Collective couplings: Rectification and supertransmittance

Abstract

We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two level systems. One coupling implements the dissipative Dicke superradiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir. After the mapping, the large spin is coupled to a collective mode with the original pure-dephasing interaction, but the collective mode is dissipatively coupled to the residual oscillators. Treating the large spin and the collective mode as the system, a standard master equation approach is now able to capture the energy transfer between the two reservoirs. Assuming fast relaxation of the collective mode, we derive a coarse-grained rate equation for the large spin only and discuss how the original Dicke superradiance is affected by the presence of the additional reservoir. Our main finding is a cooperatively enhanced rectification effect due to the interplay of supertransmittant heat currents (scaling quadratically with N ) and the asymmetric coupling to both reservoirs. For large N , the system can thus significantly amplify current asymmetries under bias reversal, functioning as a heat diode. We also briefly discuss the case when the couplings of the collective spin are locally dissipative, showing that the heat-diode effect is still present. I. MOTIVATIONThe study of radiative effects in two-level systems has a long history. Here, the spin-boson model [1] takes a very prominent role. Originating from the interaction of a two-level atom with the electromagnetic field [2], it is often used as a toy model in many other contexts. Not surprisingly, it has become a canonical model to explore fundamental methods of open systems [3][4][5] and effectively arises in a rather large number of physical systems and effects, including e.g. the dynamics of light-harvesting complexes [6], detectors [7], and the interaction of quantum dots with generalized environments [8].Ideally, one aims at a reduced description taking only the finite-dimensional spin dynamics into account. However, when the number of spins is increased, the curse of dimensionality -the exponential growth of the system Hilbert space with its size -usually inhibits investigations of large spin-boson models. When additional symmetries come into play -e.g. when the spins have the same splitting and couple collectively to all other componentssimplified descriptions are applicable. Collective effects may for example dramatically influence the dephasing behavior of the environment, leading to phenomena such as super-and sub-decoherence [9,10]. Furthermore, they play a significant role in the modelling of light-harvesting complexes [11][12][13][14]. Perhaps one of the clearest manifesta- * gernot.schaller@tu-berlin.de tions of collective behaviour is Dicke superradiance [15]. Here, the collectivity of the coupling between N two-level atoms and a low-temperature bosonic reservoir induces an...

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