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: