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