Jonathan P. Dowling

1. QUANTUM IMAGING: HAPPY-N00N YEAR! Jonathan P. Dowling Hearne Institute for Theoretical Physics Department of Physics & Astronomy Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu Quantum Imaging MURI Annual Review, 01 October 2007, Boston

2. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

3. I’m Ryan Glasser I’m Bill Plick Who Am I, & Why Am I Here? Hearne Institute for Theoretical Physics QuantumScience & Technologies Group I’m Hugo Cable

4. The Pizza’s Mine! I Bet He Cheated… However, As We all Know, Some Students Require a Little Arm Twisting!

5. Quantum Imaging Theory Objective: • Entangled Photons Beat Diffraction Limit • Lithography With Long-Wavelengths • Dispersion Cancellation • Masking Techniques • N-Photon Resists Accomplishments FY07: • Properties of N00N States • Efficient N00N Generators • Bright N00N Generators Thy/Exp • Masking Lithography • N-Photon Absorption • Loss in N00N-State Imaging • Loss in Interaction Free Imaging Approach: • Investigate Which States are Optimal • Design Efficient Quantum State Generators • Investigate Masking Systems • Develop Theory of N-Photon Resist • Integrate into Optical System Design

6. PROGRAMMATICS Budget: $100K/Y Personnel Commitment Per Year: Dowling: 1 Month ARO & 1.5 Months LSU Matching Hugo Cable (Postdoc): 12 Months ARO Ryan Glasser (Grad): 12 Months LSU Matching William Plick (Grad): 12 Months LSU Matching Facilities: 4 Dell Work Stations — 2 From DURIP

7. FY07: PUBLICATIONS & PREPRINTS Durkin, GA; Dowling, JP, Local and Global Distinguishability in Quantum Interferometry, PHYSICAL REVIEW LETTERS, 99 (7): Art. No. 070801 AUG 17 2007. Kapale, KT; Dowling, JP, Bootstrapping Approach for Generating Maximally Path-Entangled Photon States, PHYSICAL REVIEW LETTERS, 99 (5): Art. No. 053602 AUG 3 2007. Cable H & Dowling JP, Efficient Generation of Large Number-path Entanglement Using Only Linear Optics and Feed-forward, PHYSICAL REVIEW LETTERS, in press, arXiv:0704.0678 <quant-ph>. Wildfeuer CF, Lund A, Dowling JP, Strong Violations of Bell-type Inequalities for Path-Entangled Number States, PHYSICAL REVIEW A, in press, arXiv:quant-ph/0610180. VanMeter NM, Lougovski P, Uskov DB, Kieling K, Eisert J, Dowling JP, A General Linear-Optical Quantum State Generator, submitted to PHYSICAL REVIEW LETTERS, arXiv:quant-ph/0612154. DeMartini F, Sciarrino F, Vitelli C, Glasser RT, Cable H, Dowling JP, Experimental Sub-Rayleigh Resolution by an Unseeded High-gain Optical Parametric Amplifier for Quantum Lithography, submitted to PHYSICAL REVIEW LETTERS.

8. FY07: LECTURES AT CONFERENCES “Generation and Characterization of N00N States Using Linear Optics,” Hugo Cable and Jonathan P. Dowling, Symposium on Quantum Information and Computation, Laser Physics Workshop, 20–24 August 2007, León, Mexico (invited). “Quantum Sensors,” Jonathan P. Dowling, Fourth SPIE International Symposium on Fluctuations and Noise, 20–24 May 2007, Florence, Italy (invited). “Linear Optical Quantum Computing, Imaging, and Metrology,” Jonathan P. Dowling, International Conference on Quantum Communication, Measurement, and Computing, 28 November – 3 December, Tokyo, Japan. “Quantum Imaging and Precision Measurements with N00N States,” Jonathan P. Dowling, Optical Society of America Annual Meeting, 8–12 October 2006, Rochester, NY (invited).

