Energetic and entropic effects of bath-induced coherences

Abstract

The unavoidable interaction of a quantum system with its surrounding (bath) is not always detrimental for quantum properties. For instance, under some specific conditions (that we identify as indistinguishability), a many-body system can gain internal coherences thanks to the interaction with its bath. The most famous consequence of this phenomenon is superradiance. Beyond that, the thermodynamic effects on the system of these bath-induced coherences have been mostly unexplored. We show here, for a simple and common system (a pair of two-level systems), that the energetic and entropic impacts can indeed be dramatic and diverse, including amplification of the action of the bath but also its mitigation. Our results can be tested experimentally. They suggest that bath-induced coherences can be harnessed to enhance thermodynamic tasks, opening up interesting perspectives for thermal machines, quantum battery charging, natural or artificial energy harvesting systems, and state preparation and protection.

Thermodynamics from indistinguishability: Mitigating and amplifying the effects of the bath

“…] holds for any β 0 ∈] − ∞; ∞[, which coincides with what was observed in the case of a pair of two-level systems [6].…”

“…This is an indication that the mechanism presented here is different in nature from the one in place in [13]. Moreover, the power enhancement suggested here stems from a steady state effect, which is itself related to bathinduced coherences as shown in [6] for a pair of twolevel systems and extended in Appendixes H, I, and J for ensemble of n spins of size s. Thus, it is not obvious whether such phenomena have a classical analogue (see also discussion in the next Section VIII B). By contrast, the result from [13] stems from superradiance, which is a dynamical effect.…”

“…This last property is particularly welcome when aiming at exploiting the bath's properties, like in thermal machines. These phenomena of mitigation and amplification of the bath's action were already pointed out in [6] for a pair of two-level systems, but here we show that not only these phenomena remain arXiv:1908.10384v1 [quant-ph] 27 Aug 2019 for ensembles of any number of spins n of any size s, but also that they scale up with n and s. For instance, an ensemble of n spins can see its steady state energy and entropy reduced by a factor up to 1/n with respect to the value reached by independent interaction with the bath (and therefore without bath-induced coherences). This is indeed an intriguing phenomenon as intuitively one would think that non-energetic coherences (the type of coherences induced by the bath, between degenerate energy levels) are not able to affect the energy of the system.…”

“…The phenomenon of collective dissipation relies on the indistinguishability of the subsystems (here spins or twolevel atoms) from the point of view of the bath [6]. Such indistinguishability is in general not present naturally but can be engineered [13,[62][63][64]77] for instance by introducing an ancillary system between the spin ensemble and the bath (erasing part of the information "seen" by the bath).…”

“…The analytical expression of β l is challenging to obtain in general, but one can estimate it graphically. For any β h and β c (such that β c > β h ) belonging to the interval [0; In the previous study on a pair of two-level systems [6] it was possible to explicitly relates the steady state energy to the amount of bath-induced coherences. In the present situation however such direct relation is much more complex to exhibit.…”