Minimal Self-Contained Quantum Refrigeration Machine Based on Four Quantum Dots

Abstract

We present a theoretical study of an electronic quantum refrigerator based on four quantum dots arranged in a square configuration, in contact with as many thermal reservoirs. We show that the system implements the minimal mechanism for acting as a self-contained quantum refrigerator, by demonstrating heat extraction from the coldest reservoir and the cooling of the nearby quantum-dot.PACS numbers: 03.65. Yz, 73.63.Kv, The increasing interest in quantum thermal machines has its roots in the need to understand the relations between thermodynamics and quantum mechanics [1,2]. The progress in this field may as well have important applications in the control of heat transport in nano-devices [3]. In a series of recent works [4-6] the fundamental limits to the dimensions of a quantum refrigerator have been found. It has been further demonstrated that these machines could still attain Carnot-efficiency [5] thus launching the call for the implementation of the smallest possible quantum refrigerator. Refs.[4-6] considered selfcontained thermal machines defined as those that perform a cycle without the supply of external work, their action being grounded on the steady-state heat transfer from thermal reservoirs at different temperatures. The major difficulty in the realization [7,8] of self-contained refrigerators (SCRs) is the engineering of the crucial three-body interaction enabling the coherent transition between a doubly excited state in contact with a hot (H) and cold (C) reservoir, and a singly-excited state coupled to an intermediate (or "room" -R) temperature bath. We get around this problem by proposing an experimentally feasible implementation of a minimal SCR with semiconducting quantum dots (QDs) operating in the Coulomb blockade regime. We are thus able to establish a connection between the general theory of quantum machines and the heat transport in nanoelectronics [3].QDs contacted by leads were proposed as ideal systems for achieving high thermopower [9][10][11] or anomalous thermal effects [12]. Here we study a four-QD planar array (hereafter named a "quadridot" for simplicity) coupled to independent electron reservoirs as shown in Fig. 1; with proper (but realistic) tuning of the parameters, we will show that the quadridot acts as a SCR which pumps energy from the high temperature reservoir H and the low temperature reservoir C to the intermediate temperature reservoirs R 1 , R 2 . Furthermore we will analyze the conditions under which the quadridot is able to cool the dot QD 2 which is directly connected to the bath C, at an effective temperature that is lower than the one it would have had in the absence of the other reservoirs. This will lead us to introduce an operative definition of the local effective temperature depending on the measurement FIG. 1: [Color online]The quadridot. The four quantum dots QD1, QD2, QD3, and QD4 are weakly coupled to the reservoirs R1, C, R2, and H, respectively, which are all grounded and maintained at temperatures TH > (TR 1 = TR 2 = TR) > TC. Tunneling is allowed onl...

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