Quantum Computing with Polar Molecules: quantum optics - solid state interfaces

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Quantum Computing with Polar Molecules quantum
optics - solid state interfaces
UNIVERSITY OF INNSBRUCK
Peter Zoller
A. Micheli (PhD student)P. Rabl (PhD
student)H.P. Buechler (postdoc)G. Brennen
(postdoc)
AUSTRIAN ACADEMY OF SCIENCES
SFBCoherent Control of Quantum Systems U
networks
Harvard / Yale collaborationsMisha Lukin
(Harvard) John Doyle (Harvard)Rob Schoellkopf
(Yale)Andre Axel (Yale) David DeMille (Yale)
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Cold polar molecules
exp DeMille, Doyle, Mejer, Rempe, Ye,

• Whats 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

electric dipole moments
molecular ensembles / single molecules
superconducting circuits

• compatible setups parameters
• strength / weakness complement each other

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Quantum Optics with Atoms Ions
Polar Molecules

• cold atoms in optical lattices

laser
rotation
dipole moment

• trapped ions / crystals of

• 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

• CQED

cavity
atom
laser

• atomic ensembles

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Polar molecules

• basic properties

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1a. Single Polar Molecule rigid rotor

• single heteronuclear molecule

"D"
N2
d

• dipole d10 Debye
• rotation B10 GHz (anharmonic ?)
• (essentially) no spontaneous emission ?(i.e.
  excited states useable)

"P"
N1
d
"S"
N0
rigid rotor

• Strong coupling to microwave fields / cavities
  in particular also strip line cavities

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1b. Identifying Qubits

• rigid rotor

• adding spin-rotation coupling (S1/2)

H B N2
H B N2 ? NS
"D5/2"
"D"
J5/2
N2
"D3/2"
J3/2
N2
"P"
"P3/2"
N1
J3/2
N1
"P1/2"
J1/2
spin-rotation splitting
"S"
"S1/2"
N0
N0
J1/2
charge qubit
spin qubit(decoherence)

• How to encode qubits?

looks like an Alkali atom on GHz scale(we
adopt this below as our model molecule)
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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
attraction
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What can we do with Polar Molecules?

• a few examples ideas

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1. Hybrid Device solid state processor
molecular memory optical interface
R. Schoelkopf, S. Girvin et al. see talk by A.
Blais on Tuesday
superconducting (1D) microwave transmission line
cavity(photon bus)
Yale-typestrong coupling CQED
Cooper Pair Box (qubit)
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1. Hybrid Device solid state processor
molecular memory optical interface
P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin
optical (flying) qubit
superconducting (1D) microwave transmission line
cavity(photon bus)
strong coupling CQED
Cooper Pair Box (qubit) as nonlinearity
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Trapping single molecules above a strip line
Andre Axel, R. ScholekopfM. Lukin et al.

• 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 h0.1 mm from surface
• High trap frequencies (? gt 1-10 MHz)
• large trap depths
• Challenges
• Loading no laser cooling (?)
• Interaction with surface
• e.g. van der Waals interaction

Electrostatic Z trap (EZ trap)

• DC voltage same trap potential for N1,2 states
  at 10 kV/cm

• AC voltages same trap potential for
• N0,1 states at magic detuning

micron-scale electrode structure
_at_ h0.1 and ntgt 10 MHz shifts
levels by less than 1
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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
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2. Realization of Lattice Spin Models
A. Micheli, G. Brennen, PZ, preprint Dec 2005

• 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

Examples
Kitaev
Duocot, Feigelman, Ioffe et al.
xx
zz
ZZ
XX
YY
protected quantum memorydegenerate ground
states as qubits
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3. (Wigner-) Crystals with Polar Molecules
H.P. BüchlerV. SteixnerG. PupilloM. Lukin

• Wigner crystals in 1D and 2D (1/R3 repulsion
  for R gt R0)

dipole-dipole crystal for high density
Coulomb WC for low density (ions)
2D triangular lattice(Abrikosov lattice)
1st order phase transition
g(R)
solid
liquid
Tonks gas / BEC (liquid / gas)
WC
mean distance
R
quantum statistics
100 nm
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Applications
compare ionic Coulomb crystal

• 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 -gt spin waves

d1 d2 /R3

• ion trap like qc, however
• d variable
• spin dependent d
• qu melting / quantum statistics

?x
phonons (breathing mode indep of molecules)
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Quantum Optical / Solid State Interfaces
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Hybrid Device solid state processor
molecular memory optical interface
with P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin
optical (flying) qubit
superconducting (1D) microwave transmission line
cavity(photon bus)
strong coupling CQED
Cooper Pair Box (qubit) as nonlinearity
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1. strong CQED with superconducting circuits
R. Schoelkopf, M. Devoret, S. Girvin (Yale)

• Cavity QED
• ... similar results expected for coupling to
  quantum dots (Delft)
• compare with CQED with atoms in optical and
  microwave regime

SC qubit
Jaynes-Cummings
good cavity
strong coupling!(mode volume V/ ?3 ¼ 10-5 )
not so great qubits
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2. ... coupling atoms or molecules
with Yale/Harvard

• hyperfine excitation of BEC / atomic ensemble

• superconducting transmission line cavities

atoms /molecules
SC qubit

• rotational excitation of polar molecule(s)

• 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

N1
rotational excitations 10 GHz
N0
ensemble ?
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3. Atomic / molecular ensemblescollective
excitations as Qubits

• ground state
• one excitation (Fock state)
• two excitations ... eliminate?
• in AMO dipole blockade, measurements ...

microwave
microwave
harmonic oscillator
nonlinearity due to Cooper Pair Box.
etc.

• also ensembles as continuous variable quantum
  memory (Polzik, ...)
• collisional dephasing (?)

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4. Hybrid Device solid state processor molec
memory
moleculesqubit 1
SC qubit
time independent
moleculesqubit 2
solid state system
ensemblequbits
swap molecule - cavity
dissipation (master equation)
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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
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Spin Models with Optical Lattices
A. Micheli, G. Brennen PZ, preprint Dec 2005

• 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

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Duocot, Feigelman, Ioffe et al.
Kitaev
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Basic idea of engineeringspin-spin interactions
dipole-dipole anisotropic long range
spin-rotationcoupling
spin-rotationcoupling
microwave
microwave
effective spin-spin coupling
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Adiabatic potentials for two (unpolarized) polar
molecules
( here ?/B 1/10 )

• Spin Rotation

Induced effective interactions 0g S1 S2
2 S1c S2c 0g S1 S2 2 S1p S2p 1g
S1 S2 2 S1b S2b 1u S1 S2 2g S1b
S2b 0u 0 2u 0 for ebody ex and epol
ez 0g XXYYZZ 0g XXYYZZ 1g
XXYYZZ 1u XXYYZZ 2g XX
?
S1/2 S1/2
Feature 1. By tuning close to a resonance we can
select a specific spin texture
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Example "The Ioffe et al. Model"

• Model is simple in terms of long-range resonances
  

Rem. for a multifrequency field we can add the
corresponding spin textures.
Feature 2. We can choose the range of the
interaction for a given spin texture
Feature 3. for a multifrequency field spin
textures are additive toolbox
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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