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 PhysicsQuantum Science & Technologies Group

Two Roads to C-NOT

Cavity QED

I. Enhance NonlinearInteraction with aCavity or EIT —Kimble, Walther,Lukin, et al.

II. ExploitNonlinearity ofMeasurement — Knill,LaFlamme, Milburn,Franson, et al.

Photon-PhotonXOR Gate

Photon-PhotonNonlinearity

Kerr Material

Cavity QEDEIT

ProjectiveMeasurement

  LOQC  KLM

WHY IS A KERR NONLINEARITY LIKE APROJECTIVE MEASUREMENT?

Linear Single-PhotonQuantum Non-Demolition

The success probability isless than 1 (namely 1/8).

The input state isconstrained to be asuperposition of 0, 1, and 2photons only.

Conditioned on a detectorcoincidence in D1 and D2.

|1〉

|1〉

|1〉D1

D2

D0

π /2

π /2

|ψin〉 = cn |n〉Σn = 0

2

|0〉Effective κ = 1/8→ 22 Orders of

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

G. G. Lapaire, P. Kok,JPD, J. E. Sipe, PRA68 (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 MeasurementYields Effective “Kerr”!

Quantum MetrologyH.Lee, P.Kok, JPD,

J Mod Opt 49,(2002) 2325.

a† N a N

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

N-PhotonAbsorbingLithographicResist

Showdown at High-N00N!

|N,0〉 + |0,N〉How do we make N00N!?

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

With a large cross-Kerrnonlinearity!* H = κ a†a b†b

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

|1〉

|N〉

|0〉

|0〉|N,0〉 + |0,N〉

ba33

a

b

a’

b’

ba06

ba24

ba42

ba60

Probability of success:

64

3 Best we found:16

3

Projective Measurementsto 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

''''4004baba

!

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 MaximallyPath-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 GlobalDistinguishability in Quantum Interferometry,[quant-ph/0607088].

High-N00N Meets Phaseonium

Quantum Fredkin Gate (QFG) N00N GenerationKT Kapale and JPD, quant-ph/0612196.

• With sufficientlyhigh cross-KerrnonlinearityN00N generationpossible.

• Implementationvia Phaseonium

Gerry and Campos, PRA 64 063814 (2001)

!

"

Two possible methods

• As a high-refractive index material toobtain the large phase shifts

– Problem: Requires entangled phaseonium

• As a cross-Kerr nonlinearity

– Problem: Does not offer required phaseshifts of π as yet (experimentally)

Quantum Fredkin Gate (QFG) N00N GenerationKT Kapale and JPD, quant-ph/0612196.

Phaseonium for HighIndex of Refraction

Re

Im Im

Re

With larger density high index of refraction can be obtained!

N =1015cm

-3

!

Re(") =100 cm-3

!

n =10cm-3

N00N Generation viaPhaseonium as a Phase Shifter

The needed large phase-shift of π 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 viaPhaseonium have been shownto impart phase shifts of 7°controlled via single photon

• One really needs to input asmaller N00N as a controlfor the QFG as opposed to asingle photon with N=30roughly to obtain phase shiftas large as π.

• This suggests abootstrapping approach

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

!

"

Implementation ofQFG via Cavity QED

Ramsey Interferometryfor atom initially in state b.

Dispersive coupling between the atom and cavity givesrequired conditional phase shift

Low-N00N via EntanglementSwapping: The N00N gun

• Single photon gun of Rempe PRL 854872 (2000) and Fock state gun ofWhaley group quant-ph/0211134 couldbe extended to obtain a N00N gun fromatomic GHZ states.

• GHZ states of few 1000 atoms can begenerated 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 theatoms with cavity a polarizationentangled state of photons could begenerated inside a cavity

• Which could be out-coupled andconverted 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.