#### Transcript Displaced photon counting for coherent optical

Displaced-photon counting for coherent optical communication Shuro Izumi 1. Discrimination of phase-shift keyed coherent states 2. Super resolution with displaced-photon counting 3. Phase estimation for coherent state 1. Discrimination of phase-shift keyed coherent states 2. Super resolution with displaced-photon counting 3. Phase estimation for coherent state Optical communication Encode the information on the optical states Sender Laser Receiver Optical state Detector Decision Non-classical states Squeezed states Entangled states Photon number states Super position states Excellent properties However.. Changed to mixed states by losses Non-classical states are not optimal for signal carriers Optical communication with coherent states Coherent state is the best signal carrier under the losses because ✓ Remain pure state under loss condition ✓ Easily generated compared with non-classical states However ✓ It is impossible to discriminate coherent states without error because of their non-orthogonality Motivation Achievable minimum Error Probability Binary phase-shift keyed (BPSK) 0 0 1 Error 1 Standard Quantum Limit…. Achievable Error probability by measurement of the observable which characterizes the states Phase-shift keyed→ Homodyne measurement Helstrom bound…. Achievable Error probability for given states C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976). Overcome the SQL and approach the Helstrom bound!! Near-optimal receiver for BPSK signals Displaced-photon counting R. S. Kennedy, Research Laboratory of Electronics, MIT, Technical Report No. 110, 1972 Displacement operation Beam splitter Photon counter off on Local Oscillator Displaced-photon counting Error Experimental demonstration of near-optimal receiver for BPSK signals k. Tsujino et al., Phys. Rev. Lett. 106, 250503(2011) ✓Detector with high detection efficiency Transition edge sensor (TES) →Detection efficiency : 95 % for 853nm ✓Displacement optimization→Optimize the amount of Optimal receiver for BPSK signals Displaced-photon counting with feedback operation (Dolinar receiver) S. J. Dolinar, Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 111, 1973 or Photon counter Classical (electrical) feedback R. L. Cook, et al., Nature 446, 774, (2007) QPSK signals p p x ✓Displaced-photon counting → Near-optimal ✓Displaced-photon counting with feedback → Optimal x Near-optimal receiver for QPSK signals R. S. Bondurant,5 Opt. Lett. 18, 1896 (1993) Displaced-photon counting with feedback receiver p Photon counter 0.1 Error Probability x Classical (electrical) feedback 0.001 10 5 10 7 0 5 10 15 Signal mean photon number 20 2 Evaluation for finite feedforward steps S. Izumi et al., PRA. 86, 042328 (2012) p x off on N→∞ ⁼Bondurant receiver M. Takeoka et al., PRA. 71, 022318 (2005) Change the displacement operation depending on previous results Numerical evaluation S. Izumi et al., PRA. 86, 042328 (2012) Displaced-photon counting without feedforward Bondurant N=∞ N=20 N=10 Displaced-photon counting with Feedforward operation(Dolinar receiver ) S. Izumi et al., PRA. 87, 042328 (2013) p x Photon-number resolving detector *Symbol selection Bayesian estimation →The signal which maximizes the posteriori probability Change the displacement operation depending on previous results Numerical evaluation S. Izumi et al., PRA. 87, 042328 (2013) Photon-number-resolving detector On-off detector Numerical evaluation with detector’s imperfection S. Izumi et al., PRA. 87, 042328 (2013) Dark count ν :10−4 ~10−1 counts/pulse On-off detector PNRD Experimental realization of feedforward receiver for QPSK NIST demonstrated the feedforward (feedback) receiver F. E. Becerra et al., Nature Photon. 7, 147 (2013) F. E. Becerra et al., Nature Photon. 9, 48 (2015) With on-off detector With PNRD Hybrid scheme from Max-Plank institute C. R. Muller et al., New J. Phys. 14, 083009 (2012) Homodyne + Displaced-photon counting Feedforward operation dependent on the result of homodyne measurement Summary ✓ We propose and numerically evaluated the receiver for QPSK signals ✓ Displaced-photon counting with PNRD based feedforward operation improve the performance for QPSK discrimination 1. Discrimination of phase-shift keyed coherent states 2. Super resolution with displaced-photon counting 3. Phase estimation for coherent state Phase sensing with displaced-photon counting Displaced-photon counting is near-optimal receiver for signal discrimination ✓ Better performance