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Optics Express

Introduction

Jeffrey W. Krause

Published Sep 29, 1997• 1 citation
Publisher

Abstract

When a coherent superposition of Rydberg states is excited by a laser pulse, a Rydberg wave packet is created. These wave packets are supremely quantum mechanical objects. However, they can be constructed to display classical, nearly classical, or semiclassical behavior, and thus serve as a natural bridge between the microscopic and mesoscopic worlds. In addition, their comparative simplicity allows detailed studies of the fundamental interactions of light with matter. The authors of this focus issue were invited to submit papers that reflect both the range of dynamical behavior exhibited by Rydberg wave packets, and the depth of understanding of them that is possible with current experiments and theory. In particular, the papers in this issue illustrate the possibility that emerging laser technology can be used not only to observe quantum behavior, but also to control it.

DOI
10.1364/oe.1.000175

Related papers

Toward Creating a Rutherford Atom

David M. Villeneuve

Rydberg atoms are atoms with a highly excited electron. In his Perspective, Villeneuve explains that by creating a coherent superposition of Rydberg states, the electron can be made to behave almost like a classical Rutherford atom. He highlights the report by Maeda et al., who show that they can force the electron wave packet to remain localized for thousands of highly elliptical orbits around the nucleus, much like a miniature planetary system. Such experiments help to bridge the gap between the quantum mechanical world and our everyday classical world.

Science•Mar 18, 2005•1 citation

Rydberg Wave Packets and the Classical Limit

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Summary form only given. Design and excitation of novel quantum states and the measurement of those states is driven by both fundamental and technological goals. For example, the study of Schrodinger cat states touches upon the basic measurement hypotheses of quantum mechanics while the establishment of particular coherent superposition states is the starting point for the process of coherent control or for quantum information applications. The goals of the design research range from the manipulation of reaction pathways to the creation of novel states for the exploration of aspects of measurement theory. In addition to its fundamental interest the accurate measurement of both amplitude and phase of a wave function plays a key roles in the area of coherent control. The seminal work by Risken and Vogel (1989) reopened the modern discussion of the reconstruction problem that was first broached by Pauli. Since their work, reconstruction techniques have been developed for a variety of systems including the optical field in atomic systems. The measurement scheme used in the paper employs a noninterferometric technique. The subject of the measurement is a designed Rydberg wave packet in an atomic system. However, the noninterferometric character of the technique suggests that this technique may have wide applicability.

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The short-pulse dynamics of excitation and stimulated emission between highly excited states $(15<n<60)$ is studied with picosecond far-infrared pulses (40--60 $\ensuremath{\mu}\mathrm{m}$) originating from a free electron laser. We measured the excitation of a Rydberg wave packet in rubidium around $n=40$ excited from a deeper bound $(n\ensuremath{\approx}20)$ Rydberg state by a picosecond far-infrared laser pulse. Moreover, starting from a stationary $n=40$ state we found that upon irradiating with a short far-infrared laser pulse, adjacent Rydberg states are populated by resonant Raman transfer via a deeper $(n=20)$ bound state. Finally, we discuss the dynamics of wave-packet excitation at a Cooper minimum in lithium, where sign change of the excitation matrix elements causes excitation at large distances from the atomic core. Possible measurement methods for this effect are discussed and found to yield different information.

