Quantum Entanglement of Rb Atoms Using Cold Collisions ( 韓韓韓 ) Dian-Jiun Han Physics Department Chung Cheng University
Dec 31, 2015
Quantum Entanglement of Rb Atoms Using Cold Collisions
(韓殿君 ) Dian-Jiun Han
Physics Department
Chung Cheng University
Outline
• Introduction• Cold Atoms in the Potential Wells
• Quantum Entanglement (QE) of Cold Atoms in Optical Lattices (OL)
• Experimental Realization of the Quantum Entanglement
• Conclusions
IntroductionRequirements for a quantum computer : A Stean, Rep. Prog. Phys. 61, 117 (1998)
1. Qubits are sufficiently well-isolated from their environment 2. Possible to prepare the qubits in specified states 3. Apply universal quantum gates to them 4. Measure their states 5. The number of qubits must be scalable 6. There must be way to implement quantum error correction
Possible candidates: trapped ions, NMR, high-Q optical cavities, electron spin-based condensed matter system, and cold atoms in optical lattices (a newcomer in this field!!)
Cold Atoms in Two Adjacent Potential Wells
ax bx
|a> |b>
Atom 1 and atom 2 are in the internal states |a>1 and |b>2
and are trapped in the ground states of the potential wells.
Va Vbuab
Jaksch et al., Phy. Rev. Lett. 82, 1975 (1999)
Implementation of the Entanglement
|b> |a>
Xa1(t) Xb
2(t)
1x 2x
|b>|a>
Xb1(t) Xa
2(t)adiabatically move the wells atoms are still in the ground state of the trap potential
A Two-qubit Gate Transformation before and after the entanglement:
|a>1 |a>2 → e-i2φa |a>1 |a>2 ,
|a>1 |b>2 → e-i(φa+φb+φab) |a>1 |b>2 ,
|b>1 |a>2 → e-i(φa+φb) |b>1 |a>2 ,
|b>1 |b>2 → e-i2φb |b>1 |b>2← kinetic phase
← collisional phase
e.g., 87Rb atom |a>≡|F=1, mf=1> , |b> ≡|F=2, mf=2>
Experimental Realization of the Entanglement
1. Using laser cooling, magnetic trapping and evaporative cooling to reach Bose-Einstein condensation of 87Rb atoms 2. Loading Bose condensed atoms (~ 106 atoms) into an optical lattice (optical crystal) 3. Increasing lattice potential to isolate each site (i.e., Mott insulator phase) 4. Bring the adjacent lattice sites together to engage the entanglement via cold controlled collisions
The Optical Dipole Force
If laser beam is far from resonance, the spontaneous
scattering rate is low and dipole light traps are nearly
conservative.
N
e-E= E0 cos(t)
induced dipole moment: μ = αE
AC Stark shift: UAC = <-μ.E>
= -(α/2) E02
laser intensity
α > 0 atoms attracted to light α < 0 atoms repelled from light
Optical Lattices
1D:
2D:
3D:
Calculable, versatile atom trapsLight potential is state dependent
in phase
out of phasephaseinsensitive
3D Optical Lattice Light Configuration
x
y
z+⊿
I x cos2 kx x I y cos2 ky x I z cos 2 kzz
2 IxI
ycoscos k
xx cosk
yy
Phase Transition from a Superfluid to a Mott Insulator in an ultracold Rb gas
Greiner et al., Nature 415, 39 (2002)
raising up lattice potential