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
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
Isn t it the case that noise can only mean trouble??? From the Z-list (1998) Useful tool (2008)
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, 067901 (2003) Innsbruck-IFCO, October 2008 arxiv:0810.1847
Beyond noise as a mediator of generalized measurements Entanglement in open, driven, non-equilibrium systems Stochastic Resonance-like Effects
Can entanglement be generated out of just incoherent sources? Log-Negativity Thermal driving Noise Intensity Plenio & Huelga, Phys. Rev. Lett. 88, 197901 (2002) and Nature Physics Highlights May 2002 Related work: Braun, PRL 89, 277901 (2001); Benatti, Floreanini & Piani PRL 91, 070402 (2003)
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 98,170601 (2007)
Steady state entanglement Steady state is PPT (Separable)
DELOCALIZED LOCALIZATION We need delocalization to create entanglement Is non-monotonic as a function of
Information-theoretic measures of SR Mutual Information
Beyond Born-Markov: Phenomena persists Ubiquity? Phenomena keeps reappearing in a variety of scenarios
A chain of driven spins subject to a form of correlated environment
SR-effects in a quantum communication set up Di Franco, Paternostro, Tsomokos & SH, PRA 77, 062337 (2008)
New J. Phys 10 (2008), arxiv:0807.4902 Related, independent results See Aspuru-Guzik group, arxiv0806.4725, arxiv:0807.4725
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?
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
Non-uniform linear chains: Noise can significantly enhance the transmission rate of excitations
Interpretation: Line broadening due to local dephasing
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?
Quantum capacity: Propagate one half of a maximally entangled state across the chain for optimized local dephasing rates + Φ
A very simple experimental demonstration
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 2 + 12 H O 2 + energy 6 C H O + 6 O + 6 H O 6 12 6 2 2
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 2 + 12 H O 2 + energy 6 C H O + 6 O + 6 H O 6 12 6 2 2
Noise Assisted Transport and Photosynthesis Loss of excitation Exchange of excitation Reaction Centre 6 CO 2 + 12 H O 2 Transfer to reaction centre + energy 6 C H O + 6 CO + 6 H O 6 12 6 2 2
Complex Networks and light harvesting molecules (Units 1.2414 10^{-4} ev) Local dephasing enhances the transfer rate of excitations Observed exciton transfer time cannot be obtained with a purely coherent evolution
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
Beyond the Born-Markov framework Noise Assisted Transport and Photosynthesis Plenio & Huelga, New J. Phys. 2008 Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008
Noise Assisted Transport and Photosynthesis Some dephasing No dephasing Plenio & Huelga, New J. Phys. 2008 Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008
Noise Assisted Transport and Photosynthesis More dephasing Some dephasing No dephasing Plenio & Huelga, New J. Phys. 2008 Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008
Noise Assisted Transport and Photosynthesis More dephasing Some dephasing No dephasing Plenio & Huelga, New J. Phys. 2008 Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008
A very intuitive example No photons: Destructive interference! MB Plenio, Clifford Paterson Lecture at the RS London
Photons arrive thanks to noise! Related work: Quantum Babinet Principle Tsomokos, Plenio, de Vega & SH, arxiv:0808.2261
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)
QIP at UH Neil Oxtoby, Angel Rivas, Dimitris Tsomokos, Shash Virmani and SH + Alex Chin and Ivette Fuentes-Schuller)
Beyond Born-Markov: Phenomena persists Ubiquity? Phenomena keeps reappearing in a variety of scenarios
Solving the dynamics Procedure: Take Move to an interaction picture with respect to Assume that Introduce effective modes Beam splitter transformations
Solving the dynamics Hamiltonian part: Liouvillian:
Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. Plenio & Huelga, PRL 88, 197901 (2002)
Entanglement from white noise and loss Quantify entanglement between the two cavity modes, trace out atom. No cavity decay No entanglement
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
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
Understanding the dynamics Noiseless cavity: Steady state solution for effective mode is a thermal distribution Vacuum Thermal Separable Vacuum Non-classical
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, 197901 (2002)
Understanding the dynamics For finite κ, things are different Vacuum Thermal Separable Vacuum Plenio & Huelga, PRL 88, 197901 (2002) Non-classical
+ Φ + Φ