Dephasing Assisted Transport:Quantum Networks and Biomolecules

Susana F. HuelgaUniversity of Hertfordshire

Work supported by

IQIS2008, Camerino (Italy), October 26th 2008

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Collaboration:Imperial College London

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 theZ-list (1998)

Useful tool (2008)

Isn’t it the case that noise can only mean trouble???

Innsbruck-IFCO, October 2008arXiv:0810.1847

Beam splitter destroys which-pathinformation! A detected photon could havecome from any cavity. Entanglement may ariseS. Bose, Plenio, Knight, Vedral, PRL83, 5158 (1999)Browne, Plenio, SH, PRL 91, 067901(2003)

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?

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)

Thermal driving

Log-Negativity

Noise Intensity

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: coherentinter-qubit coupling J

Uncorrelatedenvironments

The system: A chain of N weakly driven, ZZ coupled spinsunder the transverse action of independent baths

Building block: N=2Amenable to analytic solution

Huelga & Plenio, PRL 98,170601 (2007)

But can one refer to this phenomenon as SR??

Steady state is PPT (Separable)

Steady state entanglement

LO

CA

LIZ

AT

ION

DE

LO

CA

LIZ

ED

We need delocalization to create entanglement

Is non-monotonic as a function of

Information-theoretic measures of SR

Mutual Information

Beyond Born-Markov: Phenomena persistsUbiquity? Phenomena keepsreappearing in a varietyof scenarios

A chain of driven “spins”subject to a form ofcorrelated environment

Di Franco, Paternostro, Tsomokos & SH, PRA 77, 062337 (2008)

SR-effects in a quantum communication set up

New J. Phys 10 (2008), arXiv:0807.4902

Related, independent resultsSee Aspuru-Guzik group, arXiv0806.4725, arXiv:0807.4725

In a given time T, how much of the initial population insite 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 choicesof

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 dephasingWhat about quantum coherence properties during the transport process?

Quantum capacity: Propagate one half of a maximally entangledstate across the chain for optimized local dephasing rates

+Φ

A very simple experimental demonstration

Noise Assisted Transport and Photosynthesis

Reaction Centre

6 CO2

+ 12 H O2

+ energy

6 C H O6 12 6

+ 6 O2+ 6 H O

2

From linear chains to fully connected networks

Motivation: Simplified models for the transfer of excitons in the FMO complex

Noise Assisted Transport and Photosynthesis

Reaction Centre

6 CO2

+ 12 H O2

+ energy

6 C H O6 12 6

+ 6 O2+ 6 H O

2

From linear chains to fully connected networks

Motivation: Simplified models for the transfer of excitons in the FMO complex

Noise Assisted Transport and Photosynthesis

Loss of excitation

Transfer to reaction centre

6 CO2

+ 12 H O2

6 C H O6 12 6

+ 6 CO2+ 6 H O

2

+ energy

Reaction Centre

Exchange of excitation

Complex Networks and light harvesting molecules

Observed exciton transfer time cannot beobtained with a purely coherent evolution

Local dephasing enhances the transfer rate of excitations

(Units 1.2414 10^{-4} eV)

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

Noise Assisted Transport and Photosynthesis

Plenio & Huelga, New J. Phys. 2008

Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

Beyond the Born-Markov framework

Noise Assisted Transport and Photosynthesis

No dephasing

Some dephasing

Plenio & Huelga, New J. Phys. 2008

Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

Noise Assisted Transport and Photosynthesis

No dephasing

Some dephasing

Plenio & Huelga, New J. Phys. 2008

Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

More dephasing

Noise Assisted Transport and Photosynthesis

No dephasing

Some dephasing

Plenio & Huelga, New J. Phys. 2008

Mohseni, Rebentrost, Lloyd, Aspuru-Guzik, J. Phys. Chem. 2008

More dephasing

No photons: Destructive interference !

A very intuitive example

MB Plenio, Clifford Paterson Lecture at the RS London

Photons arrive thanks tonoise !

Related work: Quantum Babinet PrincipleTsomokos, Plenio, de Vega & SH, arXiv:0808.2261

Conclusions

Strategy of just minimizing noise may betoo restrictive for many purposes

Learn how/when fully exploit the interplaycoherent-dissipative dynamics

What is next ?• Noise-assisted processes in general quantum channels(formal approach)• Full analysis under complex environment (non-Markovianbaths, strong coupling, forms of collective decoherence)

Neil Oxtoby, Angel Rivas, DimitrisTsomokos, Shash Virmani and SH+ Alex Chin and Ivette Fuentes-Schuller)

QIP at UH

Beyond Born-Markov: Phenomena persistsUbiquity? Phenomena keepsreappearing in a varietyof scenarios

Procedure:

Take Move to an interaction picture with respect to

Assume that Introduce effective modes

Beam splitter transformations

Solving the dynamics

Hamiltonian part:

Liouvillian:

Solving the dynamics

Entanglement from white noise and loss

Quantify entanglementbetween the two cavitymodes, trace out atom.

Plenio & Huelga, PRL 88, 197901 (2002)

Entanglement from white noise and loss

Quantify entanglementbetween the two cavitymodes, trace out atom.

No cavity decay

No entanglement

Quantify entanglementbetween the two cavitymodes, trace out atom.

No cavity decay

No entanglement

No white noise

No entanglement

Entanglement from white noise and loss

Quantify entanglementbetween the two cavitymodes, trace out atom.

No cavity decay

No entanglement

No white noise

No entanglement

Maximal entanglement at intermediate noise levels

Entanglement from white noise and loss

Separable

Vacuum

Thermal

Non-classical

Vacuum

Noiseless cavity: Steady state solution for effective mode is a thermal distribution

Understanding the dynamics

Separable

Vacuum

Thermal

Non-classical

Vacuum

Noiseless cavity: Steady state solution for effective mode is a thermal distribution

Understanding the dynamics

Plenio & Huelga, PRL 88, 197901 (2002)

Separable

Vacuum

Thermal

Non-classical

Vacuum

For finite κ, things are different

Understanding the dynamics

Plenio & Huelga, PRL 88, 197901 (2002)

+Φ

+Φ