Quantum Computation Using Optical Lattices Ben Zaks Victor Acosta Physics 191 Prof. Whaley UC-Berkeley

Contents Standing Wave Light Field Egg Crate Potential Atom Cooling Gates and Qubits

1D Optical Lattice 2 Linearly Polarized Light Waves...

1D Optical Lattice σ+σ+ σ-σ- …or 2 Circularly Polarized Standing Waves!

Atom in a Light Field: AC-Stark Shifts Choose Rotating Frame: Time Dependent Schroedinger Equation Unitary Transformation Electric Dipole Hamiltonian Finally

Example: Two-Level System

Example: J=1/2 J=3/2

Periodic Spatially-Varying Optical Trap -3 -2

Cooling in Optical Lattices Six lasers tuned slightly below the resonance frequency of atoms being trapped Atoms moving towards lasers see frequencies closer to resonance Atoms moving towards lasers absorb more momentum Magnetic field gradient creates Zeeman splitting to further trap atoms Can cool to ~1 microKelvin Optical Molasses and Magneto-Optical Traps

Cooling in Optical Lattices Sisyphus Cooling Atoms with enough energy can climb out of the well Atoms will be optically pumped from the higher energy ground state (red line) Spontaneous emission will drop the atom into the lower energy ground state (blue line) The atom loses more energy than it gains, so it is cooled

Quantum Computation Optical lattices contain neutral atoms, ions or polar molecules as qubits Electric dipoles of these particles are qubits aligned with or against an external field Qubits are entangled by the dipole-dipole interaction Need strong coupling between qubits but weak coupling with environment An Array of Qubits

Quantum Computation Prof. DeMille uses polar molecules as qubits at Yale An electric field gradient allows for spectroscopic addressing of individual qubits Microwave laser pulses can be used as single and two- qubit gates Coupling effects can be eliminated by “refocusing” Some Current Research

Quantum Computation Prof. Deutsch et al. use neutral atoms in far-off resonance optical lattices as qubits at the University of New Mexico Neutral atoms have weak dipole-dipole interactions but are also very weakly coupled to the environment Polarization is rotated to bring atoms together Once together, laser pulses set to specific resonances will only allow specific transitions, and these can be utilized as gates Some Current Research

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