Electron-photon interaction in quantum dots : spin and entanglement

The interaction of electrons and photons lies at the heart of quantum physics. The
most notable phenomena which are described by quantum physics but which obviously
invalidate a classical description of the electromagnetic field - the photoelectric
effect, the Compton effect, or the antibunching of photons emitted from a single atom,
to mention a few - are intimately related to the interaction of electrons and photons.
Electrons possess an internal degree of freedom, the spin. The spin S of an electron
can be described as an internal angular momentum, leading to a magnetic moment
m due to the electric charge of the electron. Stern and Gerlach have shown that
the projection of m onto a quantization axis (defined by an external magnetic field
in their experiment), e.g., along the z axis, is either mz = g�μB/2 (\spin up") or
mz = g�μB=2 (\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton
and g is the g-factor of the electron (g = 2 for free electrons).
An electron spin
is therefore usually referred to as a two-level system. Due to this property, the
spin of electrons which are localized in semiconductor quantum dots has recently
attracted significant attention regarding the implementation of quantum information
processing: Electron spins can be used as carriers of quantum information. One
can define that the spin pointing "up" corresponds to the logical value "0" and
the spin pointing "down" corresponds to "1". Moreover, because the electron spin
is a quantum mechanical property one can form arbitrary coherent superpositions of
"up" and "down" with a single spin. Moreover, because the electron spin
is a quantum mechanical property one can form arbitrary coherent superpositions of
"up" and "down" with a single spin. A system with this property is called a quantum
bit (qubit). The additional possibilities due to quantum superpositions of qubits are
exploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks
much more efficiently than with a classical computer (i.e., the prime factorization of
large numbers for Shor's algorithm and the search within an unstructured database for
Grover's algorithm). While quantum computation has presently only been achieved
in prototypical experiments with few qubits, the implementation of efficient largescale
quantum computation with many qubits still remains an extremely demanding
task. Yet, other quantum mechanical properties of qubits, such as entanglement,
have already been exploited experimentally with photons in quantum communication
schemes, for example, quantum teleportation and quantum data compression.
In this thesis, we investigate the interaction of electrons and photons in semiconductor
quantum dots. Optical transitions in quantum dots enable a direct link between
electron spins and photon polarizations due to conservation laws. We show that
entanglement can be transferred from electron spin qubits to qubits defined by the
photon polarization, enabling the measurement of entangled spin states via photons.
The mechanism under study can also be used for the production of entangled photons,
for instance for the implementation of quantum communication protocols. In contrast
to the presently used sources of entangled photons, the photon source we propose here
is deterministic, providing entangled photons on demand. It has been demonstrated
in several recent experiments that the most obvious way to achieve such a transfer of
entanglement - using the recombination of biexcitons in a single quantum dot - fails
in the presently available quantum dot structures. We have analyzed the problems
of this approach. As a solution, we propose schemes based on charged excitons in
single or coupled quantum dots. We discuss the generation of entangled two- and
four-photon states.
In addition to the transfer of quantum states, photons can also be used to probe
electron spin states. We investigate in detail different methods to optically measure
the decoherence time of a single electron spin in a quantum dot. The decoherence time
of a spin establishes the time scale during which coherent manipulation is possible.
Measurements of the electron spin decoherence time are therefore highly desirable
in view of the implementation of spin-based quantum information processing. We
show that the schemes we propose can be implemented with current experimental
techniques.
We then study the magneto-optical effect called Faraday rotation. Using the technique
of time-resolved Faraday rotation, a recent experiment has demonstrated the
coherent transfer of spin between quantum dots coupled by molecules. We calculate
the Faraday rotation signal for a coupled dot system and show that a two-site
Hamiltonian with a transfer term captures the essential features observed in this experiment.
We also present results for a system of two coupled dots doped with a
single electron.
We finally show that the coupled states of two qubits can be detected via the optical
interaction with a cavity in the dispersive regime. We present a Schrieffer-Wolff
transformation which removes the coupling of the two qubits to the cavity in leading
order. The different two-qubit states lead to a different spectral shift of the cavity
line. For a sufficiently low cavity linewidth, this enables the direct readout of a
two-qubit system.