Transcript 20040929114512301

Decoherence issues for atoms in cavities & near surfaces
Peter 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
Cold surface
Mirror qed
Dielectric layer
Multilayer
PBG
JCM limit
 ? kT
height
 ? kT
Drexhage/Kuhn from late 60’s
cavities
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Barton Proc Roy
Soc 1971
Milonni & Knight,
1973
Kleppner
Hinds, Haroche,
Mossberg,
Kimble
And now with ions
in Innsbruck and
Munich
Dielectric output
coupler
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Dutra & Knight,
Optics Commun
117, 256, 1995;
Phys Rev A53,
3587, (1996);
Neat Bessel beam
output for
microcavity
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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
M.B. Plenio et al, Phys. Rev. A 59, 2468 (1999)
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
Entanglement between distant cavities.
S. Bose, P.L. Knight, M.B. Plenio and V. Vedral, PRL 58, 5158 (1999); Browne et al (2003/4)
D+
Bob
D-
Alice
Beam splitter destroys whichpath information!
A detected photon could have
come from any cavity.
Cold atoms and warm surfaces
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Atom chip guides:
Ed’s talk
Atom registers
made via Mott
Transition from BEC
Addressing & gates
Heating and
decoherence
Warm surfaces: em field noise above a metal surface: Ed reprise
resistivity of metal
dissipation in surface
fluctuation of field
heating and spin flips
Spin flip lifetime above a thick slab/wire
height
skin depth
metal slab
spin flip
frequency
Ed’s vision: An atomic quantum
electrostaticregister
wires
integrated fiber
trapping light
BEC
Mott insulator
There can be exactly 1 atom per lattice site (number squeezing)
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
Atoms are completely localized to lattice sites !
Fock states with a vanishing
atom number fluctuation are
formed.
n=1
Atom number
distribution after
a measurement
Quantum gates with neutral atoms
•Bring atoms into a superposition of internal
states
•Move atoms state selectively to neighbouring
site
•Interaction phase (Collisions or Dipole-Dipole)
•Create large scale entanglement
•Ising model
QuickTime™ and a Microsoft Video 1 decompressor are needed to see this picture.
•Hamiltonian simulations
•Multi-particle interferometer
D. Jaksch et al., PRL 82,1975(1999), G. Brennen et al., PRL 82, 1060 (1999)
A. Sorensen et al., PRL 83, 2274 (1999)
Optical Lattices Mott Register Physical System
e
•Raman transition:
•Optical lattice model
*
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J iR  a b
2

a
ga
b
gb
Tunnelling transitions (J) and collisions (U)
•Hamiltonian:
[ai , a j ]  [bi , bj ]   ij
H   (Jia ai ai1  Jib bibi1  JiR aibi  H.c.)
i
U aa
U bb
2 2


2 2

ai ai  U ab  ai aibi bi 
bi bi


2 i
2 i
i
PHASE TRANSITION
8 atoms in 10 sites
Superfluid
phase
Population
Sites
In harmonic potential V~U
Superfluid
phase
Population
Sites
Mott insulator
Population
Sites
Mott insulator
Population
Sites
For U/J>11.6 approximately one atom per lattice site is
obtained. For J=0 we obtain Fock states.
Mott insulator
Population
Sites
Use it as a register: one atom per site in a or b mode is a
qubit in |0> or |1> state.
Coherent Interactions
| 10;01 
•Consider the occupational
state of two lattice sites:
a
b
| n1a nb1 ; na2 nb2 
•Atomic Raman trans.
a
b
•Tunnelling trans.
1
2
ga
JR
1
gb
2
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
 U ab
 a
 J
H2   b
 J
 0

J
a
0
0
J
J
b
0
0
b
J
a
|11;00>
0 

b
J 
a
J 
U ab 
U ab
 Jb
a
J J
K 2
U ab
b
J<<U
 Jb
Ja
•Evolution: effective exchange interaction
Heff =-K(|10><01|+|01><10|)
|00;11>
Kt

|01;10>
 0 .5
4321
SWAP
|10;01>
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
 U ab
 a
 J
H2   b
 J
 0

J
a
0
0
J
J
b
0
0
b
J
a
|11;00>
0 

b
J 
a
J 
U ab 
U ab
 Jb
a
J J
K 2
U ab
b
J<<U
 Jb
Ja
•Evolution: effective exchange interaction
Heff =-K(|10><01|+|01><10|)
|00;11>
Kt

|01;10>
876
 10.9
SWAP
|10;01>
Quantum Computation
• One qubit gate by Raman transitions between the states
|0>=|ga > and |1 >=|gb >.
• Two qubit gates by modulations of lattice potential
i
 Conditional Phase gate: |11>
e |11>

SWAP
: |01>
(|01>+i|10>)/ 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>.
SWAP ]
• 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.
2. What about decoherence?
(A) Technical noise in the em field
Above current-carrying wires
audiofrequency
vibrates the trap
heating
radiofrequency
excites spin flips
loss
In a far-detuned light trap
fluctuations of intensity, phase, polarization
heating and loss
In permanent magnet traps
is there technical noise?
We are just learning how to control technical noise in microtraps
time scale ~ 1-100s
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: