multiparticle entangled states of the w- class, their properties and applications
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Multiparticle Entangled States of the W- class, their Properties and Applications. A. Rodichkina , A. Basharov, V. Gorbachev Laboratory for Quantum Information & Computation, AeroSpace University, St.-Petersburg 190000, Bolshaia Morskaia 67, Russia , - PowerPoint PPT PresentationTRANSCRIPT
Multiparticle Entangled States of the W- class, their Properties and Applications
A. Rodichkina, A. Basharov, V. Gorbachev
Laboratory for Quantum Information & Computation,AeroSpace University, St.-Petersburg 190000, Bolshaia Morskaia 67,
Russia,Laboratory for nonlinear optics, RRC "Kurchatov Institute",
Moscow 123182, Russia.
Supported by
Delzell Foundation Inc. and RFBR grant 06-02-16769.
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Outline
• Introduction to W states
• Generation schemes
• Robustness
• Applications
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Introduction to W states
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• Two level atom • Polarized light |H>, |V>• Fock states of light |n>, with n=1,0 photons.
Experiment
• Polarized photons. H.Weinfurter et al PRL, 92, 087902 and 077901 (2004) .• Ions Са40. F.Schmidt-Kaler et al Science, 304, 1478, (2004).• Decoherence-free communications. H.Weinfurter et al PRL, 92, 107901 (2004).
|0>, |1> are logical states
Reviews on W states A. Karlsson, M. Bourennane et al. Quant. Computer and Computing, 4, 3, (2003) .
V.N. Gorbachev, A.I. Trubilko. Laser Phys. Lett. 3, No. 2, 59-70 (2006).
Multiparticle entangled states
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Dicke states
• Dicke states are specified by three quantum numbers j,m,a.
where
k=1,2,3
are Pauli matrices of the m-th atom
|m| j, j=o,.. n-1, n is number of particles, quantum number a describes
values.
R. Dicke. Phys. Rev. 93, 99, 1954.
• For two level atoms
degeneracy, it takes
where
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These states are also known as Zero Sum Amplitude states
(A.K. Pati. J. Physics, 59, 217 (2002)).
(V.N. Gorbachev, A.I. Trubilko, JETP, 101, 33, 2005)
Connection with Dicke states
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…
where is the antisymmetric Bell state.
• The Young scheme [n-1 n] 1
2
3 k n 1
3
2 k n
1
k
2 3 n 1
n
2 3 k
++
+
• If
• Collective evolution of n particles reduces to evolution of n-2 particles.
A representation
… …
… …+
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Generation schemes
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Optical experiment by H.Weinfurter et al PRL, 92, 087902 and 077901 (2004)
• Input 4-photon state
• The three-polarized photon state
is prepared with probability 1/36 (after post selection)
Generation
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Experiment with trapped ions 40 Ca+ by F. Schmidt-Kaler et al. Science, 304, 1478, (2004)
• Qubits are encoded in the ground and metastable states D and S
S
D• Laser pulse can rotate each ion
• Each ion interacts with a vibration mode
• Operations R and R+ have been implemented experimentally.
R
Generation - 2
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• Atomic W states
n atoms
• W states from atomic ensembles
detector
V. Gorbachev et al Phys.Lett. A, 310, 339, 2003 .
Schemes for generation of atomic states
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1
Biphoton
Bs
Detector• Transformation of the Fock state
• The state of biphoton
• Rate of generation. A pulsed-pumped laser with pulse 100 fs and 100 MGHrepetition rate, average power of 200 mW, , a pair per 104 pulses, the generation rate of biphoton or desired state Is about 104 per second. In experiment of generation of polarized W the rate was about 1 per minute.
Optical scheme on biphotons
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Robustness
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• Robustness to loss of particle. "Persistency of entanglement”, Briegel et. al. Phys. Rev. Lett., 86, 910, (2001)
if
is annihilated by the collective operator :
• Immunity to collective interactions.
• Application for storage of quantum states. (A. Basharov et al PRA, 2006)
Let a physical process be described by the equation
where
then the state Is conserved:
Robustness
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M F
Two-level atomsCavity mode
Broad band field or bath
• Hamiltonian where
• Tavis-Cummings model
• Master Equation for atoms
• The presented model describes impurities in nanocrystal
(A. Basharov et al. Russian Quant Electronics, 2006)
A
Collective decay of atoms
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1. Dispersive limit2. Bath is in vacuum state3. Non-collective relaxation is neglected
• Approximations
• Master equation for atomic density matrix
• Exact solution for the density matrix
where
Master equation for atoms
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• If then = Const(t) and it has immunity to decay
• In contrast
• Scheme for writing and storing atoms in the cavity
photon
• Swapping:
Swapping photon-atoms: V. Gorbachev et al. Phys. Lett. A, Vol 323/5-6, 339, (2004)
BS
Storage of entangled states
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Applications
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• Using W states in the standard protocols
Conditional teleportation(B.-S. Shi, A Tomita. Phys.Lett. A, 296, 161, (2002),
J.Joo, Y.J. Park, S.Oh, J.Kim. New Journal of Phys. 5, 136, (2003)
Unconditional teleportation of entangled states, three-qubit dense coding (V. Gorbachev et al Phys. Lett. A 314, 267, (2003) )
and
Quantum key distribution.(J. Joo,J. Lee, J. Jang, Y.-J Park. E-print, LANL, quant-ph/0204003 (2002))
• Application due to features of W states
Collective decay and storage of quantum states in collective thermostat.(A. Basharov et. al. PRA, (2006) in print)
Applications
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Thank you