Manifesto of Many-Body Open Quantum Systems Community

The scientific community is witnessing the birth of a new area of physics that will supplement traditional macrophysics of large systems and physics of the micro-world, namely mesoscopic physics. This name can be applied to systems that are sufficiently large to display generic statistical behavior but at the same time sufficiently small to allow researchers to study in detail individual quantum states. The general challenge for theory of mesoscopic systems is to understand the principles of building up complexity out of “elementary” blocks, which in fact have a complicated structure of their own.


Small quantum systems, whose properties are profoundly affected by environment, i.e., continuum of scattering and decay channels, are intensely studied in various fields of physics (nuclear physics, atomic and molecular physics, nanoscience, quantum optics, etc.). These different open quantum systems (OQS), in spite of their specific features, have generic properties, which are common to all weakly bound/unbound systems close to the threshold. While many of those phenomena have been originally studied in nuclear reactions, it is not possible to experimentally control the behavior of the nucleus by varying external parameters as in, e.g., atoms and molecules, quantum dots, or microwave resonators. Here, the new quality of precision tabletop experiments have been recently achieved to study and prove fundamental quantum-mechanical laws that govern OQSs. For instance, the exact mapping between observed eigenstates of the Schrödinger equation in microwave experiments (as well as in certain experiments in quantum optics) allows to view the microwave resonator as an analog computer solving the Schrödinger equation in different regimes of level densities. This analogy can be further used, e.g., to test assumptions of the compound-nucleus reaction theory in the microwave resonator experiments.


A) Nuclear Physics Context


Nuclear physics contains the core of sub-atomic science with main focus on self-organization and stability of nucleonic matter. Nuclei themselves are prototypical mesoscopic OQSs and splendid laboratories of many-body physics. While the number of degrees of freedom in heavy nuclei is large, it is still very small compared to the number of electrons in a solid or atoms in a mole of gas. Nevertheless, nuclei exhibit behaviors that are emergent in nature and present in other complex systems. Moreover, nuclear properties are profoundly affected by environment, i.e., the many-body continuum representing scattering and decay channels.


The history of nuclear physics, an essential element in the history of our times – the atomic age, shows a field driven by experimental discoveries and radiation phenomena. This was Nature’s way of opening up the nuclear quantum world, starting with natural emission of alpha particles, electrons and gammas, followed by emission of neutrons and fission and in the last two decades the discovery and production of nuclei with exotic properties (such as halos, proton-, and cluster emitters) in Radioactive Nuclear (Ion) Beam (RNB/RIB) experiments. Cold and strongly diluted nucleonic matter having large neutron-to-proton asymmetry is created and investigated in dripline nuclei, i.e. nuclei at the very limits of nucleonic binding. Thus an essential part of the motion of those exotic systems is in classically forbidden regions, and their properties are profoundly impacted by both the continuum and many-body correlations, see Fig. 1.




Fig. 1. Schematic diagram illustrating various aspects of physics important in neutron-rich nuclei. One-neutron separation energies, Sn, relative to the one-neutron drip-line limit (Sn=0), are shown for some isotopic chain as a function of the neutron number. The unbound nuclei beyond the one-neutron drip line are resonances. Their widths (represented by a dark area) vary depending on excitation energy and angular momentum. At low excitation energies, well-bound nuclei can be considered as closed quantum systems (QS). Weakly bound (and unbound) nuclei, such as halos, are open quantum systems that are strongly coupled to the environment of scattering and decay channels. The region of particularly strong many-body correlations is indicated. The astrophysical r-process is expected to proceed in the region of low separation energies, around 2-4 MeV. In this region, effective interactions are strongly affected by isospin, and the many-body correlations and continuum effects are essential.


A unifying theme in the studies of transient nucleonic matter is: (i) How to create it; (ii) How it evolves; and (iii) How does the coupling to the environment of scattering and decay channels affect its properties. Thus a simultaneous understanding of the structural and reaction aspects is at the very hearth of understanding short-lived nucleonic matter. By studying the limits of nuclear existence we also improve our understanding of the ordinary nuclei around us, extending the nuclear paradigm. As compared to the other mesoscopic systems, research with nuclei offers a number of advantages. The temperature is zero; the number of constituents is known; setting the nucleus into rapid rotation can simulate the effect of strong magnetic fields. Many aspects of open quantum systems that are independent of the system dimensionality have been originally studied in nuclear reactions and now they are explored in molecules in strong external fields, quantum dots and wires and other solid-state micro-devices, crystals in laser fields, and microwave cavities.


