Syllabus 2011-12

C2: Laser Science and Quantum Information Processing

Knowledge of the laser physics covered in paper B2.III will be assumed.

Lasers: Line broadening mechanisms, linewidths and gain saturation. Q-switched operation. Modelocking. Frequency control and frequency locking. Solid state lasers. Semiconductor lasers. Fibre lasers. Ultrafast lasers: chirped pulse amplification, terawatt and petawatt laser systems. Examples of laser systems: Nd:Glass, Nd:YAG. Ti:sapphire; Er:Glass fibre lasers and the Er-doped fibre amplifier (EDFA); AlGaAs and GaN semiconductor lasers.

Optics: Diffraction. Ray matrices and Gaussian beams. Cavity eigenfunctions: the concept of cavity mode, the stability criterion, cavity design. Beamsplitters. Transverse coherence and Michelson stellar interferometer. Longitudinal coherence: optical coherence tomography and Fourier transform spectroscopy. (Not correlation functions, Wiener-Khintchine theorem). Optics in Structured Materials: optical fields in planar waveguides and fibres.

Non-linear Optics: Crystal symmetries and the linear electrooptic tensor. Amplitude and phase modulation of light using the linear electro-optic effect. Second harmonic generation. Critical,non-critical and quasi-phase matching. Sum and difference frequency generation and optical parametric down conversion.

Quantum optics: Elementary introduction to quantum fields and photons. Light-matter interactions and the Jaynes-Cummings model. Generation and detection of nonclassical states of light: parametric down conversion and photon entanglement, photon action at a beam splitter, bosonic statistics. Berry and Pancharatnam phases.

Quantum mechanics and Quantum Bits: Two level systems as quantum bits. Superposition states, the Bloch sphere, mixed states, density matrices, Pauli matrices. Single qubit dynamics (gates): NOT, square root of NOT-gate, Hadamard, phase shift, networks of gates, the measurement gate. Implementations: atom/ion in a laser field, photon polarisation, spin in a magnetic field. Mechanisms: Raman transitions, Rabi flopping, Ramsey fringes, spin echoes. Decoherence (simple treatment). Separable and inseparable (entangled) states of two spin systems. Two qubit gates: controlled-NOT, controlled-phase. Universality of gates (result only). Characterising an unknown state, state and gate fidelity (very basic), the no-cloning theorem. EPR, the four Bell states, the Bell inequalities.

Quantum Computation: Reversible computation with unitary gates. Quantum parallelism and readout. The Deutsch and Grover algorithms. Other quantum algorithms: Shor (result only), quantum simulation. Error correction (3 qubit code for phase or flip only) and decoherence free subspaces. DiVincenzo criteria. Experimental methods with trapped atoms and ions. The controlled phase gate by "collisions". Optical lattices and massive entanglement. Experimental methods with NMR. Qualitative treatment of other quantum computing technologies.

Quantum Communication: Elementary ideas about information content. Quantum dense coding. Testing Bell inequalities. Quantum key distribution, the BB84 protocol and detecting eavesdropping (only intercept/resend strategy). EPR based cryptography. Fibre and free space cryptography, polarisation and phase encoding. Phase encoding methods. Quantum teleportation and entanglement swapping

Back to Lasers and Quantum Information