Quantum ground states: Manipulation and approximation

Rogers, Nick

In this thesis I present a theory of a macroscopic singlet-triplet qubit in quantum dots embedded in nanowires, each containing 4 electrons and together simulating an artficial Haldane gap material. A Haldane gap material exhibits a 4-fold degenerate ground state separated by an energy gap from excitations. The ground state is equivalent to a degenerate spin-singlet and -triplet state. The 4 degenerate states exhibit the characteristics of spins-1/2 localized on either end of the chain. These states may be used as a coded qubit for quantum information processing. Using the effective mass approximation, I calculate single-particle energy levels of one and two quantum dots in a quantum wire. Using these energy levels I compute the Coulomb matrix elements of the interacting Hamiltonian. Using configuration interaction I demonstrate that the ground state of a quantum dot with 4 electrons is a spin-1 state. I then show that the two dot system behaves approximately like two spin-1 objects interacting via an antiferromagnetic Heisenberg Hamiltonian. While the Heisenberg model is approximate, the two dots have a spin-0 ground-state, indicating antiferromagnetic coupling. I then present a simpler spin model to illustrate the physical parameters which control this interaction. Finally, I present a brief solution to the Heisenberg Hamiltonian for finite spin-chains, and show how one can manipulate the singlet-triplet combined ground state of the spin-chain via localized magnetic field, realizing a singlet-triplet qubit in a macroscopic semiconductor device.

Ryuji Ukai

Eduardo Nahmad-Achar, Octavio Castaños, Ramón López–Peña +1 more

We show that the ground state of the Tavis-Cummings (TC) model of N 2-level systems in interaction with a 1-mode radiation field can be mirrored by a semi-classical state to an excellent approximation. The latter is obtained through a projection of a variational tensorial product of coherent states onto the value of the constant of motion of the TC Hamiltonian which minimises the (classical) energy of the ground state. This projection restores the Hamiltonian symmetry, and is amiable to analytical calculations. The observed super-radiant phase-transitions are reflected by this projected state, and an excellent agreement with the exact quantum solution for the ground state is obtained as regards to the entanglement entropy between the matter and field, the squeezing parameter of the state, the probability distributions of photons and atoms, and the expectation value of all field and matter observables of interest, including the photon number dispersion. All these are given in analytic form. The fitness between our approximation and the exact quantum solution is measured through the evaluation of the fidelity parameter; this is very close to 1, except in the region of classical phase transitions, as is to be expected. The presented approach may enable novel investigations of super-radiant and sub-radiant states of artificial atoms, where the relevant control parameters can be manipulated to cross the separatrix.

Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine

Jérémie Gillet, Miguel Ángel García-March, Thomas Busch +1 more

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double-well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground-state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.

Paolo Tombesi, David Vitali