Feasibility studies for quantum computation with spectral hole burning media

Abstract

In this thesis I consider a scheme for quantum computation in which quantum bits (qubits) are stored in individual spectral holes of an in homogeneously broadened medium, such as a cryogenically cooled crystal of Pr:Y2 SiO 3 . Qubits are transferred between spectral holes by virtue of mutual coupling of the atoms to a single quantized cavity mode, which allows for easy implementation of two bit gate operations. I show that laser induced adiabatic passage can be used to transfer an arbitrary symmetric ground state coherence between two many-atom spectral holes. However, it is not clear how to construct entangled states of qubits which are represented by many atoms, and therefore we require that each spectral hole contain only a single atom. The many-atom coherence transfer is still useful for constructing N-photon Fock states in the cavity. The coherence transfer is susceptible to spontaneous emission and cavity decay; the latter is the dominant decay channel for Pr:YSO. I have shown that the coherence transfer can proceed in a cavity dark state which is invulnerable to cavity decay, at the cost of becoming especially susceptible to spontaneous emission, and vice versa for coherence transfer with an atomic dark state. We can achieve the strong atom-cavity coupling necessary for coherence transfer by using extremely high-finesse optical resonators and by reducing the cavity mode volume. The latter is achieved by either reducing the total cavity volume as with a microcavity, or by tightly focusing the mode to a small active volume as with a near-concentric cavity. I consider how the presense of multiple degenerate cavity modes affects the two-atom coherence transfer, and find that the transfer is only exact when both atoms couple to the same mode. For the prototype Pr:YSO material, using a tightly focused mode in a centimeter-length cavity, we can couple as many as 400 qubits with a ground state coherence lifetime of about 1 s, which would allow us to apply as many as 20 sequential gate operations.