviates the additional measurements and iterative solutions that beset other techniques. The approach, which is found to be quite robust against errors in the experimental data, can be readily generalized to the reconstruction of polyatomic vibrational wave functions.

We develop an inversion scheme for obtaining the signs of transition-dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained we show how to extract highly accurate excited state potential(s) and the transition-dipole(s) as a function of inter-nuclear displacements. The same dipole amplitudes can also be used to extract the phase and amplitude of unknown time-evolving wave packets, in essentially a quantum non-demolition manner. The procedure, which is demonstrated for the A((1)∑) and B((1)Π(u)) states of the Na(2) molecule, is shown to yield reliable results even when we are given incomplete or uncertain data. We also demonstrate the success of our approach in extracting double minimum potentials. The inversion scheme is in principle applicable to any polyatomic molecule.

We show how to obtain the signs of transition dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained, we show how to extract the highly accurate excited-state potential(s) and the transition dipole(s) as a function of the nuclear displacements, as well as the phase and amplitude of unknown time evolving states. The procedure, illustrated here for the Na2 molecule, is, in principle, applicable to any polyatomic molecule.

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