Decoherence issues for atoms in cavities & near surfacesPeter Knight, Imperial College London

work with P K Rekdal,Stefan Scheel, Almut Beige, Jiannis Pachos, Ed Hinds and many others

• Cold surfaces: cqed in bad and good cavity limits?

• Warm surfaces & cold atoms: Atom chips, Mott transition & registers and spin flips

height

Cold surface

Mirror qed

Dielectric layer

Multilayer

PBGJCM limit

hω ? kT

hω ? kT

Drexhage/Kuhn from late 60’s

cavities

Barton Proc Roy Soc 1971

Milonni & Knight, 1973

Kleppner Hinds, Haroche,

Mossberg, Kimble And now with ions

in Innsbruck and Munich

Dielectric output coupler

Dutra & Knight, Optics Commun 117, 256, 1995; Phys Rev A53, 3587, (1996);

Neat Bessel beam output for microcavity

Put single atom or dot source in PBG or Bragg Stack

Rippin & Knight, J Mod Opt 43, 807, (1996) Bragg stack

Scheel, Dowling, PLK et al quant-ph0207075

Does it work?

Beige, Knight, Tregenna, Huelga, Plenio, Browne, Pachos…how to live with noise, and use of decoherence-free subspaces

Cqed good cavity fundamentals

Slide from Tom Mossberg

Cqed fundamentals

Slide from Tom Mossberg

Two atoms in a cavity: entanglement via decay

Cavity in vacuum state, with two atoms in their ground state.

Excite one atom!

Exchange of excitation between the atoms and the cavity mode.No jump detection and Bell states

M.B. Plenio et al, Phys. Rev. A 59, 2468 (1999)

Alice

Bob

D

D

-

+

Entanglement between distant cavities.S. Bose, P.L. Knight, M.B. Plenio and V. Vedral, PRL 58, 5158 (1999); Browne et al (2003/4)

Beam splitter destroys which-path information!A detected photon could have come from any cavity.

Cold atoms and warm surfaces

Atom chip guides: Ed’s talk

Atom registers made via Mott Transition from BEC

Addressing & gates Heating and

decoherence

Spin flip lifetime above a thick slab/wire

Henkel, Pötting and Wilkens Appl. Phys B 69,379 (1999);Scheel, Rekdal, PLK & Hinds

metal slab

height

Warm surfaces: em field noise above a metal surface: Ed reprise

dissipation in surface

resistivity of metal

fluctuation of field

heating and spin flips

spin flipfrequency

skin depth

Ed’s vision: An atomic quantum register

trapping light

integrated fiber

electrostatic wires

BEC

There can be exactly 1 atom per lattice site (number squeezing)

Mott insulator

Light-induced lattices

Superfluid Limit

Atoms are delocalized over the entire lattice !

Macroscopic wave function describes this state very well.

Poissonian atom number distribution per lattice site

n=1

Atom number

distribution after a

measurement

Atomic Limit of a Mott-Insulator

n=1

Atoms are completely localized to lattice sites !

Fock states with a vanishing atom number fluctuation are formed.

Atom number distribution

after a

measurement

Quantum gates with neutral atoms

D. Jaksch et al., PRL 82,1975(1999), G. Brennen et al., PRL 82, 1060 (1999)

A. Sorensen et al., PRL 83, 2274 (1999)

•Create large scale entanglement

•Ising model

•Hamiltonian simulations

•Multi-particle interferometer

•Bring atoms into a superposition of internal states

•Move atoms state selectively to neighbouring site

•Interaction phase (Collisions or Dipole-Dipole)

QuickTime™ and aMicrosoft Video 1 decompressorare needed to see this picture.

