Real-space correlations in dissipative quantum systems (English shop)

Preview

Table of Contents, PDF (30 KB)
Extract, PDF (110 KB)

While multiple qubits in a quantum register should behave independently, their connection to a common environment may spoil that independence, as they start to influence each other via the environment. In this work two qubits, modelled by magnetic spin-1/2 impurities, are investigated which are coupled at a finite distance to the same dissipative environment. From the spin-boson model it is known that there exists a phase for weak coupling where the spin is not localised in any state and may thus explore the whole SU Bloch sphere, while for strong coupling it is localised in one of two configurations, completely destroying its quantum mechanical nature.
As a second spin is coupled in direct vicinity of the first, the environment mediates an effective ferromagnetic interaction between the spins, rendering them no longer independent.

Within the Numerical Renormalization Group (NRG) it is investigated at which point the two spins can be treated independently as the distance between them is increased. To this end a two-channel bosonic NRG is developed that can deal with the model and its limit of two independent spin-boson models. The two-channel NRG is first tested on a model incorporating a single oscillator as an impurity. While the latter model only involves a single channel, a self-interaction of the impurity oscillator provides accessible limits, where the numerical implementation of the two-channel NRG can be tested. Furthermore signals of the different impurities are traced in the environment by means of thermal averages and their changes due to the presence of the impurities.

This work addresses the influence of quantum impurities within a dissipative environment both on each other and on their environment. The impurities are realised either by an oscillator or by two qubits. Since the systems under consideration are not analytically solvable for a large range of parameters, a two-channel NRG (Numerical Renormalization Group) for bosonic models is developed. Details of this NRG and its implementation are presented in the work.
An investigation of the flow diagrams of the two-qubit systems points to a ground state in which the quantum impurities are effectively ferromagnetically coupled.

In this state, both the mean occupation and the mean displacement of the environmental orbitals show a marked increase directly at the impurities.
An unambiguous assignment of a length scale on which the signals under consideration decay is currently not possible.