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arXiv:2209.03674 · Physical Review Research

Quantum refrigerator driven by nonclassical light

Hui-Jing Cao, Fu Li, Sheng-Wen Li

Published Dec 2, 2022• 7 citations
arXivHTMLPDF

Abstract

We study a three-level quantum refrigerator which is driven by a generic light state, even a nonclassical one. With the help of $P$ function expansion of the driving light, we obtain the heat current generated by different types of light states. It turns out all different input light states give the same coefficient of performance for this refrigerator, while the cooling power depends not only on the light intensity but also the specific photon statistics of the driving light. Comparing the coherent light with the same intensity, the driving light with super(sub)-Poissonian photon statistics could raise a smaller (stronger) cooling power. We find that this is because the bunching photons would first excite the system but then successively induce the stimulated emission, which draws the refrigerator back to the starting state of the cooling process and thus decreases the cooling current generation. This mechanism provides a more delicate control method via the high order coherence of the input light.

DOI
10.1103/physrevresearch.4.043158

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We study a three-level quantum refrigerator which is driven by a generic light state, even a nonclassical one. With the help of PPP function expansion of the driving light, we obtain the heat current generated by different types of light states. It turns out all different input light states give the same coefficient of performance for this refrigerator, while the cooling power depends not only on the light intensity but also the specific photon statistics of the driving light. Comparing the coherent light with the same intensity, the driving light with super(sub)-Poissonian photon statistics could raise a smaller (stronger) cooling power. We find that this is because the bunching photons would first excite the system but then successively induce the stimulated emission, which draws the refrigerator back to the starting state of the cooling process and thus decreases the cooling current generation. This mechanism provides a more delicate control method via the high order coherence of the input light.
Abstract We study the photoelectric current generated by a driving light with nonclassical photon statistics. Due to the nonclassical input photon statistics, it is no longer enough to treat the driving light as a planar wave as in classical physics. We make a quantum approach to study such problems, and find that: when the driving light starts from a coherent state as the initial state, our quantum treatment well returns the quasi-classical driving description; when the the driving light is a generic state with a certain P function, the full system dynamics can be reduced as the P function average of many ‘branches’—in each dynamics branch, the driving light starts from a coherent state, thus again the system dynamics can be obtained in the above quasi-classical way. Based on this quantum approach, it turns out the different photon statistics does make differences to the photoelectric current. Among all the classical light states with the same light intensity, we prove that the input light with Poisson statistics generates the largest photoelectric current, while a nonclassical sub-Poisson light could exceed this classical upper bound.
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT(t)/dt∼-T^{ζ} when approaching absolute zero, T→0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.
We study the characteristics of the light generated by a few emitters in a cavity at strong light-matter coupling. By means of the Glauber g(2){g}^{(2)}g(2) function we can identify clearly distinguished parameter regimes with super-Poissonian and sub-Poissonian photon statistics. We establish a relation between the emission characteristics for one and multiple emitters and explain its origin in terms of the photon-dressed emitter states. Cooperative effects lead to the generation of nonclassical light already at reduced light-matter coupling if the number of emitters is increased. Our results are obtained with a full input-output formalism and master equation valid also at strong light-matter coupling. We compare the behavior obtained with and without counterrotating light-matter-interaction terms in the Hamiltonian and find that the generation of nonclassical light is robust against such modifications. Finally, we contrast our findings with the predictions of the quantum optical master equation and find that it fails entirely at predicting regimes with different photon statistics.
We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and χ function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power can be maximized with respect to one control frequency, while χ function can be maximized globally with respect to two control frequencies. Additionally, we show that in the low-temperature regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and χ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum χ function with the maximum cooling power.
The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But is this connection always an evidence of "quantum-thermodynamic supremacy"? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot and it may exhibit a larger cooling rate and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a "cyclic" pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.
Harnessing a beam of slow free electrons in artificial photonic structures offers a powerful, tunable platform for generating nonclassical light without the need for heavy physical equipment. Here we present a theory of nonclassical lasing, demonstrating how incoherent electrons in photonic crystal cavities can coherently emit photons through collective dynamics. When photon emission rate exceeds cavity losses, nonclassical lasing with sub-Poissonian photon statistics emerges, driven by multi-photon Rabi oscillations. At specific coupling strengths, quantum state trapping effect emerges, producing high-fidelity Fock states at room temperature (e.g. nearly 90%-fidelity of four photon Fock state). Notably, the frequency of the emitted photons can be readily tuned via the velocity of the injected electrons to match cavity modes. This approach supports photonic integration and offers a scalable, energy-efficient platform for room-temperature quantum light sources and advanced studies in quantum electrodynamics.