B) Atomic Molecular, and Optical Physics Context

Many splendid manifestations of mesoscopic physics can be found in quantum optics. Over the last decades, quantum optics has become truly interdisciplinary field dealing with genuine many-body systems. In its youth, quantum optics was called quantum electronics and dealt with the interaction of classical light and quantum matter. With the development of ion and atom traps as well as high Q-cavities in the microwave and optical regime, quantum electronics evolved into quantum optics. Henceforth, measurements of a single quantum system or the observation of quantum jumps between atomic levels of a single ion became possible. Today, the emphasis is on playing the game of quantum Lego where one starts from well-controlled individual quantum systems, let them interact with each other and build hereby a new quantum system with properties very different from the individual building blocks. One such example is represented by entangled states which result from the interaction of two or more quantum systems. In order to arrive at a very specific state we need to search for an interacting many-body system where we have access to and control over every degree of freedom. So far very few quantum systems have allowed such an intrusion. Two photons emerging from a non-linear crystal with their polarizations entangled constitute one such example of complete control. These two-photon entangled states are the work horse of many phenomena in quantum optics, such as teleportation, quantum cloning and quantum communication to name just a few.

Likewise, the field of ultra-cold atoms stored in optical traps has created a new area of research at the borderline of quantum optics and solid state physics. The interaction potentials between cold atoms can be effectively controlled with the help of Feshbach resonances by tuning a magnetic field. As a consequence, we now have a many-body system at our disposal where we can design at will the interaction between the individual particles driving them even into a quantum degenerate situation. In this way new diatomic molecules have been formed out of an ensemble of cold atoms. The formation of Cs­3 cluster of atoms allowed for the first time to confirm the elusive Efimov effect which was searched for in nuclear systems and in helium clusters for decades. Strong ties between cold atoms and nuclear physics can also be demonstrated in the scattering of a BEC off another BEC which is reminiscent of the scattering of two nuclei from each other. Collective excitations in cold atoms are yet another phenomena with interesting connections to nuclear physics.


C) Condensed Matter Physics Context

In spite of the fact that quantum dots (QDs) behave as artificial atoms and arrays of QDs behave as artificial molecules, not much is known about electron correlations in QDs. For example, even the Hund's rules for QDs are not explored until now. The main difference between QDs and real atoms and molecules is that in QDs the number of bound states is finite. Therefore, it might be possible to see one-electron excitations from the most diffused orbital resulting in a resonance state rather than a true bound state.


2D quantum dots bear some resemblance to 2D waveguides. In the 2D waveguides, microwave experiments have shown the existence of exceptional points associated with self-orthogonal eigenfunctions of the non-Hermitian Hamiltonian. Indirect effects of exceptional points have been reported in electron scattering from hydrogen molecule, where the self-orthogonality phenomenon may lead to an unexpected long-lived electron trapping by a hydrogen molecule. Can one find a similar phenomenon in QDs? The fingerprints of exceptional points in QDs should be seen in electron transitions through QDs and their arrays. An inter-disciplinary expertise could largely enrich research of those phenomena in QDs.



D) Computational Science and Mathematical Context


One of the most striking trends in physics today is the increasingly important role played by computational science. Young nuclear theorists nowadays often refer to themselves as computational physicists, reflecting not only a practical need and aspect of their work, but also a desire to emphasize that they belong to a much larger community, MBOQS being a manifestation of this. Thanks to computational advances, fundamental questions that earlier had to be left behind can now be addressed and reliable and quantitative predictions can be made. We are witnessing a cross fertilization along the full atomic to sub-atomic axis, where methods born in one area are exported to another area and domain. Fundamental questions related to MBOQS, such as decaying multi-particle resonances, bound states embedded in the continuum, threshold phenomena, and exceptional points, involve issues of interest also in the mathematical community: non-Hermitian operators and the rigged quantum mechanics. Some of the interdisciplinary connections in the MBOQS science are:




Scientists dealing with many-body phenomena have been traditionally in the forefront of interdisciplinary inquiry and collaboration and this is even more so today. Many-body science is as broad as ever; it forms the intellectual bridge between the very large and the very small in our natural world; it is a natural connector between fundamental and complex. The goal of the Many Body Open Quantum Systems community, described in this manifesto, is to establish and strengthen connections in the area of open mesoscopic systems across the frontiers of various fields of science in order to exchange knowledge and ideas, and look for new generic phenomena.