Georgios Kordas

Publications

2019


1. Reply to “Comment on ‘Coherent-state path integrals in the continuum’”.
   G. Kordas, S. I. Mistakidis and A. I. Karanikas
   Physical Review A, 99 (2019) 026102.

   
   Abstract
   In this Reply we briefly clarify the main points of our method to construct coherent-state path integrals in the continuum and we reply to the critique raised by in the preceding Comment by Kochetov [Phys. Rev. A 99, 026101 (2019)]. By using definite examples, we prove that our approach is capable of resolving the inconsistencies accompanying the standard coherent-state path-integral representation of interacting systems.
   
   


2018


2. Mean-field dynamics of a Bose-Hubbard chain coupled to a non-Markovian environment.
   G. Kordas, G. E. Pavlou and A. I. Karanikas
   Physical Review A, 98 (2018) 013637.
   arXiv:1808.01253
   

   
   Abstract
   We study the dynamics of an interacting Bose-Hubbard chain coupled to a non-Markovian environment. Our basic tool is the reduced generating functional expressed as a path integral over spin-coherent states. We calculate the leading contribution to the corresponding effective action, and by minimizing it, we derive mean-field equations that can be numerically solved. With this tool at hand, we examine the influence of the system's initial conditions and interparticle interactions on the dissipative dynamics. Moreover, we investigate the presence of memory effects due to the non-Markovian environment.
   
   


2016


3. Coherent-state path integrals in the continuum: The SU(2) case.
   G. Kordas, D. Kalantzis and A. I. Karanikas
   Annals of Physics, 372 (2016) 226.
   arXiv:1605.06757
   

   
   Abstract
   We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
   
   


2015


4. Dissipative Bose-Hubbard model: Methods and examples.
   G. Kordas, D. Witthaut, P. Buonsante, A. Vezzani, R. Burioni, A. I. Karanikas and S. Wimberger
   European Physical Journal ST, 224 (2015) 2127. Review Article.
   arXiv:1510.00127
   

   
   Abstract
   Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.
   
   
5. Entropy generation in Gaussian quantum transformations: applying the replica method to continuous-variable quantum information theory.
   C. N. Gagatsos, A. I. Karanikas, G. Kordas and N. J. Cerf
   npj Quantum Information, 2 (2015) 15008.
   arXiv:1408.5062
   

   
   Abstract
   In spite of their very simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations in quantum optics remain poorly understood in terms of entropies. For instance, determining the von Neumann entropy produced by an optical beam splitter or a two-mode squeezer is notably a hard problem, with generally no known analytical solution. Here, we overcome this difficulty by using the replica method, a tool borrowed from statistical physics and quantum field theory. We find a first application of this method to the field of quantum optics, where it enables accessing the entropic characteristics of the Bogoliubov transformation effected by a two-mode squeezer or optical amplifier. In particular, we determine the entropy produced by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple analytical expression.
   
   
6. Non-equilibrium dynamics in dissipative Bose-Hubbard chains.
   G. Kordas, D. Witthaut and S. Wimberger
   Annalen der Physik, 527 (2015) 619. Special issue: Complex Quantum Systems.

   
   Abstract
   Open many-body quantum systems have recently gained renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. A series of results in diverse setups is presented, based on a Master equation approach to describe the dissipative dynamics of ultracold bosons in a one-dimensional lattice. The creation of mesoscopic stable many-body structures in the lattice is predicted and the non-equilibrium transport of neutral atoms in the regime of strong and weak interactions is studied.
   
   


2014


7. Coherent-state path integrals in the continuum.
   G. Kordas, S. Mistakidis and A. I. Karanikas
   Physical Review A, 90 (2014) 032104.
   arXiv:1408.3210
   

   
   Abstract
   We discuss the time continuous path integration in the coherent-state basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and nonperturbative approximations already known in the quantum-field-theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.
   
   


2013


8. Bosonic transport through a chain of quantum dots.
   A. Ivanov, G. Kordas, A. Komnik and S. Wimberger
   European Physical Journal B, 86 (2013) 345. EPJ B Highlight.
   arXiv:1304.5503
   

   
   Abstract
   The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclassical method, known as the Truncated Wigner approximation. The steady-state particle flow through the chain and the mean particle occupations are explained via the spectral properties of the interacting system.
   
