QUANTUM SENSORS: WHAT S NEW WITH N00N STATES? Jonathan P. Dowling

Transcription

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

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

3 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

4 Outline 1. Quantum Computing & Projective Measurements 2. Quantum Imaging, Metrology, & Sensing 3. Showdown at High N00N! 4. Efficient N00N-State Generating Schemes 5. Conclusions

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

6 Two Roads to Optical CNOT I. Enhance Nonlinear Interaction with a Cavity or EIT Kimble, Walther, Lukin, et al. Cavity QED II. Exploit Nonlinearity of Measurement Knill, LaFlamme, Milburn, Franson, et al.

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

8 Projective Measurement Yields Effective Kerr! GG Lapaire, P Kok, JPD, JE Sipe, PRA 68 (2003) 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 KLM CSIGN Hamiltonian Franson CNOT Hamiltonian

9 Single-Photon Quantum Non-Demolition You want to know if there is a single photon in mode b, without destroying it. Cross-Kerr Hamiltonian: H Kerr = κ a a b b ψ in 1 b a Kerr medium 1 D 2 D 1 1 Again, with κ = 10 22, this is impossible. *N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).

10 Linear Single-Photon Quantum Non-Demolition The success probability is less than 1 (namely 1/8). D 0 1 The input state is constrained to be a superposition of 0, 1, and 2 photons only. Conditioned on a detector coincidence in D 1 and D 2. 1 π /2 D 1 D 2 Effective κ = 1/8 21 Orders of Magnitude 0 2 ψ in = Σ c n n n = 0 Improvement! P Kok, H Lee, and JPD, PRA 66 (2003) π /2

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

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

13 Showdown at High-N00N! How do we make High-N00N!? N,0 + 0,N With a large cross-kerr nonlinearity!* H = κ a a b b 1 0 N 0 This is not practical! need κ = π but κ = 10 22! N,0 + 0,N N00N States In Chapter 11 *C Gerry, and RA Campos, Phys. Rev. A 64, (2001).

14 Solution: Replace the Kerr with Projective Measurements! OPO 3 a 3 a b b single photon detection at each detector a b a b 2 a b 4 a b 6 a b Probability of success: a b a 3 b 4 0! 0 4 a ' b' a' b ' 3 Best we found: Cascading Not Efficient! H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R (2002).

15 10::01> 10::01> 20::02> 20::02> 30::03> 40::04> 30::03>

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

17 NOON-States Violate Bell s Inequalities CF Wildfeuer, AP Lund and JP Dowling, quant-ph/ Probabilities of correlated clicks and independent clicks P ab (",#),P a ("),P b (#) Building a Clauser-Horne Bell inequality from the expectation values P ab (",#),P a ("),P b (#) "1# P ab ($,%) " P ab ($,% &) + P ab ( $ &,%) + P ab ( $ &,% &) " P a ( $ &) " P b (%) # 0 Shared Local Oscillator Acts As Common Reference Frame! Bell Violation!

18 Efficient Schemes for Generating N00N States! N> 0> Constrained Desired 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/ Linear! N VanMeter, P Lougovski, D Uskov, JPD, quant-ph/ Linear! KT Kapale & JPD, quant-ph/ (Nonlinear.)

19 Quantum P00Per Scooper! H Cable, R Glasser, & JPD, quant-ph/ mode squeezing process χ OPO beam splitter U(50:50) 4> 4> Old Scheme linear optical processing New Scheme How to eliminate the POOP? amplitude ^ > 8> 2> 6> 4> 4> 6> 2> 8> 0> Fock basis state quant-ph/ G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable and JPD

20 Quantum P00Per Scoopers! H Cable, R Glasser, & JPD, quant-ph/ 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!

21 Linear-Optical Quantum-State Generation: A N00N-State Example N VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/ U ( ) 2 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(m 2 ).

22 Conclusions 1. Quantum Computing & Projective Measurements 2. Quantum Imaging & Metrology 3. Showdown at High N00N! 4. Efficient N00N-State Generating Schemes 5. Conclusions