Quantum Algorithms

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Cooling and superpositions of
dielectric objects
ORIOL ROMERO-ISART Mathieu Juan Romain Quidart
Steady-state entanglement with atomic
ensembles
CHRISTINE MUSCHIK Eugene Polziks group
QIPC09, Rome, September 21st, 2009
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PHENOMENOLOGY SPIN WAVES
Cooling and superpositions of
dielectric objects
(Romero-Isart, Juan, Quidart, IC, arXiv0909.1469)
(see also Chan et al, arXiv0909.1548)
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QUANTUM CONTROL PHYSICAL SYSTEMS
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OPTO-MECHANICAL SYSTEMS
Aspelmeyer, Bouwmeester, Harris, Heidmann,
Kippenberg, Treulein, ...
Theory Hammerer, Girvin, Marquardt, Meystre,
Milburn,Tombesi/Vitali,,
Goals
Ground-state cooling
Testing QM with larger and larger objects
Decoherence heating by coupling to other thermal
modes
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OPTO-MECHANICAL SYSTEMS DIELECTRIC OBJECTS
Levitating dielectric objects
Nano-spheres, other shapes,
Sizes up to hundreds of nm
Ground state cooling
Superpositions, entangled states, etc
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DIELECTRIC OBJECTS TRAPPING
Dielectric objects can be trapped with optical
tweezers
Dipole force
Dielectric constant (possible
inhomogeneous)
Achieved with many objects
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DIELECTRIC OBJECTS TRAPPING
Dielectric objects can be trapped with optical
tweezers
(Romain Quidarts lab)
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DIELECTRIC OBJECTS PROPOSAL
Proposal
Introduce in a high Q cavity
Laser-cool it.
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DIELECTRIC OBJECTS PROPOSAL
Proposal
Introduce in a high Q cavity
Laser-cool it.
Preparation of superpositions.
or
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DIELECTRIC OBJECTS PROPOSAL
Features
Not attached to any mechanical object no heating
by thermal contact.
Harmonic trapping Center of mass decouples from
all other modes
(External potential)
(Elastic potential)
Heating by background gas Pressures
Not heated by laser
Other sources of decoherence black-body
radiation, laser fluctuations, etc
We have access to translational and rotational
degrees of freedom
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DIELECTRIC OBJECTS DESCRIPTION
Mecanism
Frequency shift depending on the position
Frequency shift by perturbation theory
Hamiltonian
Cavity
Same as with any other opto-mechanical system
same tricks
Laser driving
Frequency detuning
Cavity damping
enhanced by
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DIELECTRIC OBJECTS COOLING
Resolved sideband regime
Tuning to the lower motional sideband

• Ground state cooling
• Beam-splitter Hamiltonian

Tuning to the upper motional sideband

• Two-mode squeezing Hamiltonian

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DIELECTRIC OBJECTS SUPERPOSITIONS
Lower sideband
Input
or
Final state
Homodyne detection
It requires strong coupling
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DIELECTRIC OBJECTS SUPERPOSITIONS
Lower sideband
Input
or
Final state
Homodyne detection
Solution change g(t)
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DIELECTRIC OBJECTS SUPERPOSITIONS
Upper sideband
Entangled state motion-output.
Imperfect teleportation.
It does not require strong coupling
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DIELECTRIC OBJECTS SPECIFIC PARAMETERS
Sphere (polysterene)
Trapping laser
Cavity
Other parameters
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DIELECTRIC OBJECTS LIVING ORGANISMS
Also magnetic trapping
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PHENOMENOLOGY SPIN WAVES
Long-lived entanglement
atomic ensembles
(Muschik, Polziks group, in preparation)
(See Christines poster)
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ENTANGLEMENT
Physical systems
Photons.
Ions.
Neutral atoms.
Electrons.
Atomic ensembles.
Procedure
Pure state (cooling, polarization, etc)
Coherent interaction (gate)
Isolation (no decoherence)
Lifetime lt 1 second
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ENTANGLEMENT QUANTUM RESERVOIR ENGINEERING
Procedure
Engineer the coupling
Steady state desired state
Arbitrary initial state
Proposals
Single trapped ion (Poyatos, IC, and Zoller 98).
Atoms in two cavities (Kraus and IC 04).
Many-body systems (Kraus et al, Verstraete, Wolf
and IC 09).
State preparation.
Quantum phase transitions.
Quantum computing.
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ENTANGLEMENT ATOMIC ENSEMBLES
Set-up
magnetic fields
magnetic fields
laser
Reservoir common modes of the electromagnetic
field.
Control laser and magnetic fields
Result
Steady-state is an entangled state.
Immune to noise
Long-lived entanglement
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ATOMIC ENSEMBLES DESCRIPTION
Set-up
magnetic fields
magnetic fields
laser
Processes
Forward direction
Other directions spontaneous emission
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ATOMIC ENSEMBLES DESCRIPTION
Master equation
magnetic fields
magnetic fields
laser
noise (spont. emission, decoherence, etc)
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ATOMIC ENSEMBLES DESCRIPTION
Master equation
magnetic fields
magnetic fields
laser
Adiabatic ellimination excited states
Two independent bands of modes
Born-Markov approximation
Room temperature (average atomic motion)
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ATOMIC ENSEMBLES DESCRIPTION
Steady state
magnetic fields
magnetic fields
laser
Dark state
Entanglement ideal
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ATOMIC ENSEMBLES DESCRIPTION
Steady state
magnetic fields
magnetic fields
laser
Dark state
Entanglement with noise
noise rate
polarization
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ATOMIC ENSEMBLES EXPERIMENT
Experiment Cesium
magnetic fields
magnetic fields
laser
Many levels
F4
F3
Quasi steady-state
polarization
depopulation
Longer time scale
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ATOMIC ENSEMBLES EXPERIMENT
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SUMMARY
Small dielectric objects can be trapped and cooled
Creation of superpositions
Tests of QM with larger/different objects
Entanglement
Quantum interfaces
Future
Living organisms?
Larger objects
Magnetic trapping
Proposal for long-lived entanglement
Atomic ensembles at room temperature.
Experimental results
Future
Multi-level systems
More systems