jonathan p. dowling - lsu
TRANSCRIPT
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.