Dynamically induced heat rectification in quantum systems

Abstract

Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. We present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. The rectification can be further enhanced, even achieving maximal performance, by detuning the oscillators of the driven network. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.Rectifiers are physical systems capable of conducting energy asymmetrically -whether electric, magnetic, thermal...-and are an essential building block in many technological applications. Although thermal rectifiers are crucial components to manipulate heat currents and construct phononic devices, so far no efficient and feasible thermal diodes have been found. Such device, when connected to two thermal baths at different temperatures, conducts heat asymmetrically if the temperatures of the baths are interchanged. This effect allows for an effective heat dissipation with a suppressed backflow reaction.To date, most theoretical proposals on classical heat rectifiers (see [1] and references therein) have been based either on the use of inohomogenous materials [2-7] exploiting nonlinear interactions, or doping the systems with impurities while remaining in the linear regime [8]. Also, the feasibility of microscopic systems acting as thermal devices has been recently addressed in, for instance, phononic refrigerators in the classical [9] and quantum [10] regimes, or heat rectifiers in diferent platforms: quantum dots [11], nonlinear solid-state quantum circuits [12], few-level systems [13,14], or hybrid configurations [15].Here, we address analytically and in full generality heat rectification in quantum systems under generic linear interactions. To this aim, we assume a network of harmonic oscillators coupled to two thermal reservoirs and investigate how asymmetric heat fluxes can be induced in such setup. First, we revisit the static scenario showing that linearity forbids heat rectification, regardless of any asymmetry in the harmonic network or in its coupling with the baths. Second, we demonstrate that heat rectification in a linear quantum system is possible if the system is periodically driven. This is our main result. Such feature is a consequence of two facts: (i) injecting/extracting work into/from a system by an external agent is a useful resource to redistribute energy and (ii) by periodically driven a system, new asymmetric heat transport processes -that have no analog in static scenarios-are induced. By using the Floquet formalism we identify precisely the quantum processes leading to heat rectification. Finally, we also demonstrate the suitability of driven harmonic net-works as heat transistors. Q r 1 FIG. 1. Sketch of a heat rectification setup where a system S with linear interactions V (t) is connected ...

Heat current control in trapped Bose–Einstein Condensates

“…We find that it shows to maxima at for two values of the driving frequency Ω d ä {Ω, 3Ω}. Note that, as shown in [44], heat rectification should be maximum at the following frequencies n n W =  | | ( ) . 7 2 d j i Figure 3.…”

“…We comment here on the experimental feasibility of the measurements of the two proposed quantities above, namely the heat current and the current variance. As is proven in detail in [44] in appendix C, the heat current depends on the covariance matrix element ( ) C 0 XP defined in appendix of our paper, where the nonzero elements of this matrix are á ñ x p i j with ¹ i j. Hence one needs to measure simultaneously the position of one particle and the momentum of the other.…”

“…Now we consider the case where a driving is applied on the central system. In particular we assume that the driving is either on the oscillators' frequencies or on their inbetween coupling, as in [44]. The analytic treatment of this case is slightly more involved than the static one.…”

“…d e e t t k k k t i i d that can be selfconsistently solved. By following this procedure, in [44] the authors were able to obtain expressions for these coefficients…”

“…On the contrary, decreasing the number of atoms significantly increases R, in fact reaching R>1. What is more, rectification could also be optimized with respect to the detuning between the trapping frequencies of the impurities as in [44].…”