Despite the best efforts of experimentalists, no quantum system is ever completely isolated from its environment especially so as the control of a quantum system is always achieved by outside interventions such as shining in lasers. On the level of the system the influence of an environment whose state is usually outside of our control and observation appears as noise and thus a deviation from the typical unitary dynamics that we learn about in our first quantum mechanics course. We have recently written a monograph that describes the foundations of the theory of open quantum systems with an emphasis on providing a mathematical background on standard derivations found in the quantum optical literature.

• Ángel Rivas, Susana F. Huelga, "Open Quantum Systems. An Introduction", Springer Briefs in Physics, ISSN 2191-5423 Springer 2011 also available as a preprint in arXiv:1104.5242.

Noise assisted quantum dynamics: It is actually interesting to note that the action of an environment can even assist the generation of quantum features such as entanglement as we have been amongst the first to show and have explored ever since in topics ranging from quantum technologies to quantum biology.

• M.B. Plenio, S.F. Huelga, A. Beige, and P.L. Knight. Cavity Loss Induced Generation of Entangled Atoms. Phys. Rev. A 59, 2468 – 2475 (1999).
• M.B. Plenio and S.F. Huelga. Entangled light from white noise. Phys. Rev. Lett. 88, 197901 (2002).
• S.F. Huelga and M.B. Plenio. Vibrations, Quanta and Biology. To appear in Contemporary Physics 2013 and E-print arXiv:1307.3530

Environments with memory: Open quantum systems are traditionally studied in two extreme regimes, depending of the strength of the coupling to the environment as compared with typical coupling constants within the system dynamics. When the interaction strength of the coupling between system and environment dominates over internal couplings, the system dynamics is amenable to a “classical” description in terms of rate equations between different population states. Conversely, when the coupling to the environment is sufficiently weak, a master equation holds for the reduced dynamics of the system involving also the time evolution of quantum coherences. In general however the correct dynamics lies in between these two regimes and the interaction between system and environment exhibits memory effects that is, it follows a non-Markovian dynamics. How to quantitatively characterize non-Markovianity without resorting to specific physical models has become an active line of research.

• A. Rivas, S.F. Huelga and M.B. Plenio. Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010)
• A. Rivas, D.A.K. Plato, S.F. Huelga and M.B. Plenio. Markovian Master equations: A Critical Study. New J. Phys. 12, 113032 (2010)

Metrology in noisy environments: The ever-increasing precision of quantum metrology is achieved by a persistent fight with environmental noise. The precise nature of the system-environment interaction is of considerable importance in this respect. Currently we are exploring which consequences non-Markovianity on the fundamentally important problem of metrology and dissipative state preparation.

• S.F. Huelga, C. Macchiavello, T. Pellizzari, A.K. Ekert, M.B. Plenio and J.I. Cirac. On the improvement of frequency standards using quantum entanglement. Phys. Rev. Lett. 79, 3865 – 3868 (1997).
• A.W. Chin, M.B. Plenio and S.F. Huelga. Metrology in the presence of non-Markovian noise. Phys. Rev. Lett. 109, 233601 (2012)
• S.F. Huelga, A. Rivas, and M.B. Plenio. Non-markovianity-assisted steady state entanglement. Phys. Rev. Lett. 108, 160402 (2012)
• A. Bermudez, C. Cormick, S.F. Huelga and M.B. Plenio. Preparation of the ground state of a spin chain by dissipation in a structured environment. New J. Phys. 15, 073027 (2013)

Numerical modeling of system-environment interaction: In some situations, the conditions for adopting a perturbative approach are not justified, and novel methods are required to faithfully describe the system’s dynamics. Starting with mathematical concepts from the theory of orthogonal polynomials, we have derived an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes (spin boson model) to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbour interactions. This setting is then amenable to numerical simulation methods from condensed matter physics most notably the density matrix renormalization group method. We are developing the method and are applying it to the simulation of a wide variety of physical systems ranging from solid state physics, quantum information technologies to quantum biology. The exact results obtained using this technique has allowed us for example recently to put forward a microscopic mechanism to explain the observed long lasting exciton beating in a range of photosynthetic complexes.

• J. Prior, A.W. Chin, S.F. Huelga and M.B. Plenio. Efficient simulation of strong system-environment interactions. Phys. Rev. Lett. 105, 050404 (2010)
• A.W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S.F. Huelga and M.B. Plenio. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes. Nature Physics 9, 113 - 118 (2013)