Quantum computation using optical lattices
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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

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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+

…or 2 Circularly Polarized Standing Waves!

σ-

1D Optical Lattice


Atom in a Light Field: AC-Stark Shifts

Electric Dipole Hamiltonian

Time Dependent Schroedinger Equation

Choose Rotating Frame:

Unitary Transformation

Finally


Example: Two-Level System


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


-1

-2

-3

Periodic Spatially-Varying Optical Trap


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 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

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 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 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

  • 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


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