Application of nonlinear deformation algebra to a physical system with P\"oschl-Teller potential

We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with P\" oschl-Teller potential, and is used to derive the well-known su(1,1) spectrum-generating algebra of this problem. We show that one of the defining relations of the nonlinear algebra, presented by the authors, is only valid in the limiting case of an infinite square well, and we determine the correct relation in the general case. We also use it to establish the correct link with su(1,1), as well as to provide an algebraic derivation of the eigenfunction normalization constant.Comment: 9 pages, LaTeX, no figure

Full control of quadruple quantum dot circuit charge states in the single electron regime

We report the realization of an array of four tunnel coupled quantum dots in the single electron regime, which is the first required step toward a scalable solid state spin qubit architecture. We achieve an efficient tunability of the system but also find out that the conditions to realize spin blockade readout are not as straightforwardly obtained as for double and triple quantum dot circuits. We use a simple capacitive model of the series quadruple quantum dots circuit to investigate its complex charge state diagrams and are able to find the most suitable configurations for future Pauli spin blockade measurements. We then experimentally realize the corresponding charge states with a good agreement to our model.Comment: 4 pages, 3 figure

Photon mediated interaction between distant quantum dot circuits

Engineering the interaction between light and matter is an important goal in the emerging field of quantum opto-electronics. Thanks to the use of cavity quantum electrodynamics architectures, one can envision a fully hybrid multiplexing of quantum conductors. Here, we use such an architecture to couple two quantum dot circuits . Our quantum dots are separated by 200 times their own size, with no direct tunnel and electrostatic couplings between them. We demonstrate their interaction, mediated by the cavity photons. This could be used to scale up quantum bit architectures based on quantum dot circuits or simulate on-chip phonon-mediated interactions between strongly correlated electrons

Nonlinear deformed su(2) algebras involving two deforming functions

The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution, less common nonlinear deformations of su(2), introduced by Delbecq and Quesne and involving two deforming functions of J_0, are reviewed. Such algebras include Witten's quadratic deformation of su(2) as a special case. Contrary to the former deformations, for which the spectrum of J_0 is linear as for su(2), the latter give rise to exponential spectra, a property that has aroused much interest in connection with some physical problems. Another interesting algebra of this type, denoted by ${\cal A}^+_q(1)$, has two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed. The resulting algebraic structure, referred to as a two-colour quasitriangular Hopf algebra, is described.Comment: 8 pages, LaTeX, no figures, submitted to Proc. 5th Int. Coll. ``Quantum Groups and Integrable Systems'', Prague, 20-22 June 1996 (to be published in Czech. J. Phys.