Jonathan P. Dowling

Jonathan P. Dowling Optical Quantum Imaging, Computing, and Metrology: WHATS NEW WITH N00N STATES?quantum.phys.lsu.eduHearne Institute for Theoretical PhysicsLouisiana State UniversityBaton Rouge, Louisiana07 JUNE 2007 DAMOP-07, Calgary

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: M.A. Can, A.Chiruvelli, GA.Durkin, M.Erickson, L. Florescu, M.Florescu, M.Han, KT.Kapale, SJ. Olsen, S.Thanvanthri, Z.Wu, J.Zuo Hearne Institute for Theoretical PhysicsQuantum Science & Technologies Group

OutlineQuantum Computing & Projective MeasurementsQuantum Imaging, Metrology, & SensingShowdown at High N00N!Efficient N00N-State Generating SchemesConclusions

CNOT with Optical NonlinearityThe Controlled-NOT can be implemented using a Kerr medium:R is a /2 polarization rotation,followed by a polarization dependentphase shift .|0= |H Polarization|1= |V Qubits

Two Roads to Optical CNOTI. Enhance Nonlinearity with Cavity, EIT Kimble, Walther, Haroche, Lukin, Zubairy, et al.II. Exploit Nonlinearity of Measurement Knill, LaFlamme, Milburn, Franson, et al.

Linear Optical Quantum ComputingLinear Optics can be Used to Construct CNOT and a Scaleable Quantum Computer:Knill E, Laflamme R, Milburn GJNATURE 409 (6816): 46-52 JAN 4 2001Franson JD, Donegan MM, Fitch MJ, et al.PRL 89 (13): Art. No. 137901 SEP 23 2002Milburn

Road to Entangled- Particle Interferometry: First Example of Entanglement Generation by Erasure of Which-Path Information Followed by Detection!?

Photon-PhotonXOR GatePhoton-PhotonNonlinearityKerr Material Cavity QEDEITProjectiveMeasurement LOQCKLMWHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?

GG Lapaire, P Kok, JPD, JE Sipe, PRA 68 (2003) 042314KLM CSIGN HamiltonianFranson CNOT HamiltonianNON-Unitary Gates Effective Unitary GatesA Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature!Projective Measurement Yields Effective Kerr!

Nonlinear Single-Photon Quantum Non-DemolitionYou want to know if there is a single photon in mode b, without destroying it.*N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).

Linear Single-PhotonQuantum Non-DemolitionThe 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.

Effective =1/8 21 Orders of Magnitude Improvement!P Kok, H Lee, and JPD, PRA 66 (2003) 063814

Quantum Metrology with N00N StatesH Lee, P Kok, JPD, J Mod Opt 49, (2002) 2325.Supersensitivity!Shotnoise to Heisenberg Limit

a N a NAN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733Superresolution!

Quantum Lithography Experiment|20>+|02>|10>+|01>

Canonical MetrologyP Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811Suppose we have an ensemble of N states | = (|0 + ei |1)/2,

and we measure the following observable:The expectation value is given by: and the variance (A)2 is given by: N(1cos2)A = |0 1| + |1 0||A| = N cos The unknown phase can be estimated with accuracy:This is the standard shot-noise limit. = = A| d A/d |N1

Quantum Lithography & Metrology Now we consider the state

and we measureP. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).Quantum Lithography*:Quantum Metrology: N |AN|N = cos NH = = AN| d AN/d |

Showdown at High-N00N!|N,0 + |0,NHow do we make High-N00N!?*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).With a large cross-Kerr nonlinearity!* H=aabbThis is not practical! need =p but =1022 !|1|N|0|0|N,0 + |0,N

Solution: Replace the Kerr with Projective Measurements!H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).OPO

These Ideas Implemented in Recent Experiments!

|10::01>|20::02>|40::04>|10::01>|20::02>|30::03>|30::03>

A statistical distinguishability based on relative entropy characterizes the fitness of quantum states for phase estimation. This criterion is used to interpolate between two regimes, of local and global phase distinguishability.

The analysis demonstrates that, in a passive MZI, the Heisenberg limit is the true upper limit for local phase sensitivity and Only N00N States Reach It!N00N Local and Global Distinguishability in Quantum InterferometryGA Durkin & JPD, quant-ph/0607088

NOON-States Violate Bells InequalitiesCF Wildfeuer, AP Lund and JP Dowling, quant-ph/0610180Building a Clauser-Horne Bell inequality from the expectation values Probabilities of correlated clicks and independent clicksShared Local Oscillator Acts As Common Reference Frame!Bell Violation!

Efficient Schemes for Generating N00N States!Question: Do there exist operators U that produce N00N States Efficiently?

Answer: YES!

H Cable, R Glasser, & JPD, quant-ph/0704.0678. Linear!N VanMeter, P Lougovski, D Uskov, JPD, quant-ph/0612154. Linear!KT Kapale & JPD, quant-ph/0612196. (Nonlinear.)

How to eliminate the POOP?beamsplitterquant-ph/0608170 G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable and JPDQuantum P00Per Scooper!2-mode squeezing processH Cable, R Glasser, & JPD, quant-ph/0704.0678.OPOOld SchemeNew Scheme

Chart1

0.2734375

0.15625

0.140625

0.15625

0.2734375

Fock basis state

|amplitude|^2

U(50:50)|4>|4>

Sheet1

|4>|4>j2j2N-2jcoefficientsquare coefficient

|N>|N>0080.52291251660.2734375

N=41260.39528470750.15625

2440.3750.140625

3620.39528470750.15625

4800.52291251660.2734375

1

|0>|8>0.2734375

|2>|6>0.15625

|4>|4>0.140625

|6>|2>0.15625

|8>|0>0.2734375

Sheet1

Fock basis state

|amplitude|^2

U(50:50)|4>|4>

Sheet2

Sheet3

Spinning glass wheel. Each segment a different thickness. N00N is in Decoherence-Free Subspace!Generates and manipulates specialcat states for conversion to N00N states. First theoretical scheme scalable to many particle experiments!PizzaPiePhase ShifterFeed-Forward-Based CircuitQuantum P00Per Scoopers!H Cable, R Glasser, & JPD, quant-ph/0704.0678.

Linear-Optical Quantum-State Generation: A N00N-State ExampleN VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/0612154UThis counter example disproves the N00N Conjecture: That N Modes Required for N00N.The upper bound on the resources scales quadratically! Upper bound theorem:The maximal size of a N00N state generated in m modes via single photon detection in m2 modes is O(m2).

ConclusionsQuantum Computing & Projective MeasurementsQuantum Imaging & MetrologyShowdown at High N00N!Efficient N00N-State Generating SchemesConclusions

Documents

Jonathan P. Dowling