Coupled quantum systems in structured environments: Master equations and applications to quantum-enhanced solar energy harvesting

Coherently coupled nanostructures can provide a rich playground for developing more efficient devices that exploit quantum mechanical properties, and for fundamental studies of open quantum systems. In this presentation, I will first show how to tailor the optical properties of molecules by using particular geometries of coupled chromophores. I will discuss the illustrative examples of engineered ‘superabsorption’ [1], and the notion of optical ratchet states [2]. In the second part of the talk, I will discuss the general problem of deriving time-local master equations for two coupled systems interacting with a bosonic environment [3].

The Dicke model of superradiance describes a signature quantum effect: N atoms collectively emit light at a rate proportional to N-squared [4,5]. By using environment engineering [4] together with a ring of coupled chromophores, I will show that this phenomenon can be inverted to make a quantum-enhanced absorption device [1]. Potential applications of this effect include photon detection, enhanced light energy harvesting and light-based power transmission.

In my second example, I will discuss how to make optically excited states that can absorb more photons, but do not re-emit [2]. Natural and artificial light harvesting systems often operate in a regime where the flux of photons is relatively low. Besides absorbing as many photons as possible it is therefore paramount to prevent excitons from annihilating via photon re-emission until they have undergone an irreversible conversion process. Again using a coupled ring system, I will introduce a class of states we call ratchets: excited states capable of absorbing but not emitting light. This allows our antennae to absorb further photons whilst retaining the excitations from those that have already been captured. Simulations for a ring of four sites reveal a peak power enhancement of 35% under ambient conditions owing to a combination of ratcheting and the prevention of emission through dark state population. In the slow extraction limit the achievable current enhancement exceeds hundreds of percent.

The final section of my talk will be devoted to the structure of master equations for coupled systems in general [3]. Specifically, for two boson modes with similar frequencies we will show that secularisation - the usual trick used in order to make sure a resulting master equation is in Lindblad form - does not lead to agreement with an exact solution. On the other hand, Lindblad form is required to guarantee that a density operator stays completely positive as time evolves [6]. Nonetheless, it is possible to derive a time-local form for the master equation that is accurate but not in Lindblad form, by relaxing the requirement of secularization. We find that these considerations have profound consequences for the existence of long time correlations between the two coupled systems.




[1] K. D. B. Higgins, S. C. Benjamin, T. M. Stace, G. J. Milburn, B. W. Lovett and E. M. Gauger, Nature Communications 5 4705 (2014).
[2] K. D. B. Higgins, B. W. Lovett and E. M. Gauger, arXiv:1504.05849 (2015).
[3] P.R. Eastham, P. Kirton, H. M. Cammack, B. W. Lovett, J. Keeling arxiv.org/abs/1508.04744 (2015)
[4] R. H. Dicke, Phys. Rev. 93 99 (1954).
[5] M. Gross and S. Haroche, Physics Reports 93 301 (1982).
[6] H. P. Breuer and F. Petruccione, The Theory of Open Quantum
Systems, OUP (2002)