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

Conclusions

• Long decoherence time in an optical lattice• Allow state selected measurements by shining lase

r beams

High spatial resolution should be possible

and allow to address single site• Many sites are loaded.

It might allow for error correction• High fidelity for the quantum entanglement