518. WE-Heraeus-Seminar: Quantum-Optical Analogies: A Bridge Between Classical and Quantum Physics

Scientific background:

Analogy is a basic concept for understanding nature, since it analyses and connects different phenomena linked by common properties or similar behavior. In particular, analogy can to some extent apply to specific quantum phenomena and their corresponding classical effects, although quantum physics differs from classical physics in both formalism and fundamental concepts. In particular, the analogies between classical physical theories and quantum phenomena reveal the fact that similar mathematical formalisms apply to phenomena that cannot be related in all aspects and are a priori conceptually different. The role of mathematics is crucial, because the essence of the analogy resides in the fact that completely different systems can be modeled by similar mathematical equations. However, one aspect of quantum physics that has no counterpart in classical physics is the collapse of the wave function associated with the measurement process.

Quantum-classical analogies are a source of understanding and further developments of quantum physics. Indeed, many quantum physical concepts have originated from classical notions: a striking example is given by the non-relativistic Schrödinger equation, whose roots are found in classical optical concepts.

In particular, analogies between wave optics and quantum mechanics have been highlighted since the early days of quantum mechanics: wave effects like interference and diffraction were borrowed from optics and applied to demonstrate the wavy nature of quantum particles, as electrons, neutrons and atoms. After the full development of quantum theory and the rise of coherent light sources, the exchange of concepts in the opposite direction started to occur [1-2].

In the last few years, experimental and theoretical investigations of quantum-optical analogies have seen a brilliant revival, especially in engineered optical waveguide structures (which have proven themselves to provide a very rich laboratory tool to study with optical waves the classical analogues of a wide variety of coherent quantum effects typical of atomic, molecular or condensed-matter physics: see Ref.[3] for a review of these analogies) or in other engineered electromagnetic systems, such as metamaterials and plasmonic devices, where problems like Fano resonances[4] and Electromagnetic Induced Transparency [5] have been recently studied.

Accessing and understanding these coherent phenomena in a real microscopic system is, in fact, very challenging because of complications arising from many-body effects, decoherence and nonlinearities; studying classical wave optics analogues which accurately model the striking signatures gives the possibility to overcome these non-idealities.

Moreover, thanks to the formal analogy between the Schrödinger equation of a quantum system and the paraxial wave equation of light that propagates in a guiding structure, quantum-optical analogies can provide a useful laboratory tool to easily visualize the temporal evolution of a quantum system, a task that in a real microscopic system is very challenging, due to the presence of many-body effects and decoherence,

The possibility to mimic at a classical level the dynamics of a quantum system created a wide amount of literature in the past years that dealt with such analogies. In order to better navigate through this vast literature, a division in category of interest could be very useful.

A first category of such analogies regards general issues of quantum mechanics and quan- tum information and include topics as Aharonov-Bohm and Berry phase [6], spin Hall effect [7] (recently observed even for photons in tilted paraxial beams [8]), classical simulators of entanglement and random walks [9], decay of metastable state via the continuum and the Zeno effect [10-11], and wave dynamics in non-Hermitian quantum systems with parity-time symmetry [12- 15]; this last topic, for example, is of great interest nowadays, since it gives the possibility to directly study a relatively new aspect of quantum mechanics that has not yet found a counterpart in a real microscopic system, and at the same time they give the possibility to exploit concepts from quantum mechanics to engineer the flow of light in guiding structures with novel techniques.

A second category of optical analogies deals with coherent effects of atoms and molecules driven by laser fields, such as Rabi oscillations [16], adiabatic transfer of population between atomic levels [17] and stabilization in ultra-strong laser field [18].

A third category deals with problems related to solid-state physics, like Bloch oscillations [19-20], Zener tunneling [21], Anderson localization [22], dynamical localization and surface physics [23-24], to name a few.

Very recently, the study of these analogies covered even the field of relativistic quantum mechanics, mimicking the effects of Klein tunneling [25] (that was also recently observed in gra- phene heterojunctions [26]), Zitterbewegung [27-28], pair production [29], Hermitian and non-Hermitian dynamics in the relativistic domain [30-31], propagation of non-classical light in these structures [32] and the realization of Glauber-Fock lattices [33] were also considered.

Quantum-optical analogies constitute then a very powerful bridge between the world of quantum physics and waveguide optics, opening a path that can allow the transfer of concepts from optics to quantum physics and vice versa, then creating the possibility to improve, from one side, the control of light flow in guiding structures by using quantum protocols or, on the other side, finding new ways to access real quantum systems.

Aims:

This seminar which is kindly supported by the Wilhem and Else Heraeus Foundation will try to bring together experts from the diverse communities that are working in the topics of quantum-optical analogies, quantum physics and quantum optics. From the early pioneers, to the current researchers in the field, experts of complementary experience and knowledge, both theoretical and experimental, will be invited.

The main aim of this seminar would be to create strong interactions between these areas of physics, in order to bring new ideas, developments and collaborations between these fields.

The seminar is intended to provide a good introduction for newcomers in the field of quantum-optical analogies and a good occasion for people from the area of quantum physics and quantum optics that are interested in exploring and exploiting the potential applications of these methods and frameworks.

Thus the seminar will be a good opportunity for PhD students and young postdocs to get introduced to this exciting field. Bringing together an international group of young researchers will further initiate mutually beneficial exchanges between these groups and can be expected to stimulate stringer collaborations in the field between the participating research groups.

List of invited speakers:

D. N. Christodoulides, CREOL College of Optics, University of Central Florida, USA
G. Della Valle, Polytechnic Institute of Milan, Italy
D. Dragoman, University of Bucharest, Romania
J. H. Eberly, University of Rochester, USA
Y. Lahini, Weizmann Institute of Science, Israel
F. Lederer, Institute of Condensed Matter Theory and Solid State Optics, Jena
S. Longhi, Polytechnic Institute of Milan, Italy
J. Meinecke, Center of Quantum Photonics, Bristol
A. Mostafazadeh, Koc University, Turkey
U. Peschel, Max Planck Institute for the Science of Light, Erlangen
L.L. Sanchez-Soto, University of Madrid, Spain
B. Sanguinetti, Gap Optique, University of Geneva, Switzerland
W. P. Schleich, Institute for Quantum Physics, Ulm
A, Schreiber, University of Padeborn, Germany
M. Segev, Technion, Israel Institute of technology, Israel
R. J. C. Spreeuw, Van der Wals-Zeeman Institute, Amsterdam
C. Silberhorn, Unversity of Padeborn, Germany
A.A. Sukhorukov, Nonlinear Physics Center, Australian National University, Australia
A.Szameit, Institute of Applied Physics, Jena
J. P. Woerdman, University of Leiden, Netherlands