In this thesis the reasons for pursuing an optically addressable quantum object
in silicon are outlined before introducing some possible technological applications.
Chalcogen donor electron systems in silicon are then discussed as a candidate for
these quantum technologies. The chalcogen donor complexes in silicon allow the
solid-state analogues of hydrogen and helium to be studied. The time-resolved
Fourier transform technique was employed to measure the photoluminescence from
a selenium doped silicon sample when pumped above band gap at the temperatures
10 K, 80 K and 300 K. The excited state lifetime of the 2p0 state was found to
be 28.2 ns for atomic centres and 66.4 ns for molecular centres at 10 K. The lifetimes
were seen to be similar across large emission bands indicating a rate limiting
step. A multi-colour pump-probe experiment, using time-resolved Fourier transform
spectroscopy, was performed at the FELIX institute to determine the excited state
lifetimes of the 2p0 and 1s(T2) to be <2.5 ns and 10.62 ns respectively. A system of 5
coupled rate equations was then implemented to verify the experimental results. The
lifetimes were theoretically determined from three sets of initial conditions. Carriers
were initially positioned in the conduction band, modelling the photoluminescence
experiment, the 2p and 1s states, imitating the FELIX experiment. The 2p state
was shown to have two decay lifetimes, one 15.1 ps and the second of 7.24 ns. The
first fast decay is due to the pure 2p state relaxation while the second long lifetime is
a result of the 1s(T2) state in
uencing the 2p excited state lifetime. The 1s(T2) excited
state lifetime that back-fills the 2p state elongates the 2p excited state lifetime,
causing the lifetime to appear longer than the true lifetime. This research implies
that silicon has the potential to be an accessible test bed for quantum experiments
by showing that it could be possible to create isolated non-interacting donor centres
that are individually optically addressable by mid-IR laser light.
We investigate the impact of charge transfer energy and band filling on the stability of the two-hole resonance relevant for Auger electron spectroscopy (AES) in transition-metal oxides. As a minimal model to study charge transfer effects in a transition metal (TM) and oxygen (OX) chain, we consider a one-dimensional chain with spinless fermions with an alternating motif of site-pairs with nearest-neighbor (NN) repulsion U and uncorrelated site-pairs, separated by a charge transfer gap $\mathrm{\ensuremath{\Delta}}$. We first show that while two holes added in a filled band of NN interacting fermions in one dimension can stabilize to a two-hole bound pair, the bound pair delocalizes with a
U-dependent bandwidth. In contrast, we establish that the bandwidth of two holes added on a TM site pair in a filled band is dramatically suppressed, realizing a ``local'' two-hole resonance (L2HR) at the same TM site pair mimicking the AES phenomenology. Employing a memory-efficient exact numerical scheme and standard Lanczos-based diagonalization, we then study two-hole spectra for holes added at TM site pairs in partially filled bands. We analyze the multiple features that arise in the two-hole spectra at partial filling of the ground state. We uncover that in the strong-
U limit, there is a filling-dependent ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{crit}}$ above which the L2HR remains stable for any band filling greater than 75%. In this regime, the energy location of the L2HR provides a direct estimate of the correlation strength at TM site pairs for partial filling and is reminiscent of the Cini-Sawatzky theory for the filled band case. At 75% band filling, an abrupt redistribution of two-hole spectral weight destroys the L2HR regardless of the
U or $\mathrm{\ensuremath{\Delta}}$ values. We discuss the relevance of these nonperturbative results, obtained with full lattice symmetry, for understanding the AES of partially filled bands in terms of the local two-hole spectrum.