PT-Symmetric Quantum Mechanics

Since the seminal papers by Prof. Carl Bender et al [1], one of the key axioms underlying the theory of quantum mechanics has been generalized. In conventional quantum mechanics the Hamiltonian is Hermitian; this mathematical condition is imposed to ensure that the eigenvalues of the Hamiltonian are all real and therefore observable [2]. Prior to the above articles, the condition of Hermiticity has been regarded as necessary for the description of physical systems. However, Prof. Bender has shown that if the Hamiltonian is non-Hermitian but PT symmetric, its eigenvalues may still be all real in some parametric region and thus describe an experimentally accessible system. In addition, there may exist another parametric region of the Hamiltonian, in which the eigenvalues are not all real. The boundary between these regions is a phase transition that is observable. Recently, this transition from the PT symmetric to the PT broken phase was observed in various experimental settings [3]. These observations have moved the field from the theoretical drawing board to the laboratory and stipulate the physical relevance of PT symmetric Hamiltonians. 

The extension of conventional Hermitian quantum mechanics to allow for PT symmetric Hamiltonians has far-reaching consequences for all fields of physics. The purpose of this symposium is to bring together experimentalists and theoreticians in different fields of physics who are actively doing research in this rapidly developing area. Particular emphasis will be on very recent progress, both in theory and experiment, and on the possible implications of PT symmetric quantum mechanics. 

Interdisciplinarity 

Quantum mechanics lies at the heart of all of physics and has striking implications for modern technology. Consequently, any possible extension of, or new developments in quantum mechanics immediately affects many branches of science and technology. As such, the members of this symposium have their background in differing fields of physics such as quantum optics, high-energy physics, atomic physics, and nanotechnology. 

Current Status of Research 

In the past 18 months, the two first experiments ever were published [3], that observed a (classical) PT phase transition, as predicted by one of the organizers of this symposium. This in itself opens up  a wide range of research for the future, as these experimentalists consider synthesizing integrated PT symmetric photonic devices capable of double refraction or tailored energy flows that can be used as a new generation of optical isolators and light-beam steering components. Further extensions into the spatiotemporal domain are also envisaged.  

Following the publication of these experiments and their implications, there has been much excitement in the field and the discussion about the necessity of extensions into quantum mechanical systems has grown rapidly. New experiments, targeted at obtaining the first evidence of a quantum PT symmetric phase transition are currently being carried out all over the world, including here in Heidelberg by one of the organizers of this symposium (MDK). This symposium aims to gather a select number of researchers active in the field for intensive exchange at a high level.

International Networking

This symposium is a key event within the framework of the Excellence Initiative - "Global Networks / Joint Appointments" of the University of Heidelberg, which, through the direct grant to Prof. C. Bender, sponsors this meeting. Scientifically the symposium should encourage and intensify discussions between different research groups and disciplines within the worldwide academic network. It is absolutely crucial that communication and exchange is fast and effective in this rapidly developing area of physics. 

Contact:
Prof. Dr. Maarten DeKieviet
Physikalisches Institut
Universität Heidelberg
Philosophenweg 12
69120 Heidelberg
Telefon: +49 (0) 6221 54 9356
E-Mail: maarten.dekieviet@physi.uni-heidelberg.de

Current literature 

The seminal papers that founded the field of PT symmetric quantum mechanics are listed in [1] and [2]. From an experimental point of view, the first important papers are those by Guo, Rüter, and Kottos et al [3,4]. More recent experimental work is reported in [5-10] and recent theoretical developments in [11-20]. This list of references ([5-20]) underlines the breadth of PT symmetric research and includes analyses on pattern formation, graphene ribbons, atomic diffusion, Bose-Einstein condensates, neutrino oscillations, cosmological inflation, the existence of families of particles, laser absorption, quantum noise, periodic potentials, superconducting weak links, and high temperature quantum field theory. 

[1] C.M. Bender and S. Boettcher, Physical Review Letters 80, 5243 (1998)

C.M. Bender, D. Brody, and H. Jones, Physical Review Letters 89, 270401 (2002)

C.M. Bender, D. Brody, and H. Jones, Physical Review Letters 93, 251601 (2004)

C.M. Bender, Reports on Progress in Physics 70, 947 (2007)

[2] P. Dorey, C. Dunning, and R. Tateo, Journal of Physics A 34, 5679 (2001)

P. Dorey, C. Dunning, and R. Tateo, Journal of Physics A 40, R205 (2007)

[3] A. Guo, G.J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G.A. Siviloglou, and D.N. Christodoulides, Physical Review Letters 103, 093902 (2009)

C.E. Rüter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, and D. Kip, Nature Physics 6, 192 (2010)

[4] T. Kottos, Nature Physics 6, 166 (2010)

[5] K.F. Zhao, M. Schaden, and Z. Wu, Physical Review A 81, 042903 (2010)

[6] N.M. Chtchelkatchev, A.A. Golubov, T.I. Baturina, and V.M. Vinokur, arXiv:1008.3590v2 (2010)

[7] Z. Yan, B. Xiong, and W-M Liu, arXiv:1009.4023v1 (2010)

[8] K. Li, and P.G. Kevrekidis, arXiv:1102.0809v1 (2011)

[9] M. Fagotti, C. Bonati, D. Logoteta, P. Marconcini, and M. Macucci, arXiv:1102.2129v1

[10] A.D. Stone, Y.D. Chong, L. Ge, and H. Cao, http://www.pqeconference.com/pqe2011/abstractd/170.pdf

[11] E. Graefe, H. Korsch, and A. Niederle, Physical Review Letters 101, 150408 (2008)

[12] S. Klaiman, U. Günther, and N. Moiseyev, Physical Review Letters 101, 230404 (2008)

[13] O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Physical Review Letters 103, 030402 (2009)

[14] S. Longhi, Physical Review Letters 103, 123601 (2009)

[15] H. Schomerus, Physical Review Letters 104, 233601 (2010)

[16] S. Longhi, Physical Review Letters 105, 1013903 (2010)

[17] C. West, T. Kottos, T. Prosen, Physical Review Letters 104, 054102 (2010)

[18] Jones-Smith, K. and Mathur, H.: arXiv:0908.4257v1 [hep-th]

[19] Bender, C.M. and Klevansky, S. P.: Phys. Rev. Lett. 105, 031601 (2010)

[20] Y. Wang private communication