Optical Lattices Mott Register Physical System

•Raman transition:

•Optical lattice model

Tunnelling transitions (J) and collisions (U)

•Hamiltonian: ijjiji bbaa δ== ++ ],[],[

ga gb

e

aΩ bΩ

ΔΔΩΩ

=2

*baR

iJ

€

H = − (Jiaai

+ai+1 + Jibbi

+bi+1 + JiRai

+bi + H.c.)i

∑

+Uaa

2ai

+2ai

2

i

∑ +Uab ai+aibi

+bii

∑ +Ubb

2bi

+2bi

2

i

∑

Population

Sites

PHASE TRANSITION

8 atoms in 10 sites

Superfluid phase

In harmonic potential V~U

Population

Sites

Superfluid phase

Mott insulator

Population

Sites

Population

Sites

Mott insulator

For U/J>11.6 approximately one atom per lattice site is obtained. For J=0 we obtain Fock states.

Use it as a register: one atom per site in a or b mode is a qubit in |0> or |1> state.

Population

Sites

Mott insulator

Coherent Interactions

•Consider the occupational state of two lattice sites:

>2211 ;| baba nnnna

b

1 2

•Atomic Raman trans.

a b

RJ

•Tunnelling trans.

1 2

ga gb

>01;10|

Exchange Interaction• Consider the evolution of the state |01;10> and |10;01>

when we lower the potential of both a and b-modes. They are coupled to |00;11> and |11;00> by

|11;00> |00;11>

|01;10> |10;01>

abU

•Evolution: effective exchange interaction

Heff =-K(|10><01|+|01><10|)

J<<U

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−−−−−−

−−

=

abab

ab

ba

baab

UJJ

JJ

JJ

JJU

H

0

00

00

0

2bJ−bJ−

aJ−

ab

ba

U

JJK 2=

0=πKt

1.0=πKt

2.0=πKt

3.0=πKt

4.0=πKt

5.0=πKt

SWAP

Exchange Interaction• Consider the evolution of the state |01;10> and |10;01>

when we lower the potential of both a and b-modes. They are coupled to |00;11> and |11;00> by

|11;00> |00;11>

|01;10> |10;01>

abU

•Evolution: effective exchange interaction

Heff =-K(|10><01|+|01><10|)

J<<U

6.0=πKt

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−−−−−−

−−

=

abab

ab

ba

baab

UJJ

JJ

JJ

JJU

H

0

00

00

0

2bJ− bJ−

aJ−

ab

ba

U

JJK 2=

7.0=πKt

8.0=πKt

9.0=πKt

1=πKt

SWAP

Quantum Computation• One qubit gate by Raman transitions between the states |

0>=|ga > and |1 >=|gb >.

• Two qubit gates by modulations of lattice potential

Conditional Phase gate: |11> |11>

: |01> (|01>+i|10>)

ϕieSWAP 2/

Gates• “Charge based” quantum computation with Optical

Lattice.

• Mott Insulator of 1 atom/site serves as a register. Two in-phase lattices trap two ground states of the atom [logical |0> and |1>].

• One qubit gates by Raman transitions |0> |1>.

• Two qubit gates [control phase-gates or ] performed by exchange interactions in one or both of the optical lattices, respectively.

• Can perform multi-qubit gates in one go.

SWAP

2. What about decoherence?

In permanent magnet traps

(A) Technical noise in the em field

Above current-carrying wires

In a far-detuned light trap

We are just learning how to control technical noise in microtraps

time scale ~ 1-100s

audiofrequency vibrates the trap heating

radiofrequency excites spin flips loss

fluctuations of intensity, phase, polarization

heating and loss

is there technical noise?

Heating rate calculations: Rekdal, Scheel, Knight & Hinds (2004)

Basic idea

Numerical results• Copper core, radius a1 185

microns plus 55 micron radius a2 Al layer

• Use quoted resistivities to get skin depths delta of 85 microns for Cu and 110 microns for Al at frequency 560 kHz used by Ed’s group

• One conclusion: Ed is a bit more wiry than slabby…

conclusions

– Quantum information with optical lattices and atom chips has great potential

– Quantum optics techniques on atom chips can probably make basic gates

– Decoherence is an interesting problem: heating rates of seconds gives loads of time for gates.

– Quantum memories are harder to realize: few qubit applications?

• Funding: