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AUSTRIAN ACADEMY OF SCIENCES UNIVERSITY OF INNSBRUCK Quantum Computing with Polar Molecules: quantum...
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Transcript of AUSTRIAN ACADEMY OF SCIENCES UNIVERSITY OF INNSBRUCK Quantum Computing with Polar Molecules: quantum...
AUSTRIANACADEMY OF
SCIENCES
UNIVERSITY OF INNSBRUCK
Quantum Computing with Polar Molecules: quantum optics - solid state interfaces
SFBCoherent Control of Quantum Systems
€U networks
Peter Zoller
A. Micheli (PhD student)P. Rabl (PhD student)H.P. Buechler (postdoc)G. Brennen (postdoc)
Harvard / Yale collaborations:
Misha Lukin (Harvard) John Doyle (Harvard)Rob Schoellkopf (Yale)Andre Axel (Yale) David DeMille (Yale)
Cold polar molecules
What‘s next in AMO physics?
• Cold polar molecules in electronic & vibrational ground states
– control & very little decoherence
What new can we do?
• AMO physics:
– new scenarios in quantum computing & cold gases
• Interface AMO – CMP
– example:
F–
exp: DeMille, Doyle, Mejer, Rempe, Ye, …
molecular ensembles / single molecules
superconducting circuits
compatible setups & parameters
strength / weakness complement each other
electric dipole moments
Quantum Optics with Atoms & Ions
• trapped ions / crystals of …
• CQED
atomcavity
laser
• cold atoms in optical lattices
laser
• atomic ensembles
Polar Molecules
• single molecules / molecular ensembles
• coupling to optical & microwave fields– trapping / cooling– CQED (strong coupling)– spontaneous emission / engineered
dissipation
• interfacing solid state / AMO & microwave / optical
– strong coupling / dissipation
• collisional interactions– quantum deg gases / Wigner (?) crystals– dephasing
dipole moment
rotation
Polar molecules
• basic properties
1a. Single Polar Molecule: rigid rotor
• single heteronuclear molecule
dipole d~10 Debye
rotation B~10 GHz (anharmonic )
(essentially) no spontaneous emission (i.e. excited states useable)
N=0
N=1
N=2
"S"
"P"
"D"
F–
…
d
rigid rotor
d
• Strong coupling to microwave fields / cavities; in particular also strip line cavities
"P"
1b. Identifying Qubits
• rigid rotor • adding spin-rotation coupling (S=1/2)
N=0
N=1
N=2
N=0
N=1
N=2
J=1/2
J=1/2
J=3/2
J=3/2
J=5/2
"S"
"D"
"S1/2"
"P3/2"
"D5/2"
"D3/2"
"P1/2"
H = B N2 H = B N2 + N·S
• How to encode qubits? ``looks like an Alkali atom on GHz scale´´(we adopt this below as our model molecule)
spin qubit(decoherence)
charge qubit
spin-rotation splitting
2. Two Polar Molecules: dipole – dipole interaction
• interaction of two molecules
features of dipole-dipole interaction
long range ~1/R3
angular dependence
strong! (temperature requirements)
repulsion
attractionVdd d1d2 3 d1eb ebd2
R3
What can we do with Polar Molecules?
• a few examples & ideas
Cooper Pair Box (qubit)
superconducting (1D) microwave transmission line
cavity(photon bus)
1. Hybrid Device: solid state processor & molecular memory + optical interface
Yale-typestrong coupling CQED
R. Schoelkopf, S. Girvin et al.
see talk by A. Blais on Tuesday
Cooper Pair Box (qubit)
as nonlinearity
superconducting (1D) microwave transmission line
cavity(photon bus)
molecular ensembleoptical
cavity
laser
optical (flying) qubit
1. Hybrid Device: solid state processor & molecular memory + optical interface
polar molecular ensemble 1:quantum memory
(qubit or continuous variable)[Rem.: cooling / trapping]
polar molecular ensemble 2:quantum memory
(qubit or continuous variable)
strong coupling CQED
P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin …
Trapping single molecules above a strip line
• Three approaches:– magnetic trapping (similar to neutral atoms)– electrostatic trap: d.E interaction DC– microwave dipole trap: d.E interaction AC
• Goals– Trapping of relevant states h~0.1 mm from surface– High trap frequencies ( > 1-10 MHz)– large trap depths …
• Challenges: – Loading – no laser cooling (?)– Interaction with surface
e.g. van der Waals interaction
micron-scaleelectrode structure
0.1m
Electrostatic Z trap (EZ trap)
• DC voltage: same trap potential for N=1,2 states at ~10 kV/cm• AC voltages: same trap potential for
N=0,1 states at “magic” detuning
Andre Axel, R. ScholekopfM. Lukin et al.
@ h~0.1 and t> 10 MHz shifts levels by less than 1%
|2>
|1>
Sideband cooling with stripline resonator (“g cooling”)
• “g” cooling: position dependence of coupling g(r) to cavity gives rise to force
• “” cooling: spatially uniform g but different traps in upper/lower states → gives rise to force
engineered dissipation + analogy to laser cooling
2. Realization of Lattice Spin Models
• polar molecules on optical lattices provide a complete toolbox to realize general lattice spin models in a natural way
• Motivation: virtual quantum materials towards topological quantum computing
XX YY
ZZ
xx
zz
Duocot, Feigelman, Ioffe et al. Kitaev
HspinI
i 1 1
j 1 1 J i,jz i,j 1
z cos i,jx i 1,jx Hspin
II J x links
jx kx J y links
jy ky
Jz z links
jz kz
#
# protected quantum memory:
degenerate ground states as qubits
A. Micheli, G. Brennen, PZ, preprint Dec 2005
Examples:
3. (Wigner-) Crystals with Polar Molecules
• “Wigner crystals“ in 1D and 2D (1/R3 repulsion – for R > R0)
Coulomb: WC for low density (ions)
dipole-dipole: crystal for high density
2D triangular lattice(Abrikosov lattice)
mean distance
WCTonks gas / BEC
(liquid / gas)
~ 100 nm
e2/R
2/2MR2~R
1st order phase transition
H.P. BüchlerV. SteixnerG. PupilloM. Lukin…
quantum statistics
g(R)
R
solid
liquid
potential energy
kinetic energy d2/R3
2/2MR2~ 1R
n1/3
• Ion trap like quantum computing with phonons as a bus.
• Exchange gates based on „quantum melting“ of crystal– Lindemann criterion x ~ 0.1 mean distance– [Note: no melting in ion trap]
• Ensemble memory: dephasing / avoiding collision dephasing in a 1D and 2D WC– ensemble qubit in 2D configuration– [there is an instability: qubit -> spin waves]
x
phonons
(breathing mode indep of # molecules)
ion trap like qc, however:
d variable
spin dependent d
qu melting / quantum statistics
compare: ionic Coulomb crystal
d1 d2 /R3
Applications:
Quantum Optical / Solid State Interfaces
Cooper Pair Box (qubit)
as nonlinearity
superconducting (1D) microwave transmission line
cavity(photon bus)
molecular ensembleoptical
cavity
laser
optical (flying) qubit
Hybrid Device: solid state processor & molecular memory + optical interface
polar molecular ensemble 1:quantum memory
(qubit or continuous variable)[Rem.: cooling / trapping]
polar molecular ensemble 2:quantum memory
(qubit or continuous variable)
strong coupling CQED
with P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin
1. strong CQED with superconducting circuits
• Cavity QED
• [... similar results expected for coupling to quantum dots (Delft)]
• [compare with CQED with atoms in optical and microwave regime]
R. Schoelkopf, M. Devoret, S. Girvin (Yale)
SC qubit
strong coupling!(mode volume V/ 3 ¼ 10-5 )
good cavity
“not so great” qubits
Jaynes-Cummings
• rotational excitation of polar molecule(s)
• superconducting transmission line cavities
• hyperfine excitation of BEC / atomic ensemble
atoms /molecules
SC qubit
hyperfine structure
» 10 GHz
rotational excitations
» 10 GHz
N=1
N=0
… with Yale/Harvard
ensemble
2. ... coupling atoms or molecules
• Remarks:– time scales compatible– laser light + SC is a problem: we must move atoms / molecules to interact with light (?)– traps / surface ~ 10 µm scale– low temperature: SC, black body…
3. Atomic / molecular ensembles:collective excitations as Qubits
• ground state
• one excitation (Fock state)
• two excitations ... eliminate?– in AMO: dipole blockade, measurements ...
etc.
microwave
|g|q
|r
microwave
nonlinearity due to Cooper Pair Box.
harmonic oscillator
• also: ensembles as continuous variable quantum memory (Polzik, ...)
• collisional dephasing (?)
molecules:qubit 1
SC qubit
molecules:qubit 2
solid state system swap molecule - cavity
ensemblequbits
4. Hybrid Device: solid state processor & molec memory
time independent
+ dissipation (master equation)
5. Examples of Quantum Info Protocols
• SWAP
• Single qubit rotations via SC qubit
• Universal 2-Qubit Gates via SC qubit
• measurement via ensemble / optical readout or SC qubit / SET
Cooper Pair
cavity (bus)
molec ensemble
Atomic ensembles complemented by deterministic entanglement operations
Spin Models with Optical Lattices
• we work in detail through one example
• quantum info relevance:
– polar molecule realization of models for protected quantum memory (Ioffe, Feigelman et al.)
– Kitaev model: towards topological quantum computing
A. Micheli, G. Brennen & PZ, preprint Dec 2005
Duocot, Feigelman, Ioffe et al. Kitaev
HspinI
i 1 1
j 1 1 J i,jz i,j 1
z cos i,jx i 1,jx Hspin
II J x links
jx kx J y links
jy ky
Jz z links
jz kz
#
#
microwave microwavespin-rotation
couplingspin-rotation
coupling
dipole-dipole: anisotropic + long range
effective spin-spin coupling
Basic idea of engineeringspin-spin interactions
Adiabatic potentials for two (unpolarized) polar molecules
• Spin Rotation ( here: /B = 1/10 )
Induced effective interactions:
0g+ : + S1 · S2 { 2 S1
c S2c
0g{ : + S1 · S2 { 2 S1
p S2p
1g : + S1 · S2 { 2 S1b S2
b 1u : { S1 · S2
2g : + S1b S2
b
0u : 02u : 0
for ebody = ex and epol = ez
0g+ : +XX{YY+ZZ
0g{ : +XX+YY{ZZ
1g : {XX+YY+ZZ1u : {XX{YY{ZZ2g : +XX
S1/2 + S1/2
Feature 1. By tuning close to a resonance we can select a specific spin texture
Example: "The Ioffe et al. Model"
• Model is simple in terms of long-range resonances …
Feature 2. We can choose the range of the interaction for a given spin texture
Rem.: for a multifrequency field we can add the corresponding spin textures.
Feature 3. for a multifrequency field spin textures are additive: toolbox
Summary: QIPC & Quantum Optics with Polar Molecules
• single molecules / molecular ensembles
• coupling to optical & microwave fields
– trapping / cooling
– CQED (strong coupling)
– spontaneous emission / engineered dissipation
• interfacing solid state / AMO & microwave / optical
– strong coupling / dissipation
• collisional interactions
– quantum deg gases / Wigner crystals (ion trap like qc)
– WC / dephasing