1. Metrology and integrated optics Geoff Pryde Griffith University

2. Precision measurement Precision measurement is at the heart of all quantitative science Advances in measurement precision lead to new physics Measurement precision is ultimately limited by quantum noise

3. Standard Interferometry N photons are sent independently. Estimate of  is based on which outputs the photons are detected in. The phase  (t ) can be varied in a preset way. The variance scales as V ~ 1/N – the Standard Quantum Limit (SQL).  est N photons   (t ) (t )

4. Previous “HL style” experiments Many optical and atomic measurements surpassing the SQL mainly squeezing, 1 but also entangled states, 1,2 and adaptive measurements 3 depends on state and measurement 1 eg Meyer et al PRL 86 (2001); 2 eg Nagata et al Science 316 (2007); Mitchell et al Nature 429 (2004) 3 eg Armen et al PRL 89 (2002); Cook et al Nature 446 (2007)

5. Gradient increases sensitivity

6. Previous “HL style” experiments Many optical and atomic measurements surpassing the SQL mainly squeezing, 1 but also entangled states, 1,2 and adaptive measurements 3 Some experiments aim to achieve the HL there exist many proposals using path-entangled states, phase squeezed states, large Fock states … usually with some limitations (eg limited range of  ) Many experiments use NOON states or similar: 1 eg Meyer et al PRL 86 (2001); 2 eg Nagata et al Science 316 (2007); Mitchell et al Nature 429 (2004) 3 eg Armen et al PRL 89 (2002); Cook et al Nature 446 (2007) depends on state and measurement

7. “HL” style experiments … Three key problems: 1. NOON states are hard to make! (N = 2,3,4,6) 2. Often practical states don’t violate SQL, let alone show HL 3. Basic NOON estimates phase only over  mirror State preparation device 1 1 e.g. Pryde & White, PRA 68, 052315 (2003) “Period 1/N” fringes

8. Problems 1 & 2:  State preparation device Solving the 3 problems  est 1 photon (t)(t)  1.Avoid complicated entangled states … 2.… while getting the N-fold sensitivity enhancement … 3.… and extending the estimate over Rudolph & Grover PRL 91 (03); de Burgh & Bartlett PRA 72 (05); Giovannetti et al PRL 96 (06)

9. The real experiment

10. Results Heisenberg limit scaling (M = 6) > 10dB (var) 378 vs 4333 resources

11. Bandwidth considerations tt Total time T ~ N  t Bandwidth ~ 1/ (N  t)  Solution: NOON states!  tt Bandwidth ~ 1/  t

12. Generation efficiency The efficiency of generating a NOON state by the usual methods is ~ e –N Proposals for improved efficiency exist. 1 These are, however, very challenging. Wedge states of (2m–1) photons can be generated from the input Fock states with an efficiency This decreases from 25% at m = 1 and saturates at ~ 18% as m   1 Cable and Dowling, PRL 99, 163604 (2007)

13. Experiment Lens BS PBS HWP IF 1 2 a b c Coincidence Ti: Sapphire Laser (820nm) Frequency Double BBO  m m

14. Data (3-photon) Projection onto  2,1  Max Fisher information ~ 5 c.f. 3 for SNL, 9 for HL, 7 for ideal wedge

15. Data (5-photon) Projection onto  3,2 

16. Making path-entangled states Network of paths and beam splitters Complex circuits hard to make in bulk optics Should be easier (?) in integrated optics Pryde & White, PRA 68, 052315 (2003)

17. Networks

18. Making path-entangled states Network of paths and beam splitters Complex circuits hard to make in bulk optics Should be easier (?) in integrated optics Questions: Splitting ratios - controllability Phase shifts - how? Stability? Loss Polarization Pryde & White, PRA 68, 052315 (2003)

19. Source integration In multi-photon experiments, efficiency is everything. Integrating the source into the circuit offers the opportunity for high efficiency collection.

20. Stable interferometers Quantum metrology experiments have enough problems without having to worry about the stability of the interferometer Want stable interferometers for simple demonstrations What visibility can we get over short time scales (~ s)? Long time scales (~ day)?

21. Detection Short-term necessity - split out modes with (potentially) different splitting ratios Potential for many more modes than we use in free space, particularly if array APDs come online. Probability of two photons going to one detector drops rapidly with each extra detector

22. H H H X X X     H = hadamard X = bit flip  = phase rotation photons are in equal superposition of both entering top rail, both entering 2nd rail, etc Collaboration with Tim Ralph = PBS Other path entanglement: Simplifying quantum circuits

23. Other stuff (II) Spectrally tailored sources

24. Future of quantum metrology Short term Proof of principle demonstrations Exploration and demonstration of limits eg performance, efficiency, loss tolerance, etc Scale-up of large entangled states Low flux application (?) Long term Practical sensing and measurement beyond the SQL