   Press release - Heidelberg University
   idw - Informationsdienst Wissenschaft
   Europhysics News
   AlphaGalileo
   
   
9. Decay and fragmentation in an open Bose-Hubbard chain.
   G. Kordas, S. Wimberger and D. Witthaut
   Physical Review A, 87 (2013) 043618.
   arXiv:1307.1538
   

   
   Abstract
   We analyze the decay of ultracold atoms from an optical lattice with loss from a single lattice site. If the initial state is dynamically stable, a suitable amount of dissipation can stabilize a Bose-Einstein condensate, such that it remains coherent even in the presence of strong interactions. A transition between two dynamical phases is observed if the initial state is dynamically unstable. This transition is analyzed here in detail. For strong interactions, the system relaxes to an entangled quantum state with remarkable statistical properties: The atoms bunch in a few breathers forming at random positions. Breathers at different positions are coherent, such that they can be used in precision quantum interferometry and other applications.
   
   
10. Non-hermitian approach to decaying ultracold bosonic systems.
    S. Wimberger, C. A. Parra-Murillo and G. Kordas
    Journal of Physics: Conference Series, 442 (2013) 012029.
    arXiv:1310.5937

    
    Abstract
    A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.
    
    
11. Mutual information and Bose-Einstein condensation.
    C. N. Gagatsos, A. I. Karanikas and G. Kordas
    Open Systems and Information Dynamics, 20 (2013) 1350008.
    arXiv:1207.0303

    
    Abstract
    In this work we study an ideal bosonic quantum field system at finite temperature, and in a canonical and a grand canonical ensemble. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the von Neumann entropy that corresponds to the spatially separated subsystem (i.e. the geometric entropy) and then we subtract its extensive part which coincides with the thermal entropy of the subsystem. In the framework of the grand canonical description, we examine the influence of the underlying Bose-Einstein condensation on the behaviour of the mutual information, and we find that its derivative with respect to the temperature possesses a finite discontinuity at exactly the critical temperature.
    
    


2012


12. Dissipation-induced macroscopic entanglement in an open optical lattice.
    G. Kordas, S. Wimberger and D. Witthaut
    Europhysics Letters, 100 (2012) 30007.
    arXiv:1307.0828
    

    
    Abstract
    We introduce a method for the dissipative preparation of strongly correlated quantum states of ultracold atoms in an optical lattice via localized particle loss. The interplay of dissipation and interactions enables different types of dynamics. This ushers in a new line of experimental methods to maintain the coherence of a Bose-Einstein condensate or to deterministically generate macroscopically entangled quantum states.
    
    


2011


13. Decay of a Bose-Einstein condensate in a dissipative lattice - the mean-field approximation and beyond.
    F. Trimborn, D. Witthaut, H. Hennig, G. Kordas, T. Geisel and S. Wimberger
    European Physical Journal D, 63 (2011) 63.
    

    
    Abstract
    The dynamical evolution of a Bose-Einstein condensate in an open optical lattice is studied. Based on the Bose-Hubbard model we rederive the mean-field limit for the case of an environmental coupling including dissipation and phase-noise. Moreover, we include the next order correlation functions to investigate the dynamical behavior beyond mean field. We observe that particle loss can lead to surprising dynamics, as it can suppress decay and at the same time restore the coherence of the condensate. These behavior can be used to engineer the evolution, e.g. in the form of a stochastic resonance-like response, to inhibit tunneling or to create stable nonlinear structures of the condensate.
    
    
14. Beyond mean-field dynamics in open Bose-Hubbard chains.
    D. Witthaut, F. Trimborn, H. Hennig, G. Kordas, T. Geisel and S. Wimberger
    Physical Review A, 83 (2011) 063608.
    arXiv:1203.3657.
    

    
    Abstract
    We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restore the coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.
    
    
15. Complex time evolution of open quantum systems.
    C. N. Gagatsos, A. I. Karanikas and G. Kordas
    Open Systems and Information Dynamics, 18 (2011) 261.
    arXiv:1104.3671.
    

    
    Abstract
    We combine, in a single set-up, complex time parametrization in path integration, and closed time formalism of non-equilibrium field theories to produce a compact representation of time evolution of the reduced density matrix. In this framework we introduce a cluster-type expansion that facilitates perturbative and non-petrurbative calculations in the realm of open quantum systems. The technical details of some very simple examples are discussed.