Wave-packet entanglement

Abstract

We propose and analyze a scheme by which a many-particle system can be prepared in highly entangled wave-packet states. One of the particles is prepared initially in a quantum superposition of multiple coherent states and then coupled via a quadratic interaction Hamiltonian to a number of other particles. The system evolves into a highly entangled wave-packet state. An appropriate measure of this time-dependent entanglement is given. This scheme is applicable to a number of systems of interest in quantum-information science.

Calculation of the convex roof for an open entangled harmonic oscillator system

“…When an oscillator is excited, we take it to be in a generalized Schrödinger-cat superposition that is symmetric in phase around the phasespace orbit [41]. We then have…”

“…To evaluate the entanglement of the system, an orthonormal basis for these coherent states is required. We form a minimal dynamic orthonormal basis, that is, a basis that evolves with time, by transforming from the |α σ,p basis to the orthonormal |V σ,p basis given in [41]. From [41,Eq.…”

“…At first sight, it seems the convex roof in such a model would be quite difficult to calculate because in this case we are dealing with continuous variable entanglement. However, by utilizing the symmetry of the Hamiltonian in the choice of initial state, one can reduce the continuous system to one with effectively a finite number of levels [41]. Under such a change of basis, the convex roof is in fact numerically computable with modest resources.…”

Many fields interaction: Beam splitters and waveguide arrays

“…Nonclassical states that have attracted the greatest interest include (a) macroscopic quantum superpositions of quasiclassical coherent states with different mean phases or amplitudes, also called "Schrödinger cats" [1][2][3][4][5], (b) squeezed states [2,6], whose fluctuations in one quadrature or the amplitude are reduced beyond the SQL, and (c) the particularly important limit of extreme squeezing, i.e. Fock or number states [7].…”

“…Major efforts have been directed towards the generation of nonclassical states of electromagnetic fields, in which certain observables exhibit less fluctuations (or noise) than in a coherent state, whose noise is referred to as the standard quantum limit (SQL). Nonclassical states that have attracted the greatest interest include (a) macroscopic quantum superpositions of quasiclassical coherent states with different mean phases or amplitudes, also called "Schrödinger cats" [1][2][3][4][5], (b) squeezed states [2,6], whose fluctuations in one quadrature or the amplitude are reduced beyond the SQL, and (c) the particularly important limit of extreme squeezing, i.e. Fock or number states [7].…”