PT-Symmetric Schrödinger Operators with Unbounded Potentials

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References: MZ, Phys. D 78 or arXiv: MZ, Annals of Physics pp.

The energy spectrum of complex periodic potentials of the Kronig–Penney type - Semantic Scholar

The interaction potential gets completely regularized, which adds to the energy spectrum an infinite tower of previously non-normalizable states. For integral values of the coupling, extra degeneracy occurs and a nonlinear conserved charge enlarges the ring of Liouville charges.

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Symmetries have characteristic effect on the energy spectrum of quantum systems. This is also the case with PT symmetric quantum mechanics: the energy eigenvalues of PT-symmetric complex potentials are either real, or appear as complex conjugate pairs, depending on whether PT symmetry is unbroken or broken. There are, however, further symmetry concepts characterizing quantum systems, which also have influence on their energy spectrum.

Derivation and Numerical analysis of an Attenuation Operator for non-relativistic waves

In supersymmetric quantum mechanics SUSYQM , superymmetric transformations connect energy eigenstates belonging to the same energy, but different potentials. Similarly to PT symmetry, supersymmetry can also be broken, and this also leads to consequences concerning the energy spectrum. We discuss complex quantum mechanical potentials characterized by both PT symmetry and supersymmetry and discuss the combined effect of these symmetries on the energy spectrum.

We pay special attention to situations in which either or both of these symmetries break down.

We illustrate the interplay of these symmetry concepts with exactly solvable potentials. We demonstrate that some potentials are also characterized by symmetries associated with Lie algebras, and discuss the relation of this symmetry concept with PT symmetry and supersymmetry. Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods.

Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins—N-methylacetamide—and simulate thermal relaxation and the effect of anharmonicities in H2O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH3.

Additional information

These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry. Reference: C. Sparrow, E.

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Martin-Lopez, N. Maraviglia, A. Neville, C. Harrold, J. Carolan, Y. Joglekar, T. Hashimoto, N. Matsuda, J. Tew, and A. Laing, Nature , We propose a methodical approach to enhancing non-exponential decay in quantum and optical systems by exploiting recent progress surrounding another subtle effect: the bound states in continuum [1], which have been observed in optical lattice array experiments just in the last decade [2, 3]. Specifically, by populating an initial state orthogonal to that of the bound state in continuum, it is possible to engineer system parameters for which both the usual exponential decay process and fractional decay associated with the BIC or any other bound states present in the system are suppressed in favor of non-exponential dynamics.

We demonstrate our method using a model based on one of the previously mentioned optical lattice array experiments. We further show the energy gap between the continuum threshold and a nearby virtual bound state determines the timescale that characterizes the inverse power law decay [4]. Hsu, B.

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Zhen, A. Stone, J. Joannopoulos, and M. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Weimann, Y. Xu, R. Keil, A. Miroshnichenko, A. Sukhorukov, A. Szameit, and Y. Kivshar, Phys.

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Garmon, T. Petrosky, L. Simine, and D. Segal, Fortschr.

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  • [PDF] Level Crossings in a PT-symmetric Double Well | Semantic Scholar.
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  • Atom laser is one of the great discoveries in modern science serving as an alternative theory to quantum optics. Atom laser replaces the study of many fundamental effects of quantum theory by using massive particles rather than the photons. Apart from that, it has several other applications including the high-accuracy interferometry. Squeezed atom laser is one step ahead of the ordinary atom lasers, as they provide more efficiency in producing the coherent laser beam.

    We construct a squeezed atom laser from the deformed Bose-Einstein condensate motivated by the genralized uncertainty principle. These modified quantum mechanical framework is under intense investigation in recent days and is a strong candidate for the quantum theory compatible with gravity.

    However, these models are mostly non-Hermitian and, therefore, PT-symmetry and non-Hermitian quantum mechanics play a great role in such scenarios. We shall discuss the detailed technicalities for the construction of the squeezed atom laser using the notions of Non-Hermitian quantum mechanics. A class of exactly solvable real as well as PT symmetric extended Calogero-Wolfes type three body potentials are obtained whose bound states are written in terms of newly discovered exceptional orthogonal polynomials EOPs.

    These potentials are isospectral to the well known usual Calogero-Wolfes type potentials. Some of the many body systems are also extended by introducing new interaction terms and obtained their exact solutions in terms of exceptional Laguerre polynomials. One prerequisite for the construction of large-scale quantum machines is rapid, high fidelity qubit measurement.

    This challenge is now regularly met in superconducting qubits read out with parametrically driven microwave amplifiers. However, their near-quantum limited performance comes at the cost of virtually every other performance metric, including dynamic range, bandwidth, and directionality. I will discuss recent efforts to combat these shortcomings by both eliminating unwanted Hamiltonian terms as well as combining multiple, simultaneous parametric drives.

    We demonstrate the merging of levels at the exceptional point, separating the PT symmetry breaking and non-breaking phases.

    (ebook) PT-Symmetric Schrodinger Operators with Unbounded Potentials

    The emergence of bound state in the continuum as zero width resonances are also derived. The connection of a conserved correlation in exceptional point stopping light is explicated. We also show the occurrence of spontaneous breaking of SUSY in the model under consideration and a hysteresis phenomenon near the exceptional point.

    Photons have recently emerged as a promising building block to realize synthetic materials. When confined in semiconductor microcavities, they acquire an effective mass and behave as massive particles. In the limit of 0D confinement, they can even act as artificial atoms. In our experiments at C2N, we arrange such artificial atoms into semiconductor lattices, thus forming crystals of light. Such manipulation of light not only presents potential for applications in photonics, but is also of great promise for fundamental studies, as I will demonstrate using the examples of a photonic benzene molecule and also photonic graphene recently realized recently in our lab.

    In the strong coupling regime with quantum well excitons, photons can finally be made to interact through formation of part-light part-matter particles called cavity polaritons. In the limit of strong enough interactions as compared to the polariton linewidth polariton blockade , it has been predicted that polaritons may be used to implement strongly interacting systems of light.

    To date, this limit has nevertheless not been reached experimentally. Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT-symmetric states. As proposed by Kreibich et al [Phys. A 87, R ], in the mean-field limit the dynamical behavior of this system, in particular that of the PT-symmetric states, can be simulated by embedding it into a fourwell system with time-dependent parameters.

    PT-Symmetric Schrödinger Operators with Unbounded Potentials PT-Symmetric Schrödinger Operators with Unbounded Potentials
    PT-Symmetric Schrödinger Operators with Unbounded Potentials PT-Symmetric Schrödinger Operators with Unbounded Potentials
    PT-Symmetric Schrödinger Operators with Unbounded Potentials PT-Symmetric Schrödinger Operators with Unbounded Potentials
    PT-Symmetric Schrödinger Operators with Unbounded Potentials PT-Symmetric Schrödinger Operators with Unbounded Potentials
    PT-Symmetric Schrödinger Operators with Unbounded Potentials PT-Symmetric Schrödinger Operators with Unbounded Potentials

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