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Quantum information with cold atoms Zheng-Wei Zhou(周正威) Key Lab of Quantum Information , CAS, USTC October, 2009 KITPC Outline • Backgrounds on Quantum Computation(QC) • Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models • Quantum Communication • Summary and Outlook Backgrounds on Quantum Computation(QC) Father of QC(1981-1985) R. Feynman D. Deutsch Elementary Gates for QC (1995) A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve (Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT), P. Shor (AT&T), T. Sleator (NYU), J. Smolin (UCLA), H. Weinfurter (Innsbruck) C. H. Bennett Quantum Algorithms 1994 1997 Some Methods to Overcome Decoherence (1)Quantum Error Correcting Codes (Shor,Steane,Calderbank,Laflamme,Preskill,etc.)(1995-2000) (2)Decoherence-Free Subspaces (Duan, Guo, Zanardi, Whaley,Bacon, Lidar, etc.)(1997-2000) (3)Dynamical Decoupling method (Lolyd,Viola,Duan,Guo, Zanardi,etc.) (1998-1999) Standard Model for QC Beyond Standard model (I) • Topological Quantum Computing A. Kitaev (1997) Beyond Standard model (II) • One Way Quantum Computing R. Raussendorf H. Briegel (2000) Beyond Standard model (III) • Adiabatic Quantum Computation Dorit Aharonov et. al (2004) J. Goldstone et. al (2000) ...... E Standard QC t Adiabatic QC Intermediate targets of QC——Simulating highly-correlated many body systems D. Jaksch P. Zoller D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998) model Adiabatic QC Beyond Classical Computer Topological QC Decoherence, Scalability, Energy gap, etc Standard QC Quantum Computer Quantum Simulation Once Fault-Tolerant QC can be realized… Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models Standard Model for QC 1. Register of 2-level systems (qubits) The physical origin of the confinement of cold atoms with laser light is the dipole force: Olaf Mandel, et al., Phys. Rev. Lett. 91, 010407 (2003) 2. Initialization of the qubit register However, nonideal conditions will always result in defects in that phase (i.e., missing atoms and overloaded sites). How to suppress these defects in the lattice? A possible approach is: the coherent filtering scheme. P. Rabl, et al., Phys. Rev. Lett. 91,110403, (2003) 3、4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit As far as ultracold atoms trapped in an optical lattice is concerned, global operations on atoms are available. However, addressing individual atom becomes very difficult. So, to implement universal quantum computation, we should answer the following questions: 1: Whether global operations are enough to implement universal quantum computation? OR 2: How to addressing single qubit in this system? Some proposals for QC via global operations Cellular-automata Machine (S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61, 020301R, 2000, PRL 88, 017904, 2002) QC via translation-invariant operations R. Raussendorf, Phys. Rev. A 72, 052301 (2005). K. G. H. Vollbrecht et al., Phys. Rev. A 73, 012324 (2006). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2005). Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006). In the above proposals, only translationally invariant global operations are required! Shortcomings: Redundant qubits (space and time overhead) Initialization Physical implementation Bose Hubbard model Ising Model PRL 81, 3108 (1998); 90, 100401(2003); 91,090402 (2003) Type I Type II PRL 91,090402 (2003) (Effective periodic magnetic field induced by left and right circularly polarized light) Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006). 1D Two-qubit operation Addressing single qubit 2D Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006). Some proposals for QC via addressing single atom Marked Qubit as Data-bus (Phys. Rev. A 70, 012306 (2004); Phys. Rev. Lett. 93, 220502 (2004)) Phys. Rev. A 70, 012306 (2004) single-qubit rotation via multiqubit addressing J. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2006) single-qubit rotation via Position-dependent hyperfine splittings C. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2006) the progress of experiments Imaging of single atoms in an optical lattice Nelson, K. D., Li, X. & Weiss, D. S. Nature Phys. 3, 556–560 (2007). effective magnetic field results from the atom‘s vector light shift: Novel quantum gates via exchange interactions Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007). Science 319, 295–299 (2008). Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008). 5. Long decoherence times How many gate operations could be carried out within a fixed decoherence time? “ For the atoms of ultracold gases in optical lattices, Feshbach resonances can be used to increase the collisional interactions and thereby speed up gate operations. However, the ‘unitarity limit’ in scattering theory does not allow the collisional interaction energy to be increased beyond the on-site vibrational oscillation frequency, so the lower timescale for a gate operation is typically a few tens of microseconds.” “ Much larger interaction energies, and hence faster gate times, could be achieved by using the electric dipole–dipole interactions between polar molecules, for example, or Rydberg atoms; in the latter case, gate times well below the microsecond range are possible.” I. Bloch, NATURE|Vol 453|19 June 2008|doi:10.1038. Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models R. Raussendorf H. Briegel R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2001) Graph states Graph States Given a graph , the corresponding graph state is Given a graph , the corresponding graph state is Stabilizer code For Example: 1 X 1Z 2 Z1 X 2 Z3 X 2 Z3 2 3 L ( 000 001 010 011 100 101 110 111 ) A Controlled Phase Gate D. Jaksch, et. al., Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (1999). Nature 425, 937 (2003) Nature 425, 937 (2003) New Journal of Physics 10 (2008) 023005 New Journal of Physics 10 (2008) 023005 Preparation of decoherence-free cluster states with optical superlattices V Vx ( x ) V y ( y ) Vx ( x) V1x cos 2 (kx) V2 x cos 2 (2kx) Vy ( x) V1 y cos 2 (ky) V2 y cos 2 (2ky) Liang Jiang, et. Al., Phys. Rev. A 79, 022309 (2009) Logical qubit in decoherence-free subspace Here, Logical qubit: H S 1,2 V S 2,3 S i, j 1 2 i S S 3,4 4,1 j i j 0 V 1 2 1 V H 32 Implementing a C-Phase Gate Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models Cold Atoms Trapped in Optical Lattices to Simulate condensed matter physics D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998) Advantages as one of promising candidates of quantum simulations Neutral atoms couple only weakly to the environment, allowing long storage and coherence times. So far, cold atoms trapped in optical lattices is the only system in which a large number of particles can be initialized simultaneously. Highly controllability Control of interaction strength with magnetic field (Feshbach Resonance) Various geometry of optical lattices Controllable tunneling rates Bosons, Fermions, or mixture Effective highly-correlated many body models Bose-Hubbard Model Two-component Bose-Hubbard Model Fermions in an Optical Lattice Feshbach resonance -- magnitude Optical lattice -- diversity Experiments: Ketterle, Esslinger etc. • Weakly interacting fermions in an optical lattice -- single-band Hubbard model (Hofstetter et al, PRL 2003) H weak t ai a j u ai ai ai ai i, j i • Strongly (resonantly) interacting fermions in optical lattice -- Boson-fermion Hubbard model ?? H strong H weak g on bi ai ai bibi i Stoof, Holland, Zhou, etc., 2005 i Inadequate! Strong interaction effects Why is it inadequate? H strong H weak g on bi ai ai bibi i i • Multi-band populations (T.-L. Ho, cond-mat/0507253; 0507255, PRL 2006) g on Ebg ~ On-site coupling rate Band gap g b pqr ipaiq air i ; pqr Different bands • Off-site collision couplings (L.-M. Duan, PRL 95, 243202,2005) g off t Off-site coupling rate Tunneling rate g off Off-site coupling t • Starting point: the field Hamiltonian •Keep all the bands •Keep the off-site couplings L.-M. Duan, PRL 95, 243202,2005 • Limiting case 1: atom limit • Limiting case2: molecule limit Quantum simulation with polar molecules A. Micheli, G. K. Brennen and P. Zoller, A toolbox for lattice-spinmodels with polar molecules, Nature Physics, 2, 341 (2006) Detection of ultracold atoms • Time-of-flight imaging expansion condensate rt rt k k density rt r0 kt / m Diagonal correlation in momentum space One can also utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states. Nature Physics, 4, 50 (2008) Nature Physics, 4, 50 (2008) Quantum Computer Quantum Simulation Limits from classical world Starting point Quantum Communication Why long-distance quantum communication is so difficult? Transmission loss/fidelity of entanglement—decreasing exponentially with the length of the connecting channel Solution: Quantum repeater combining entanglement swapping and purification [H. Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)] Atomic-ensemble-based quantum memory Atomic-ensemble-based quantum memory is used to transfer the photonic states to the excitation in atomic internal states so that it can be stored, and after the storage of a programmable time, it should be possible to read out the excitation to photons without change of its quantum state. M.D. Lukin et al., Phys. Rev. Lett. 84, 4232 (2000); M. Fleischhauer and M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000). Physical implementation of Quantum Repeater: A Scheme based on atomic ensembles, the DLCZ scheme [L.-M. Duan et al., Nature 414, 413 (2001)] The phase stability problem in the DLCZ scheme In the DLCZ protocol, two entangled pairs are generated in parallel. The relative phase between the two entangled states has to be stabilized during the entanglement generation process. As entanglement generation process is probabilistic. The experiment has to be repeated many times to ensure that there is a click at the detectors. The two phases achieved at different runs of the experiments are usually different due to the path length fluctuations in this time interval. A robust, fault-tolerant quantum repeater •a) Local preparation of entanglement (at adjacent nodes) by a linear-optical polarization entangler and then entanglement swapping •(b) Entanglement connection •(c) Linear-optical entanglement purification B. Zhao, Z.-B.Chen. et al., Phys. Rev. Lett, 98, 240502 (2007); Z.-B.Chen. et al., Phys. Rev. A 76, 022329 (2007). Summary and Outlook Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC Lowering the temperature Achieving single-site addressing QS for highly-correlated many body models Quantum Communication