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arXiv:cond-mat/0407226

The Jahn-Teller Efect: A Permanent Presence in the Frontiers of Science

R. Englman, Asher Yahalom A

Published Jul 9, 2004• 0 citations
arXivHTMLPDF

Abstract

In 1937 the Jahn-Teller (JT) effect addressed the instability (potential or actual) of non-linear symmetric molecules with degenerate orbital electronic states. In view of the large variety of JT activity that has taken place since then, we might broaden our perspective to look at works whose subjects fall under the more general heading of "Strong interactions between two dissimilar systems" (where one system is usually bosonic and the other fermionic). In these intervening years we find several highly important works in Physics and Chemistry that come under this heading and were either connected with, or arose from, JT systems, problems and approaches. Apart from high temperature superconductors, we mention Yang-Mills gauge-forces, symmetry breaking (in elementary particles), conical intersections in molecular potential surfaces, surface crossings between them in chemical reactions, entanglements in the quantum theory of measurements and Berry phases. We elaborate on the last two topics. We show first that the slow evolution of a Txe coupling from the weak to strong regime can model the quantum mechanical three-state measurement situation, when the positions of the nuclei acts as the measuring device. We then employ recently derived integral relations between component moduli and phases in a time dependent wave-function to demonstrate the equivalence between the state-reduction and the phase decoherence interpretations of the measurement process.

DOI
10.48550/arxiv.cond-mat/0407226

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In 1937 the Jahn-Teller (JT) effect addressed the instability (potential or actual) of non-linear symmetric molecules with degenerate orbital electronic states. In view of the large variety of JT activity that has taken place since then, we might broaden our perspective to look at works whose subjects fall under the more general heading of "Strong interactions between two dissimilar systems" (where one system is usually bosonic and the other fermionic). In these intervening years we find several highly important works in Physics and Chemistry that come under this heading and were either connected with, or arose from, JT systems, problems and approaches. Apart from high temperature superconductors, we mention Yang-Mills gauge-forces, symmetry breaking (in elementary particles), conical intersections in molecular potential surfaces, surface crossings between them in chemical reactions, entanglements in the quantum theory of measurements and Berry phases. We elaborate on the last two topics. We show first that the slow evolution of a Txe coupling from the weak to strong regime can model the quantum mechanical three-state measurement situation, when the positions of the nuclei acts as the measuring device. We then employ recently derived integral relations between component moduli and phases in a time dependent wave-function to demonstrate the equivalence between the state-reduction and the phase decoherence interpretations of the measurement process.
We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics , we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.
We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit-coupled Bose-Einstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the $E\ifmmode\times\else\texttimes\fi{}\ensuremath{\epsilon}$ Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection is studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of the system is addressed and we verify how it affects the dynamics.
Jahn-Teller systems and the Jahn-Teller effect are discussed in terms of cavity QED models. By expressing the field modes in a quadrature representation, it is shown that certain setups of a two-level system interacting with a bimodal cavity are described by the Jahn-Teller $E\ifmmode\times\else\texttimes\fi{}\ensuremath{\epsilon}$ Hamiltonian. We identify the corresponding adiabatic potential surfaces and the conical intersection. The effects of a nonzero geometrical Berry phase, governed by encircling the conical intersection, are studied in detail both theoretically and numerically. The numerical analysis is carried out by applying a wave packet propagation method, more commonly used in molecular or chemical physics, and analytic expressions for the characteristic time scales are presented. It is found that the collapse-revival structure is greatly influenced by the geometrical phase and as a consequence, the field intensities contain direct information about this phase. We also mention the link between the Jahn-Teller effect and the Dicke phase transition in cavity QED.
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions, driven by experiments on cuprate superconductors, heavy fermion materials, organic conductors, and related compounds. Although quantum phase transitions in simple spin systems, like the Ising model in a transverse field, were studied in the early 1970s, much of the subsequent theoretical work examined a particular example: the metal–insulator transition. While this is a subject of considerable experimental importance, the greatest theoretical progress was made for the case of the Anderson transition of non-interacting electrons, which is driven by localization of the electronic states in the presence of a random potential. The critical properties of this transition of noninteracting electrons constituted the primary basis upon which most condensed matter physicists have formed their intuition on the behavior of the systems near a quantum phase transition. However, it is clear that strong electronic interactions play a crucial role in the systems of current interest noted earlier, and simple paradigms for the behavior of such systems near quantum critical points are not widely known. It is the purpose of this book to move interactions to center stage by describing and classifying the physical properties of the simplest interacting systems undergoing a quantum phase transition. The effects of disorder will be neglected for the most part but will be considered in the concluding chapters. Our focus will be on the dynamical properties of such systems at nonzero temperature, and it will become apparent that these differ substantially from the noninteracting case.
We study the polaritonic states and dynamics of multiple Jahn-Teller (JT) active molecules coupled to the modes of a Fabry-Perot cavity. We find that collective effects dramatically alter the interplay of electronic, vibrational and cavity angular momenta, giving rise to markedly different polaritonic spectra and dynamics even when going from one to two JT molecules. Starting from the ground vibronic state, we find that JT molecules collectively coupled to a common cavity can access a cascade of high-angular-momentum vibronic states in the presence of a single cavity photon, in sharp contrast to the single molecule case where the range of accessible vibronic angular momentum values are bounded. The observable consequences are a broadening of the cavity-molecular polariton spectrum and a suppression of photon polarization dynamics under broadband excitation of the system. Our results uncover new pathways for vibronic angular momentum transfer unique to collective molecular polaritonics with potential implications for cavity-assisted photo-physics and photo-chemistry.
The Jaynes-Cummings (JC) model has been at the forefront of quantum optics for almost six decades to date, providing one of the simplest yet intricately nonlinear formulations of light-matter interaction in modern physics. Laying most of the emphasis on the omnipresence of the model across a range of disciplines, this monograph brings up the fundamental generality of its formalism, looking at a wide gamut of applications in specific physical systems among several realms, including atomic physics, quantum optics, solid-state physics and quantum information science. When bringing the various pieces together to assemble our narrative, we have primarily targeted researchers in quantum physics and quantum optics. The monograph also comprises an accessible introduction for graduate students engaged with non-equilibrium quantum phase transitions, quantum computing and simulation, and quantum many-body physics. In that framework, we aim to reveal the common ground between physics and applications scattered across literature and different technological advancements. The exposition guides the reader through a vibrant field interlacing quantum optics and condensed-matter physics. All sections are devoted to the strong interconnection between theory and experiment, historically linked to the development of the various modern research directions stemming from JC physics. This is accompanied by a comprehensive list of references to the key publications that have shaped its evolution since the early 1960s. Finally, we have endeavored to keep the presentation of such a multi-sided material as concise as possible, interspersing continuous text with various illustrations alongside an economical use of mathematical expressions.