than homodyne measurement ✓ Approach the Helstrom bound Can displaced-photon counting make improvements in phase sensing? ✓ Super resolution ✓ Phase estimation Super resolution and Sensitivity Input state Quantum measurement Phase shift Resolution →Interference pattern Sensitivity Super resolution Coherent state Narrower width Coherent state with particular quantum measurements N00N state Nagata et al., Science 316, 726 (2007) Xiang et al., Nature Photonics 5, 268 (2010) K. J. Resch et al., Phys. Rev. Lett. 98, 223601 (2007) Y. Gao et al., J. Opt. Soc. Am. B. 27, No.6 (2010) E. Distant et al., Phys. Rev. Lett. 111, 033603(2013) K. Jiang et al., J. Appl. Phys. 114, 193102(2013) Standard two-port intensity difference monitoring Input state － Intensity difference monitoring Super resolution with parity detection Y. Gao et al., J. Opt. Soc. Am. B. 27, No.6 (2010) Input state PNRD Even Parity detection Odd Super resolution Super resolution with homodyne measurement E. Distant et al., Phys. Rev. Lett. 111, 033603(2013) Homodyne measurement － Super resolution Super resolution with homodyne measurement E. Distant et al., Phys. Rev. Lett. 111, 033603(2013) Threshold homodyne measurement POVM →Count probability with the phase shift Normalized a=2.0 a=2.0 a=1.0 a=1.0 a=0.1 a=0.1 Evaluation of sensitivity E. Distant et al., Phys. Rev. Lett. 111, 033603(2013) Super resolution with displaced-photon counting General phase detection scheme Mach-Zehnder phase detection scheme Displacement operation Photon counter →Count probability with the phase shift Super resolution with displaced-photon counting Displaced-photon counting Width : Width Super resolution Homodyne measurement (with normalization) Width : Parity detection (same input power to the phase shifter) Width : Evaluation of resolution and sensitivity Sensitivity Resolution Parity detection Parity detection a=0.1 Displacedphoton counting a=1.0 a=1.0 Displacedphoton counting a=0.1 Shot noise limit Summary Super resolution can be observed with coherent state and quantum measurement →parity detection, homodyne measurement ✓Displaced-photon counting shows both super resolution and good sensitivity Parity detection a=0.1 a=1.0 Displaced-photon counting Shot noise limit 1. Discrimination of phase-shift keyed coherent states 2. Super resolution with displaced-photon counting 3. Phase estimation for coherent state Phase estimation Estimator Phase shift Input state Optimal input state Quantum measurement Optimal measurement Optimize for good estimation Figure of merit →Variance of the estimator Cramer-Rao bound Cramer-Rao bound The variance of estimator must be larger than inverse of Fisher information. For M states , B.R.Frieden, “Science from Fisher Information” ,CAMBRIDGE UNI.PRESS(2004) Fisher information (FI) S.L.Braunstein and C.M.Caves, PRL, 72, 3439 (1994) Quantum FI depends only on input state. How much information state has Possible to derive the minimum variance for given state Classical FI depends on input state and measurement. How much information we can extract from the state by measurement Possible to derive the minimum variance for given state and measurement Fisher information for coherent state Phase shift Quantum measurement Quantum FI 1.0 Classical FI Homodyne measurement Homodyne FI QFI 0.8 0.6 Heterodyne 0.4 Heterodyne measurement 0.2 0.0 S.Olivares et, al., J.Phys.B, Mol. Opt. Phys, 42(2009) 3 2 1 0 Relative phase 1 rad 2 3 Fisher information for coherent state with displaced-photon counting (PNRD) PNRD Fisher information for discrete variable Displaced-PNRD Fisher information Experimental setup ~Preliminary experiment probe PNRD 99:1 BS PZT Transition edge sensor (TES) LO ✓ Photon-number resolving up to 8-photon ✓Detection efficiency 92% Fukuda et al., (AIST) Metrologia, 46, S288 (2009) Laser 1550 nm Experimental condition Probe amplitude Displacement amplitude Detection efficiency Visibility Experimental results ~Preliminary experiment Variance Expectation value Expectation value Variance Displaced-PNRD Experiment Displaced-PNRD Theory with imperfections Heterodyne Homodyne Displaced-PNRD Theory # of measurement # of measurement Summary ✓ Displaced-photon counting gives higher fisher information than homodyne measurement around Θ=0 →Is it possible to use this result for phase sensing? ✓ We demonstrated preliminary experiment →We experimentally show that displaced-photon counting gives better performance in particular condition →Adjustment of the experimental setup more carefully is required