Physical Review A•Jun 1, 1998•8 citations
When a coherent superposition of Rydberg states is excited by a laser pulse, a Rydberg wave packet is created. These wave packets are supremely quantum mechanical objects. However, they can be constructed to display classical, nearly classical, or semiclassical behavior, and thus serve as a natural bridge between the microscopic and mesoscopic worlds. In addition, their comparative simplicity allows detailed studies of the fundamental interactions of light with matter. The authors of this focus issue were invited to submit papers that reflect both the range of dynamical behavior exhibited by Rydberg wave packets, and the depth of understanding of them that is possible with current experiments and theory. In particular, the papers in this issue illustrate the possibility that emerging laser technology can be used not only to observe quantum behavior, but also to control it.
Rydberg atoms are atoms with a highly excited electron. In his Perspective, Villeneuve explains that by creating a coherent superposition of Rydberg states, the electron can be made to behave almost like a classical Rutherford atom. He highlights the report by Maeda et al., who show that they can force the electron wave packet to remain localized for thousands of highly elliptical orbits around the nucleus, much like a miniature planetary system. Such experiments help to bridge the gap between the quantum mechanical world and our everyday classical world.
Summary form only given. Design and excitation of novel quantum states and the measurement of those states is driven by both fundamental and technological goals. For example, the study of Schrodinger cat states touches upon the basic measurement hypotheses of quantum mechanics while the establishment of particular coherent superposition states is the starting point for the process of coherent control or for quantum information applications. The goals of the design research range from the manipulation of reaction pathways to the creation of novel states for the exploration of aspects of measurement theory. In addition to its fundamental interest the accurate measurement of both amplitude and phase of a wave function plays a key roles in the area of coherent control. The seminal work by Risken and Vogel (1989) reopened the modern discussion of the reconstruction problem that was first broached by Pauli. Since their work, reconstruction techniques have been developed for a variety of systems including the optical field in atomic systems. The measurement scheme used in the paper employs a noninterferometric technique. The subject of the measurement is a designed Rydberg wave packet in an atomic system. However, the noninterferometric character of the technique suggests that this technique may have wide applicability.
Quantum excitation is usually regarded as a transient process occurring instantaneously, leaving the underlying physics shrouded in mystery. Recent research shows that Rydberg-state excitation with ultrashort laser pulses can be investigated and manipulated with state-of-the-art few-cycle pulses. We theoretically find that the efficiency of Rydberg state excitation can be enhanced with a short laser pulse and modulated by varying the laser intensities. We also uncover new facets of the excitation dynamics, including the launching of an electron wave packet through strong-field ionization, the re-entry of the electron into the atomic potential and the crucial step where the electron makes a U-turn, resulting in twin captures into Rydberg orbitals. By tuning the laser intensity, we show that the excitation of the Rydberg state can be coherently controlled on a sub-optical-cycle timescale. Our work paves the way toward ultrafast control and coherent manipulation of Rydberg states, thus benefiting Rydberg-state-based quantum technology.
Quantum mechanics, though a probabilistic theory, gives a 'deterministic' answer to the question of how the present determines the future. In essence, in order to predict future probabilities, we need to (numerically) propagate the time-dependent Schrödinger equation from the present to the future. It is interesting to note that classical mechanics of macroscopic bodies, though reputed to be a deterministic theory, does not allow, due to chaos (which unfortunately is more prevalent than integrability), such clear insights into the future. In contrast, small (e.g., atomic, molecular and photonic) systems which are best understood using the tools of quantum mechanics, do not suffer from chaos, rendering the prediction of the probability-distributions of future events possible. The field of quantum control deals with an important modification of this task, namely, it asks: given a wave function in the present, what dynamics, i.e. what Hamiltonian, guarantees a desired outcome or 'objective' in the future? In practice one may achieve this goal of modifying and finding the desired Hamiltonian by introducing external fields, e.g. laser light. It is then possible to reach the objective in a 'trial-and-error' fashion, performed either numerically or in the laboratory. We can guess or build a Hamiltonian, do an experiment, or propagate the initial wave function to the future, compare the result with the desirable objective, and correct the guess for the Hamiltonian until satisfactory agreement with the objective is reached. A systematic way of executing this procedure is the sub-field called 'optimal control'. The trial-and-error method is often very time consuming and rarely provides mechanistic insight. There are situations where analytical solutions exist, rendering the control strategies more transparent. This is especially so when one can identify quantum interferences as the heart of quantum control, the essence of the field called 'coherent control'. The experience accumulated so far by many groups is that quantum interferences are the mechanism underlying most successful control scenarios and control experiments. The identification of the control mechanism is especially facile when the time-dependence of the Hamiltonian merely serves to prepare a state which then evolves in the absence of external fields. Analytical theories also exist when the explicit time dependence of the Hamiltonian can be treated adiabatically. Under these circumstances one can identify the quantum interfering pathways that lead to control, allowing for the simultaneous exploration of entire 'landscapes' (and not just a single 'desirable' objective) resulting from varying all the experimental 'knobs' at our disposal, e.g., relative- and envelope-phases, intensities, polarizations, and pulse-sequencing. Such 'pulse-shaping' knobs are now available down to the sub-femtosecond regime in broad spectral regions ranging from the UV to the IR. We expect that comprehensive investigations of the quantum interference required to control dynamical processes will result in a more detailed understanding of the dynamics themselves. Together with experimental progress---the stage is now set for many exciting applications in fundamental and applied sciences by 'tailoring' light--matter interactions essentially at will.
The short-pulse dynamics of excitation and stimulated emission between highly excited states (15<n<60)(15<n<60)(15<n<60) is studied with picosecond far-infrared pulses (40--60 $\ensuremath{\mu}\mathrm{m}$) originating from a free electron laser. We measured the excitation of a Rydberg wave packet in rubidium around n=40n=40n=40 excited from a deeper bound $(n\ensuremath{\approx}20)$ Rydberg state by a picosecond far-infrared laser pulse. Moreover, starting from a stationary n=40n=40n=40 state we found that upon irradiating with a short far-infrared laser pulse, adjacent Rydberg states are populated by resonant Raman transfer via a deeper (n=20)(n=20)(n=20) bound state. Finally, we discuss the dynamics of wave-packet excitation at a Cooper minimum in lithium, where sign change of the excitation matrix elements causes excitation at large distances from the atomic core. Possible measurement methods for this effect are discussed and found to yield different information.