Susana F. Huelga. Dephasing Assisted Transport: Quantum Networks and Biomolecules. University of Hertfordshire. Collaboration: Imperial College London

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1 IQIS2008, Camerino (Italy), October 26th 2008 Dephasing Assisted Transport: Quantum Networks and Biomolecules Susana F. Huelga University of Hertfordshire Collaboration: Imperial College London Work supported by

2 Outline Noisy Entanglement [a selected review] Noise-assisted transport of excitations Linear Chains The role of entanglement Experimental Realizations Complex Networks --- Biomolecules Beyond Born-Markov framework Conclusions/Future work

3 Isn t it the case that noise can only mean trouble??? From the Z-list (1998) Useful tool (2008)

4 Isn t it the case that noise can only mean trouble??? Beam splitter destroys which-path information! A detected photon could have come from any cavity. Entanglement may arise S. Bose, Plenio, Knight, Vedral, PRL 83, 5158 (1999) Browne, Plenio, SH, PRL 91, (2003) Innsbruck-IFCO, October 2008 arxiv:

5 Beyond noise as a mediator of generalized measurements Entanglement in open, driven, non-equilibrium systems Stochastic Resonance-like Effects

6 Can entanglement be generated out of just incoherent sources? Log-Negativity Thermal driving Noise Intensity Plenio & Huelga, Phys. Rev. Lett. 88, (2002) and Nature Physics Highlights May 2002 Related work: Braun, PRL 89, (2001); Benatti, Floreanini & Piani PRL 91, (2003)

7 But can one refer to this phenomenon as SR?? Specific characterization of a novel SR phenomenon Need to identify suitable measures of SR for composite systems (dynamical and information theoretic) Introduce additional controllable parameter: coherent inter-qubit coupling J The system: A chain of N weakly driven, ZZ coupled spins under the transverse action of independent baths Building block: N=2 Amenable to analytic solution Uncorrelated environments Huelga & Plenio, PRL 98, (2007)

8 Steady state entanglement Steady state is PPT (Separable)

9 DELOCALIZED LOCALIZATION We need delocalization to create entanglement Is non-monotonic as a function of

10 Information-theoretic measures of SR Mutual Information

11 Beyond Born-Markov: Phenomena persists Ubiquity? Phenomena keeps reappearing in a variety of scenarios

12 A chain of driven spins subject to a form of correlated environment

13 SR-effects in a quantum communication set up Di Franco, Paternostro, Tsomokos & SH, PRA 77, (2008)

14 New J. Phys 10 (2008), arxiv: Related, independent results See Aspuru-Guzik group, arxiv , arxiv:

15 In a given time T, how much of the initial population in site 1 can be transferred to site N+1 (trapping site) and how is the transport affected by noise? Which role does entanglement play in the process?

16 Linear Chains Homogeneous linear chains with nearest neighbour interactions N+1 We find that the optimal choice of dephasing rates is zero, for arbitrary choices of Tool: Directed random walk algorithm Analytical expressions can be derived for small N in the steady state General Proof missing

17 Non-uniform linear chains: Noise can significantly enhance the transmission rate of excitations

18 Interpretation: Line broadening due to local dephasing

19 Is the percentual improvement in efficiency always small? Transport of excitations can be assisted by local dephasing What about quantum coherence properties during the transport process?

20 Quantum capacity: Propagate one half of a maximally entangled state across the chain for optimized local dephasing rates + Φ

21 A very simple experimental demonstration

22 From linear chains to fully connected networks Noise Assisted Transport and Photosynthesis Motivation: Simplified models for the transfer of excitons in the FMO complex Reaction Centre 6 CO H O 2 + energy 6 C H O + 6 O + 6 H O

23 From linear chains to fully connected networks Noise Assisted Transport and Photosynthesis Motivation: Simplified models for the transfer of excitons in the FMO complex Reaction Centre 6 CO H O 2 + energy 6 C H O + 6 O + 6 H O

24 Noise Assisted Transport and Photosynthesis Loss of excitation Exchange of excitation Reaction Centre 6 CO H O 2 Transfer to reaction centre + energy 6 C H O + 6 CO + 6 H O

25 Complex Networks and light harvesting molecules (Units ^{-4} ev) Local dephasing enhances the transfer rate of excitations Observed exciton transfer time cannot be obtained with a purely coherent evolution

26 Site 3 couples to the reaction center at site 8 = Measured lifetime of exciton is approx. 1 ns which yields Local dephasing does lead to a strong enhancement of the excitation transfer in a realistic complex network

27 Beyond the Born-Markov framework Noise Assisted Transport and Photosynthesis Plenio & Huelga, New J. Phys Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

28 Noise Assisted Transport and Photosynthesis Some dephasing No dephasing Plenio & Huelga, New J. Phys Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

29 Noise Assisted Transport and Photosynthesis More dephasing Some dephasing No dephasing Plenio & Huelga, New J. Phys Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

30 Noise Assisted Transport and Photosynthesis More dephasing Some dephasing No dephasing Plenio & Huelga, New J. Phys Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

31 A very intuitive example No photons: Destructive interference! MB Plenio, Clifford Paterson Lecture at the RS London

32 Photons arrive thanks to noise! Related work: Quantum Babinet Principle Tsomokos, Plenio, de Vega & SH, arxiv:

33 Conclusions Strategy of just minimizing noise may be too restrictive for many purposes Learn how/when fully exploit the interplay coherent-dissipative dynamics What is next? Noise-assisted processes in general quantum channels (formal approach) Full analysis under complex environment (non-markovian baths, strong coupling, forms of collective decoherence)

34 QIP at UH Neil Oxtoby, Angel Rivas, Dimitris Tsomokos, Shash Virmani and SH + Alex Chin and Ivette Fuentes-Schuller)

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36 Beyond Born-Markov: Phenomena persists Ubiquity? Phenomena keeps reappearing in a variety of scenarios

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39 Solving the dynamics Procedure: Take Move to an interaction picture with respect to Assume that Introduce effective modes Beam splitter transformations

40 Solving the dynamics Hamiltonian part: Liouvillian:

41 Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. Plenio & Huelga, PRL 88, (2002)

42 Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. No cavity decay No entanglement

43 Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. No cavity decay No entanglement No white noise No entanglement

44 Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. No cavity decay No entanglement No white noise No entanglement Maximal entanglement at intermediate noise levels

45 Understanding the dynamics Noiseless cavity: Steady state solution for effective mode is a thermal distribution Vacuum Thermal Separable Vacuum Non-classical

46 Understanding the dynamics Noiseless cavity: Steady state solution for effective mode is a thermal distribution Vacuum Thermal Separable Vacuum Non-classical Plenio & Huelga, PRL 88, (2002)

47 Understanding the dynamics For finite κ, things are different Vacuum Thermal Separable Vacuum Plenio & Huelga, PRL 88, (2002) Non-classical

48 + Φ + Φ