Nonlinear susceptibility of nonsymmetric quantum systems

A. R. Kolovskii

José Luis Paz, Edgar Márquez, Cristhian Dávila +4 more

S. Guérin, Mariam Gevorgyan, Claude Leroy +2 more

We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically for an infinite pulse area.

R.M.G. Rajapakse, T. Bragdon, Ana María Rey +2 more

We model single-photon nonlinearities resulting from the dipole-dipole interactions of cold polar molecules. We propose utilizing ``dark state polaritons'' to effectively couple photon and molecular states; through this framework, coherent control of the nonlinearity can be expressed and potentially used in an optical quantum computation architecture. Due to the dipole-dipole interaction the photons pick up a measurable nonlinear phase even in the single-photon regime. A manifold of protected symmetric eigenstates is used as basis. Depending on the implementation, major sources of decoherence result from nonsymmetric interactions and phonon dispersion. We discuss the strength of the nonlinearity per photon and the feasibility of this system.

Yu A Il'inskiĭ, Leonid V. Keldysh

Hrachya Zakaryan, Konstantinos-Rafail Revis, Zahra Raissi

Nonsymmetric GHZ states ($n\text{\ensuremath{-}}{\mathrm{GHZ}}_{\ensuremath{\alpha}}$), defined by unequal superpositions of $|00...0\ensuremath{\rangle}$ and $|11...1\ensuremath{\rangle}$, naturally emerge in experiments due to decoherence, control errors, and state preparation imperfections. Despite their relevance in quantum communication, relativistic quantum information, and quantum teleportation, these states lack a stabilizer formalism and a graph representation, hindering their theoretical and experimental analysis. We establish a graph-theoretic framework for nonsymmetric GHZ states, proving their local unitary (LU) equivalence to two structures: fully connected weighted hypergraphs with controlled-phase interactions and star-shaped controlled-unitary (CU) graphs. While weighted hypergraphs generally lack stabilizer descriptions, we demonstrate that nonsymmetric GHZ states can be efficiently stabilized using local operations and a single ancilla, independent of system size, thereby enabling entanglement witness construction and offering a pathway toward qudit quantum error correction. We extend this framework to qudit systems, constructing LU-equivalent weighted qudit hypergraphs and showing that general nonsymmetric qudit GHZ states can be described as star-shaped CU graphs. Our results provide a systematic approach to characterizing and stabilizing nonsymmetric multipartite entanglement in both qubit and qudit systems, with implications for quantum error correction and networked quantum protocols.