IWQSE 2013, NTU Oct. 15 (2013) Witnessing Quantum Coherence Yueh-Nan Chen (陳岳男) Dep. of Physics, NCKU National Center for Theoretical Sciences (South) Outline Coherence and entanglement Cavity QED The Leggett-Garg Inequalities Witnessing Quantum Coherence in Biological Systems Quantum Information Teleportation Dense coding Secret sharing Key distribution coherence and entanglement Quantum Computation Algorithms Bit : 0, 1 or +, - or boy, girl…. Any two-level system 10 time t0 t1 t2 Q-bit: Any two-level and physical system (Quantum bit) Two-level atom 1 1 1 0 1 0 0 0 time t0 t1 t2 Two qbits : two spins time B A Spin up Spin down interaction t0 A B Spin up Spin down Schrodinger eq. t A B A B entangled state Entanglement 1 1 A B A B 2 2 *.*? ( a1 + a2 A ) A Impossible to factory ( b1 + b2 B Symbol of connecting to independent system ) B 薛丁格的貓：To be or not to be? Cavity QED The Nobel Prize in Physics 2012 Serge Haroche David J. Wineland The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems" • Spontaneous emission of single two-level atom Interaction between a two-level atom and the photon reservoir: H D b e q q q iq x H .c. bq : photon operator : creating operator of In the interaction picture, the state vector : (t ) f 0 (t ) ;0 f q (t ) ;1q q , where ;0 : an atom initially in the excited state ;1q : a photon of q in the radiation field atom Results : it t f 0 (t ) e , where is the decay rate represents the Lamb Shift The radiation intensity distribution : 2 f q (t ) Dq 2 ( 0 c q ) 2 2 , where Dq ( 0 c q ), 2 q q Dq 2 0 c q 0 is the energy spacing Two-level atom inside a cavity The interaction between the atom and single-mode cavity: (t ) f (t ) ;0 f (t ) ;1 Vacuum Rabi oscillations J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001). Vacuum Rabi splitting Gate-confined Double Quantum Dots Quantum Coherence in Double Quantum Dots K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, PRL 105, 246804 (2010) Question: Are they truly quantum? The Robotic Bugs 1.0 機率 機率 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 t (s) Quantum vs Classical Bell’s Inequality: Locality and Realism 1 01 10 2 The Bell-CHSH inequality A, a, B, b 1,1 A a, A a(0,2), (2,0) A a B A ab 2,2 2 AB Ab aB ab 2 AB Ab aB ab 2 Predictions of QM for the singlet state 1 01 10 2 ˆ ˆ AB A B cos AB QM violates the Bell-CHSH inequality FQM AB Ab aB ab cos AB cos Ab cos aB cos ab Aˆ x aˆ y Bˆ ( y x ) / 2 bˆ ( y x ) / 2 FQM 2 2 2!!! Leggett-Garg Inequality (Bell’s inequality in time) Realism and non-invasive measurement Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Leggett and Garg, Phys. Rev. Lett. 54, 857–860 (1985) Palacios-Laloy, A. et al. Nature Phys. 6, 442–447 (2010). Distinguishing Quantum and Classical Transport through Nanostructures Transport Charge Inequality: N. Lambert, C. Emary, Y. N. Chen, and F. Nori, Phys. Rev. Lett. 105, 176801 (2010) Double Quantum Dot Violation of charge inequality for DQD Quantum Transport in Organism ? The Quantum Dimension Of Photosynthesis Leggett-Garg inequality ? Pigments (BChl) Reaction Center Witnessing Quantum Coherence in FMO Complex C. M. Li*, N. Lambert*, Y. N. Chen*, G. Y. Chen and F. Nori, Scientific Reports 2, 885 (2012) Avian Magnetoreception: a tale of two spins http://www.technologyreview.com/blog/arxiv/27829/ Summary 1. Coherence and Entanglement 2. Cavity QED 3. The LG Inequalities 4. Quantumness in Biological Systems Thank you for your attention!