Jonathan P. Dowling

OPTICAL QUANTUM COMPUTING

quantum.phys.lsu.edu

Hearne Institute for Theoretical PhysicsDepartment of Physics and Astronomy

Quantum Science and Technologies GroupLouisiana State UniversityBaton Rouge, Louisiana USA

PQE, 03 January 2006, Snowbird

H.Cable, C.Wildfeuer, H.Lee, S.Huver, W.Plick, G.Deng, R.Glasser, S.Vinjanampathy, K.Jacobs, D.Uskov, JP.Dowling, P.Lougovski,

N.VanMeter, M.Wilde, G.Selvaraj, A.DaSilva

Not Shown: MA.Can, A.Chiruvelli, GA.Durkin, M.Erickson, L.Florescu, M.Florescu, KT.Kapale, SJ.Olsen, S.Thanvanthri, Z.Wu

Hearne Institute for Theoretical Physics

Quantum Science & Technologies Group

Two Roads to C-NOT

Cavity QED

I. Enhance Nonlinear Interaction with a Cavity or EIT — Kimble, Walther, Lukin, et al.II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Franson, et al.

Photon-PhotonXOR Gate

Photon-PhotonNonlinearity

Kerr Material

Cavity QEDEIT

ProjectiveMeasurement

  LOQC  KLM

WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?

Linear Single-PhotonQuantum Non-Demolition

The success probability is less than 1 (namely 1/8).

The input state is constrained to be a superposition of 0, 1, and 2 photons only.

Conditioned on a detector coincidence in D1 and D2.

|1

|1

|1D1

D2

D0

/2

/2

|in = cn |nn = 0

2

|0Effective  = 1/8

22 Orders of Magnitude Improvement!

P. Kok, H. Lee, and JPD, PRA 66 (2003) 063814

G. G. Lapaire, P. Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314

KLM CSIGN Hamiltonian Franson CNOT Hamiltonian

NON-Unitary Gates Effective Unitary Gates

A Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature! 

Projective Measurement Yields Effective “Kerr”!

+NA0BeiNϕ0ANB

1 + cos N ϕ

2

1 + cos ϕ

2

ABϕ|N⟩A |0⟩B N Photons

N-PhotonDetector

ϕ = kxΔϕ: 1/√N →1/ΝuncorrelatedcorrelatedOscillates N times as fast!N-XOR GatesN-XOR Gatesmagic BSMACH-ZEHNDER INTERFEROMETERApply the Quantum Rosetta Stone!

Quantum MetrologyH.Lee, P.Kok,

JPD, J Mod Opt 49, (2002) 2325.

N Photons

N-PhotonDetectorϕ = x+NA0BeiNϕ0ANB

1 + cos N ϕ

2

1 + cos ϕ

2

uncorrelatedcorrelatedOscillates in REAL Space!N-XOR Gatesmagic BSFROM QUANTUM INTERFEROMETRYTO QUANTUM LITHOGRAPHY

Mirror

N

2 A

N

2 B

LithographicResist

ϕ →Νϕ λ →λ/Ν

ψ a†

a†

aa ψa† N a

N

AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733

N-Photon AbsorbingLithographic Resist

Showdown at High-N00N!

|N,0 + |0,NHow do we make N00N!?

*C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001).

With a large cross-Kerr nonlinearity!* H =  a†a b†b

This is not practical! — need  =  but  = 10–22 !

|1

|N

|0

|0|N,0 + |0,N

ba33

a

b

a’

b’

ba06

ba24

ba42

ba60

Probability of success:643 Best we found:

163

Projective Measurements to the Rescue

H. Lee, P. Kok, N.J. Cerf, and J.P. Dowling, Phys. Rev. A 65, R030101 (2002).

ba13

ba31

single photon detection at each detector

''''4004

baba−

NotEfficient!

|10::01>

|20::02>

|40::04>

|10::01>

|20::02>

|30::03>

|30::03>

What’s New with N00N States?

KT Kapale & JPD, A Bootstrapping Approach for Generating Maximally Path-Entangled Photon States,[quant-ph/0612196].

NM VanMeter, P Lougovski, DB Uskov, K Kieling, J Eisert, JPD, A General Linear-Optical Quantum State Generator, [quant-ph/0612154].

Durkin GA, Dowling JP, Local and Global Distinguishability in Quantum Interferometry,[quant-ph/0607088].

High-N00N Meets Phaseonium

Quantum Fredkin Gate (QFG) N00N Generation

KT Kapale and JPD, quant-ph/0612196.

• With sufficiently high cross-Kerr nonlinearity N00N generation possible.

• Implementation via Phaseonium

Gerry and Campos, PRA 64 063814 (2001)

€

Two possible methods

• As a high-refractive index material to obtain the large phase shifts– Problem: Requires entangled phaseonium

• As a cross-Kerr nonlinearity– Problem: Does not offer required phase shifts of as yet (experimentally)

Quantum Fredkin Gate (QFG) N00N Generation

KT Kapale and JPD, quant-ph/0612196.

Phaseonium for High Index of Refraction

Re

Im Im

Re

With larger density high index of refraction can be obtained€

N =1015cm-3

€

Re(χ ) =100 cm-3

€

n =10cm-3

N00N Generation via Phaseonium as a Phase Shifter

The needed large phase-shift of can be obtained viathe phaseonium as a high refractive index material.

However, the control required by the Quantum Fredkin gatenecessitates the atoms be in the GHZ state between level a and bWhich could be possible for upto 1000 atoms.

Question: Would 1000 atoms give sufficiently high refractive index?

N00N Generation via Phaseonium-Based Cross-Kerr

Nonlinearity• Cross-Kerr nonlinearities

via Phaseonium have been shown to impart phase shifts of 7controlled via single photon

• One really needs to input a smaller N00N as a control for the QFG as opposed to a single photon with N=30 roughly to obtain phase shift as large as .

• This suggests a bootstrapping approach

In the presence of single signal photon, and the strong drive a weak probe field experiences a phase shift

€

Implementation of QFG via Cavity QED

Ramsey Interferometry for atom initially in state b.

Dispersive coupling between the atom and cavity gives required conditional phase shift

Low-N00N via Entanglement Swapping: The N00N gun

• Single photon gun of Rempe PRL 85 4872 (2000) and Fock state gun of Whaley group quant-ph/0211134 could be extended to obtain a N00N gun from atomic GHZ states.

• GHZ states of few 1000 atoms can be generated in a single step via (I) Agarwal et al. PRA 56 2249 (1997) and (II) Zheng PRL 87 230404 (2001)

• By using collective interaction of the atoms with cavity a polarization entangled state of photons could be generated inside a cavity

• Which could be out-coupled and converted to N00N via linear optics.

€

N0 + 0N

Bootstrapping

• Generation of N00N states with N roughly 30 with

cavity QED based N00N gun.

• Use of Phaseonium to obtain cross-Kerr nonlinearity

and the N00N with N=30 as a control in the Quantum

Fredkin Gate to generate high N00N states.

• Strong light-atom interaction in cavity QED can

also be used to directly implement Quantum Fredkin

gate.