9. FY07: Visitors & Lecturers @ LSU Malvin Teich, Director, Photonics Center, Boston University, Boston. Francesco DeMartini, Department of Physics of the University La Sapienza, Rome, Italy. Claude Fabre, Laboratoire Kastler-Brossel Ecole Normale Superieure and University Pierre et Marie Curie, Paris. Hans Bachor, Research Director and Federation Fellow, Australian National Centre of Excellence for Quantum-Atom Optics, Australian National University, Canberra.

11. Quantum Imaging: A Systems Approach Non-Classical Photon Sources N-Photon Absorbers Imaging System Ancilla Devices

12. AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733 N-Photon Absorber a† N a N

13. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

14. N00N

15. PRA, in press, arXiv:quant-ph/0610180.

16. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

18. PRL, in press, arXiv:0704.0678

19. U submitted to PRL, arXiv:quant-ph/0612154

20. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

21. Ryan, Hugo, and Bill — The Early Years!

24. Entanglement-Seeded Dual OPARyan Glasser, Hugo Cable, JPD (in preparation) • Two identical OPAs pumped with the same laser are seeded with the entangled input: • Input state created from a spontaneous parametric downconverter and the Hong-Ou-Mandel effect. • Output state is: • The factor depends on the phase of the OPAs, the gain (r) and the values of n and m. • Inner two modes b and c are highly path entangled. • Detecting n and m photons at Da and Dd allows with certainty knowledge of the state the inner two modes are in.

25. Entanglement-Seeded Dual OPARyan Glasser, Hugo Cable, JPD (see poster) • Probability of obtaining an output state with a given n and m is: • Most probable joint detection outcome is n=m=1, which occurs at an easily experimentally obtainable gain of r=0.66 • This results in the state: • This state input on a 50/50 beamsplitter results in the N=4 N00N state : • If perfect number resolving detectors exist at Da and Dd , and we detect those modes out, we can use the entangled modes b and c for a quantum cryptography protocol. Output probabilities of a given n and m What’s Next??? • Recently finished calculation of output state including vacuum input. • Need to quantify amount of entanglement in output state. • Does output state beat the shot-noise limit? • Viable source for noiseless amplification (one quadrature)? • How do phase sensitive versus phase insensitive parametric amplifiers affect the scheme? • Is degenerate parametric amplification required for the input? • Effect of imperfect detectors on phase resolution.

26. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

27. Multi-Photon Absorption William Plick, Christoph Wildfeuer, JPD (poster) Output of a BBO Crystal: Information about pump Creation operators only part affected by beam splitter. Phase Mismatch: K(pump) – K(signal) – K(idler) Rate of two photon absorption: } Detuned Virtual Level { • Equation found by B. R. Mollow using second order perturbation theory. • For most cases of interest the atomic response (g) separates from the integral. • The most important quantity is then the second order field correlation function (G). One photon transition energy Two photon transition energy

28. Multi-Photon Absorption William Plick, Christoph Wildfeuer, JPD (poster) • Generalization of the perturbative approach to N-Photon interactions by G.S. Agarwal. • Again the key quantity is shown to be the field correlation function. This time to Nth order and scaled by the intensity (1st order correlation). • Obtaining a more concrete result for N-photon absorption rates for N00N states will require further investigation and knowledge of how these states are to be generated. The rate of change of the average number of photons in the field (in point of fact the absorption rate) is proportional to the following ratio: Note: Scaled to coherent state • In the meantime the normalized field correlation functions give a good approximation of how these absorption rates will scale.

29. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous

30. Quantum Optical Masking Imaging S. Vinjanampathy, S. Thanvanthri, H. Cable, JPD (in progress) Quantum Masking Lithography Diffraction in Ghost Imaging

31. Loss & Noise in Interaction-Free Imaging Daniel Lum & JPD (in progress) • Modeling: • Loss • Scattering • Turbulence • Clutter

32. TABLE OF CONTENTS • Programmatics • N00N State Characterization • N00N State Generation • OPA! • N00N State Absorption • Miscellaneous