We show that wave-packet interference techniques can reconstruct the quantum state of wave packets excited by strong laser pulses. The measurement may be accomplished even when the strength of the excitation is sufficient to significantly deplete the ground state. The probe of the wave packet can still remain perturbative. An inversion algorithm is also developed that is a generalization of the standard Ramsey fringe probe of a wave packet. The normalized sums and differences of the populations of two of the Rydberg states display Ramsey fringes and from these fringes the relative phase between these two states can be found. The algorithm offers advantages in efficiency over previous interferometric algorithms. The algorithm is not sensitive to the precise nature of the distribution of the phase between the pump and probe pulses.
We show that wave-packet interference techniques can reconstruct the quantum state of wave packets excited by strong laser pulses. The measurement may be accomplished even when the strength of the excitation is sufficient to significantly deplete the ground state. The probe of the wave packet can still remain perturbative. An inversion algorithm is also developed that is a generalization of the standard Ramsey fringe probe of a wave packet. The normalized sums and differences of the populations of two of the Rydberg states display Ramsey fringes and from these fringes the relative phase between these two states can be found. The algorithm offers advantages in efficiency over previous interferometric algorithms. The algorithm is not sensitive to the precise nature of the distribution of the phase between the pump and probe pulses.
We have studied the evolution of regular and ``dark'' radial wave packets under the influence of two coherent, temporally separated 100 fs laser pulses. The atomic states are probed by ramped-field ionization. The final state populations exhibit Ramsey oscillations with periods ranging from 2.6--1000 fs as a function of the delay between the two pulses. This time-domain bound-state interferometry reveals several new aspects of the dynamic evolution of wave packets in the presence of strong laser fields. Lowest order perturbation theory is inadequate to describe wave packet formations, even at the lowest intensities studied.
A wave-packet interference technique is proposed to measure exotic atomic Rydberg wave functions. For example, the subject wave packet is excited by an arbitrary pulse or pulse sequence. The resulting wave function is probed by a well-characterized pulse that shares a phase relationship with the excitation pulse(s). The observable is the population in each eigenstate after the probe pulse. By making a series of such measurements, varying the phase between excitation and probe pulses, the wave function created by the excitation pulse can be inferred. The method is experimentally feasible for atomic systems, and the extension of the method to molecular systems also appears possible.
An experiment is described which is an analog of Young's double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other.
This paper presents an experimental and theoretical analysis of quantum interference between Rydberg wave packets in Na. Pairs of phase-locked wave packets manipulate the total orbital angular momentum of Na Rydberg atoms. Initially, the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows one to predict the phase of the second wave packet required to engineer specific angular momentum compositions within the resultant wave packet. Experimentally, this final quantum state distribution is analysed in the frequency domain using state-selective field ionization and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets. Finally, it is shown that by intuitively chirping one of the laser pulses it is possible to compensate for the dispersion of the wave packet and improve the effectiveness of the angular momentum control.
This work presents expressions for the excited population resulting from a Ramsey pump-probe interferometric experiment in the short-weak-pulse limit. It describes time-resolved measurements, which have no direct frequency-resolved analogy, in terms of the eigenenergies, amplitudes, and lifetimes of the excited wave packet. An interferometric phase cross correlation is shown to affect wave packet dynamics by shifting the dispersion of a Rydberg-like wave packet with respect to zero delay. This work phenomenologically introduces eigenstate lifetimes into the expression for the excited population in the Ramsey pump-probe interferometric measurement. An interferometric intensity cross correlation is shown to produce an excited population that, as a function of the delay between pump and probe pulses, is asymmetric about zero delay when the excited eigenstate decays.
In the course of this thesis the techniques of coherent state preparation and interrogation introduced by Stern, Rabi, Ramsey and others are extended to large samples of ultracold Rydberg atoms and molecules. The key technique to realize the coherent control is a Ramsey-like excitation scheme. To achieve this, a Rydberg interferometer is set up and successfully applied in the investigation of the recently discovered ultralong-range Rydberg molecules as well as for the exploration of the dynamics of atomic Rydberg states. Therby, the coherent control of Rydberg molecules is proven. This is a major step towards time resolved investigation of the dynamics of the exotic molecule and opens new opportunities for a more sophisticated understanding of the underlying binding mechanisms. The first experimental application of the interferometer has been given for ultralong-range Rydberg molecules. Following the work of Ramsey, an experimental sequence with two excitation pulses split in time was set up. Because the Rydberg molecules are coherently photoassociated in the experiment, an interference pattern known as Ramsey fringes is created. The loss of visibility of the Ramsey fringe pattern could be described in a two-level model and from these calculations, the lifetime of the molecules was determined interferometrically. Thus aside from being an elegant and unambiguous proof for the coherence of the photoassociation, the occurrence of Ramsey fringes also allows one to see the experiment as an atom-molecule interferometer. These experiments have paved the way towards experimental exploration of the dynamics of these exotic molecule. For another open question in the field of ultralong-range Rydberg molecules - their lifetime - the findings in this thesis brought clarity. From the density-dependent investigations it could be found that the lifetime of the vibrationally excited molecular state is systematically shorter than that of the molecular ground state. These findings confirm the theory that the excited molecular states are bound by quantum reflection: The shortened lifetime can be ascribed to the inward penetration of the bound atomic pair due to imperfect quantum reflection leading to the dissociation of the molecule. In the further course of this thesis, the idea of a Ramsey setup for Rydberg molecules has been extend to Rydberg atoms. With the introduction of a control parameter to tune the relative phase shift between the ground-state arm and the Rydberg arm, the so far empty interferometer has been extended to a full working interferometer. The measurements on the 43s-state in electric fields demonstrated the usability of the interferometer in a simple and well controllable system and the interferometric studies on the 46d-state in crossed external fields can be regarded as the first investigative application of the interferometer. The key point of the investigation is the link between the two observables of the Rydberg interferometer, phase shift and visibility, and the complex value describing the Rydberg state of interest. It was found that the phase shift of the Rydberg state mostly follows the adiabatic energy curves in the electric field calculated for these experimental parameters. However, in the region where avoided crossings du to crossed electric and magnetic field occur, the phase shift behaves substantially different. While the phase rises fast by pi near one avoided crossing, a 2pi jump occurs at another avoided crossing. Since the phase can only be determined in the interval between 0 and 2pi experimentally, the jump cannot be observed as function of the electric field. This limitation has been overcome by taking the phase shift as function of time for different electric fields, which allows to reconstruct the phase at the given field-on time independently. From these measurements, the occurrence of the 2pi jump could be validated. To explore the reasons underlying the behavior of the phase in the electric field, the dynamics of the system has been modeled theoretically. The experimental findings for the phase shift as well as for the visibility are thoroughly reproduced by theory. Especially the characteristic behavior of phase shift and visibility near the avoided crossings is also seen in the calculations. With the help of this modeling one can see the fast pi rise in analogy to the phase of a driven harmonic oscillator that changes from in-phase when the driving frequency is below the resonance of the oscillator and out-of-phase above. The 2pi jump, however, emerges from the complex dynamics of the several levels involved and can not be easily broken down to a two-level picture. Altogether, these findings confirm that the Rydberg interferometer can track the dynamics of the selected Rydberg state and enabled the tomography of the Rydberg state. Moreover, these measurements show the potential of the Rydberg interferometer as tool to explore the dynamic of quantum systems.