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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. σ +.

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Quantum computation using optical lattices
Quantum Computation Using Optical Lattices

Ben Zaks

Victor Acosta

Physics 191

Prof. Whaley

UC-Berkeley


Contents
Contents

  • Standing Wave Light Field

  • Egg Crate Potential

  • Atom Cooling

  • Gates and Qubits


Quantum computation using optical lattices

1D Optical Lattice

2 Linearly Polarized Light Waves...


1d optical lattice

σ+

…or 2 Circularly Polarized Standing Waves!

σ-

1D Optical Lattice


Atom in a light field ac stark shifts
Atom in a Light Field: AC-Stark Shifts

Electric Dipole Hamiltonian

Time Dependent Schroedinger Equation

Choose Rotating Frame:

Unitary Transformation

Finally




Periodic spatially varying optical trap

-1

-2

-3

Periodic Spatially-Varying Optical Trap


Cooling in optical lattices
Cooling in Optical Lattices

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


Cooling in optical lattices1
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
Quantum Computation

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


Quantum computation1
Quantum Computation

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”


Quantum computation2
Quantum Computation

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


Thank you to the following websites for their resources
Thank you to the following websites for their resources

  • 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