Transcript Cooling in Optical Lattices

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...
y
x
z
1D Optical Lattice
σ+
σ0
4
E
2
t
3
4
Cos k z
…or 2 Circularly
Polarized
Standing Waves!
Sin k z
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
Periodic Spatially-Varying Optical Trap
-1
-2
-3
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 twoqubit 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