Quantum heat engine power can be increased by noise-induced coherence

Abstract

Laser and photocell quantum heat engines (QHEs) are powered by thermal light and governed by the laws of quantum thermodynamics. To appreciate the deep connection between quantum mechanics and thermodynamics we need only recall that in 1901 Planck introduced the quantum of action to calculate the entropy of thermal light, and in 1905 Einstein’s studies of the entropy of thermal light led him to introduce the photon. Then in 1917, he discovered stimulated emission by using detailed balance arguments. Half a century later, Scovil and Schulz-DuBois applied detailed balance ideas to show that maser photons were produced with Carnot quantum efficiency (see Fig. 1 A ). Furthermore, Shockley and Quiesser invoked detailed balance to obtain the efficiency of a photocell illuminated by “hot” thermal light (see Fig. 2 A ). To understand this detailed balance limit, we note that in the QHE, the incident light excites electrons, which can then deliver useful work to a load. However, the efficiency is limited by radiative recombination in which the excited electrons are returned to the ground state. But it has been proven that radiatively induced quantum coherence can break detailed balance and yield lasing without inversion. Here we show that noise-induced coherence enables us to break detailed balance and get more power out of a laser or photocell QHE. Surprisingly, this coherence can be induced by the same noisy (thermal) emission and absorption processes that drive the QHE (see Fig. 3 A ). Furthermore, this noise-induced coherence can be robust against environmental decoherence. Fig. 1. ( A ) Schematic of a laser pumped by hot photons at temperature T h (energy source, blue) and by cold photons at temperature T c (entropy sink, red). The laser emits photons (green) such that at threshold the laser photon energy and pump photon energy is related by Carnot efficiency ( 4 ). ( B ) Schematic of atoms inside the cavity. Lower level b is coupled to the excited states a and β . The laser power is governed by the average number of hot and cold thermal photons, and . ( C ) Same as B but lower b level is replaced by two states b 1 and b 2 , which can double the power when there is coherence between the levels. Fig. 2. ( A ) Schematic of a photocell consisting of quantum dots sandwiched between p and n doped semiconductors. Open circuit voltage and solar photon energy ℏν h are related by the Carnot efficiency factor where T c is the ambient and T h is the solar temperature. ( B ) Schematic of a quantum dot solar cell in which state b is coupled to a via, e.g., solar radiation and coupled to the valence band reservoir state β via optical phonons. The electrons in conduction band reservoir state α pass to state β via an external circuit, which contains the load. ( C ) Same as B but lower level b is replaced by two states b 1 and b 2 , and when coherently prepared can double the output power. Fig. 3. ( A ) Photocell current j = Γ ρ αα (laser photon flux P l / ℏ ν l ) (in arbitrary units) generated by the photovoltaic cell QHE (laser QHE) of Fig. 1 C ( Fig. 2 C ) as a function of maximum work (in electron volts) done by electron (laser photon) E α - E β + kT c log( ρ αα / ρ ββ ) with full (red line), partial (brown line), and no quantum interference (blue line). ( B ) Power of a photocell of Fig. 2 C as a function of voltage for different decoherence rates , 100 γ 1 c . Upper curve indicates power acquired from the sun.