Search results for "Coherent states"
showing 10 items of 77 documents
kq-Representation for pseudo-bosons, and completeness of bi-coherent states
2017
We show how the Zak $kq$-representation can be adapted to deal with pseudo-bosons, and under which conditions. Then we use this representation to prove completeness of a discrete set of bi-coherent states constructed by means of pseudo-bosonic operators. The case of Riesz bi-coherent states is analyzed in detail.
Some invariant biorthogonal sets with an application to coherent states
2014
We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-hermitian quantum mechanics.
An invariant analytic orthonormalization procedure with an application to coherent states
2007
We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators Aj, j=1,2,n, starting from a fixed normalized vector in H and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of coherentlike vectors can be produced and in which condition over the lattice spacing this can be done. © 2007 American Institute of Physics.
Construction of pseudo-bosons systems
2010
In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.
Quantum Computing with Trapped Charged Particles
2009
The concept of quantum computing has no clear cut origin. It emerged from combinations of information theory and quantum mechanical concepts. A decisive step was taken by Feynman [414, 415] who considered the possibility of universal simulation, a quantum system which could simulate the physical behavior of any other. Feynman gave arguments which suggested that quantum evolution could be used to compute certain problems more efficiently than any classical computer. His device may be considered as not sufficiently specified to be called a computer. The next important step was taken in 1985 by Deutsch [310]. His proposal is generally considered to represent the first blueprint for a quantum c…
Quantum-state manipulation via quantum nondemolition measurements in a two-dimensional trapped ion
2001
The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the occupation probability of the internal electronic level. The substantial difference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a result, the atomic Rabi oscillation is involved in the coherent superposition of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the …
Quantum Nondemolition Measurement and Quantum State Manipulation in Two Dimensional Trapped Ion
2001
An extension of QNDmeasuremen t of the vibrational energy of the trapped ion from one dimensional case to the bidimensional one is presented. Our approach exploits the fixed phase difference existing between the two orthogonal and appropriately configured classical laser beams determining the vibronic coupling. We in fact show that this phase difference may play the role of an adjustable external parameter which allows to optimize the measurement scheme itself in terms of both precision and sensitivity. Our proposal provides a cooling method for the trapped ion from the vibrational thermal state. Due to the coherent superposition of two sub Rabi oscillations, the Rabi frequency degeneration…
Complex quantum state generation and coherent control based on integrated frequency combs
2019
The investigation of integrated frequency comb sources characterized by equidistant spectral modes was initially driven by considerations towards classical applications, seeking a more practical and miniaturized way to generate stable broadband sources of light. Recently, in the context of scaling the complexity of optical quantum circuits, these on-chip approaches have provided a new framework to address the challenges associated with non-classical state generation and manipulation. For example, multi-photon and high-dimensional states were to date either inaccessible, lacked scalability, or were difficult to manipulate, requiring elaborate approaches. The emerging field of quantum frequen…
Radial coherent states for Dirac hydrogen-like atom
2002
In this paper we use an su(2) representation of the radial eigenfunction of the Dirac hydrogen-like atom and we build the Glauber coherent states and the displacement operator coherent states. We also calculate the average values of some observables corresponding to these states.
Motion of the wave-function zeros in spin-boson systems.
1995
In the analytic Bargmann representation associated with the harmonic oscillator and spin coherent states, the wave functions considered as consisting of entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of motion for the wave function is turned to a system of equations for the zeros of the wave function. The motion of these zeros as a nonlinear flow of points is studied and interpreted for linear and nonlinear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analog. Numerical solutions are derived and dicussed.