Jonathan P. Dowling QUANTUM SENSORS: WHAT’S NEW WITH N00N STATES? Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana quantum.phys.lsu.edu SPIE F&N 23 May 2007

Statue Antiche di Firenze (Ancient Statues of Florence) Scully with Projector Mother with Children

Hearne Institute for Theoretical Physics Quantum Science & Technologies Group 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: R.Beaird, 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

Outline Quantum Computing & Projective Measurements Quantum Imaging, Metrology, & Sensing Showdown at High N00N! Efficient N00N-State Generating Schemes Conclusions

The objective of the DARPA Quantum Sensor Program is to develop practical sensors operating outside of a controlled laboratory environment that exploit non-classical photon states (e.g. entangled, squeezed, or cat) to surpass classical sensor resolution.

Two Roads to Optical CNOT 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.

WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT? Photon-Photon XOR Gate   LOQC   KLM Cavity QED EIT Photon-Photon Nonlinearity ??? Kerr Material Projective Measurement

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

Single-Photon Quantum Non-Demolition You want to know if there is a single photon in mode b, without destroying it. Cross-Kerr Hamiltonian: HKerr =  a†a b†b Again, with  = 10–22, this is impossible. Kerr medium “1” a b |in |1 D1 D2 *N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).

Quantum Non-Demolition  21 Orders of Magnitude Improvement! Linear Single-Photon Quantum 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 D1 D2 D0  /2 |in = cn |n  n = 0 2 |0 Effective  = 1/8  21 Orders of Magnitude Improvement! P Kok, H Lee, and JPD, PRA 66 (2003) 063814

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

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

Showdown at High-N00N! |N,0 + |0,N N00N States In Chapter 11 How do we make High-N00N!? N00N States In Chapter 11 |N,0 + |0,N With a large cross-Kerr nonlinearity!* H =  a†a b†b |1 |0 |N |N,0 + |0,N |0 This is not practical! — need  = p but  = 10–22 ! *C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).

Solution: Replace the Kerr with Projective Measurements! single photon detection at each detector a b a’ b’ OPO Cascading Not Efficient! Probability of success: Best we found: H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).

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in Quantum Interferometry Local and Global Distinguishability in Quantum Interferometry GA Durkin & JPD, quant-ph/0607088 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

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

Efficient Schemes for Generating N00N States! Constrained Desired |N>|0> |N0::0N> |1,1,1> Number Resolving Detectors 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.)

Quantum P00Per Scooper! Old Scheme OPO New Scheme χ 2-mode H Cable, R Glasser, & JPD, quant-ph/0704.0678. 2-mode squeezing process linear optical processing Old Scheme χ OPO beam splitter New Scheme How to eliminate the “POOP”? quant-ph/0608170 G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable and JPD

Quantum P00Per Scoopers! “Pizza Pie” Phase Shifter H Cable, R Glasser, & JPD, quant-ph/0704.0678. “Pizza Pie” Phase Shifter Spinning glass wheel. Each segment a different thickness. N00N is in Decoherence-Free Subspace! Feed Forward based circuit Generates and manipulates special cat states for conversion to N00N states. First theoretical scheme scalable to many particle experiments!

The upper bound on the resources scales quadratically! Linear-Optical Quantum-State Generation: A N00N-State Example N VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/0612154 U This 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 m–2 modes is O(m2).

Conclusions Quantum Computing & Projective Measurements Quantum Imaging & Metrology Showdown at High N00N! Efficient N00N-State Generating Schemes Conclusions