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Quantum Computation Using Optical Lattices

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Ben Zaks

Victor Acosta

Physics 191

Prof. Whaley

UC-Berkeley

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

1D Optical Lattice

2 Linearly Polarized Light Waves...

σ+

…or 2 Circularly Polarized Standing Waves!

σ-

Electric Dipole Hamiltonian

Time Dependent Schroedinger Equation

Choose Rotating Frame:

Unitary Transformation

Finally

-1

-2

-3

Optical Molasses and Magneto-Optical Traps

- 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

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

An Array of Qubits

- 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

Some Current Research

- 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

- 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

- http://quaser.physics.lsa.umich.edu/projects/lattice/
- http://web.arizona.edu/~lascool/research.html
- http://nobelprize.org/physics/laureates/1997/illpres/
- http://www.yale.edu/physics/research/atomic.html
- http://physics.nist.gov/Divisions/Div842/Gp4/lattices.html