Cooperative many-body enhancement of quantum thermal machine power

Abstract

We study the impact of cooperative many-body effects on the operation of periodically-driven quantum thermal machines, particularly heat engines and refrigerators. In suitable geometries, N two-level atoms can exchange energy with the driving field and the (hot and cold) thermal baths at a faster rate than a single atom due to their SU(2) symmetry that causes the atoms to behave as a collective spin-N/2 particle. This cooperative effect boosts the power output of heat engines compared to the power output of N independent, incoherent, heat engines. In the refrigeration regime, similar cooling-power boost takes place. IntroductionOne of the central questions in the emerging field of quantum thermodynamics [1-5] pertains to possible quantum advantages ('supremacy') in the operation of thermal machines such as heat engines or refrigerators compared to their classical counterparts [6]. In that context, starting with the seminal work by Scully et al [7], extensive investigations have focused on the question whether quantum coherence in either the machine's working medium [8][9][10][11][12][13] or the energising (hot) bath (the 'fuel') [14-24] could either boost the power output or the efficiency of quantum engines. Whilst these investigations have been mainly theoretical, impressive experimental progress has also been made such as the first realisation of a heat engine based on a single atom [25], the demonstration of quantum-thermodynamic effects in the operation of a heat engine implemented by an ensemble of nitrogen-vacancy (NV) centres in diamond [26] and the simulation of a quantum engine fuelled by a squeezed-thermal bath in a classical setting [27].Here we explore the possibility of exploiting collective (cooperative) many-body effects in quantum heat engines and refrigerators [28][29][30][31][32][33][34][35][36]. These generic quantum effects have a common origin with Dicke superradiance [37], whereby light emission is collectively enhanced by the interaction of N atoms with a common environment (bath) such that its intensity scales with N 2 [37-62]. Investigations of this effect for a cloud of closely-packed emitters [43] face a severe problem: The dipole-dipole interaction (DDI) among emitters may diverge and cause an uncontrollable inhomogeneous broadening that may destroy superradiance. By contrast, DDI may be either suppressed [50] or collectively enhanced [63] in appropriate one-dimensional setups [64] such that in either case superradiance persists.Beyond the need to control DDI, the feasibility of quantum cooperative effects in heat machines depends on the resolution of another principal issue: is the timing of atom-bath interactions important for their cooperativity [65][66][67]? Since the early studies of superradiance and superfluorescence [68] the crucial role of proper initiation of the atomic ensemble has been stressed [69][70][71]. If this is the case, is continuous, steady-state interaction of the atoms with heat baths compatible with cooperativity? Here we show that, rather surprisingly, quantu...

Boosting the performance of small autonomous refrigerators via common environmental effects

“…This indicates that common noise may be also considered for enhancing the performance of small autonomous classical motors, like thermoelectric devices [73] or biomolecular systems [74] described within the framework of stochastic thermodynamics [75]. Nevertheless we notice that although the magnitude of the quantum coherent enhancements compared with their incoherent counterpart is rather modest in this fridge model, we expect that the same mechanism might be enforced in many-body configurations [76][77][78] where this effect may be greatly amplified.…”

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

“…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. Moreover, classical analogues of superradiance can be found (for instance several classical emitters in phase) [2,96].…”

“…The collective interaction implicitly requires that the bath does not distinguish the n spins [6]. This can be realised in several platforms [62][63][64] (see also [13] for ensemble of two-level atoms). The collective coupling to the bath is then of the form V := gJ x O B , where O B is a bath observable, g characterises the strength of the coupling and J x := n k=1 j x,k is the collective x-component of the angular momentum operator (generator of rotation around the x-axis), with j x,k the xcomponent of the angular momentum operator associated to the k th spin.…”

“…It is not obvious how this indistinguishability-induced enhancement would survive in a continuous engine architecture where the working medium interacts simultaneously with both hot and cold bath and tends to a (single) steady state [13]. 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).…”

“…In addition to that, there is an active debate [13,[40][41][42] around whether performance enhancements stemming from collective effects are genuinely quantum or not. We believe our results can give a valuable contribution to this debate.…”