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arXiv:2203.14116 · Physical Review A

Photon cooling: Linear versus nonlinear interactions

A. A. Hovhannisyan, V. A. Stepanyan, ARMEN E. ALLAHVERDYAN

Published Sep 16, 2022• 2 citations
arXivHTMLPDF

Abstract

Linear optics imposes a relation that is more general than the second law of thermodynamics: For modes undergoing a linear evolution, the full mean occupation number, i.e., the photon number for optical modes, does not decrease, provided the evolution starts from a (generalized) diagonal state. This relation connects to noise increasing (or heating) and is akin to the second law and holds for a wide set of initial states. Also, the Bose entropy of modes increases, though this relation imposes additional limitations on the initial states and on linear evolution. We show that heating can be reversed via nonlinear interactions between the modes. They can cool, i.e., decrease the full mean occupation number and the related noise, an equilibrium system of modes provided their frequencies are different. Such an effect cannot exist in energy cooling, where only a part of an equilibrium system is cooled. We describe the cooling setup via both efficiency and coefficient of performance and relate the cooling effect to the Manley-Rowe theorem in nonlinear optics.

DOI
10.1103/physreva.106.032214

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Linear optics imposes a relation that is more general than the second law of thermodynamics: For modes undergoing a linear evolution, the full mean occupation number, i.e., the photon number for optical modes, does not decrease, provided the evolution starts from a (generalized) diagonal state. This relation connects to noise increasing (or heating) and is akin to the second law and holds for a wide set of initial states. Also, the Bose entropy of modes increases, though this relation imposes additional limitations on the initial states and on linear evolution. We show that heating can be reversed via nonlinear interactions between the modes. They can cool, i.e., decrease the full mean occupation number and the related noise, an equilibrium system of modes provided their frequencies are different. Such an effect cannot exist in energy cooling, where only a part of an equilibrium system is cooled. We describe the cooling setup via both efficiency and coefficient of performance and relate the cooling effect to the Manley-Rowe theorem in nonlinear optics.
The past few years have witnessed a resurgence of interest in multimode structures, predominantly driven by the ever-increasing demand for higher information capacities. This renaissance, in turn, incited a flurry of activities in the general area of nonlinear multimode optics. The sheer complexity associated with the presence of hundreds or thousands of nonlinearly interacting modes that collectively act as a many-body system, has led to new opportunities in observing a multitude of novel optical effects that would have been otherwise impossible in single mode settings. In this talk, a thermodynamic theory capable of describing complex, highly multimoded, nonlinear optical systems is presented. It is shown that the mode occupancies in such nonlinear multimode arrangements follow a universal behavior that always tends to maximize the system’s entropy at steady-state. This thermodynamic response takes place irrespective of the type of nonlinearity involved and can be utilized to either heat or cool an optical multimode system. Aspects associated with adiabatic compressions and expansions will be discussed along with the possibility for all-optical Carnot cycles.
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Abstract The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio between the natural linewidth and the recoil energy and tends to E R as tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio and contains the semiclassical theory of laser cooling as the limiting case in which .
The nonlinear equation of motion that accomplishes a self-consistent unification of quantum mechanics (QM) and thermodynamics conceptually different from the (von Neumann) foundations of quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but which reduces to the same mathematics for the thermodynamic equilibrium (TE) states, and contains standard QM in that it reduces to the time-dependent Schrodinger equation for zero entropy states is discussed in full mathematical detail. By restricting the discussion to a strictly isolated system (noninteracting, disentangled and uncorrelated), we show how the theory departs from the conventional QSM/QIT rationalization of the second law of thermodynamics, which instead emerges in QT (quantum thermodynamics) as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituent particles. To achieve this, the theory assumes Trρ lnρ B −k for the physical entropy and is designed to implement two fundamental ansatzs: (1) that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated and uncorrelated system admits also states that must be described by non-idempotent density operators (nonzero entropy); (2) that for such additional states the law of causal evolution is determined by the simultaneous action of a Schrodinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituent particles, and in forward time drives the density operator in the 'direction' of steepest entropy ascent (maximal entropy generation). The resulting dynamics is well defined for all non-equilibrium states, no matter how far from TE. Existence and uniqueness of solutions of the Cauchy initial value problem for all density operators implies that the equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also in backward time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates. Zero entropy states as well as a well defined family of non-dissipative states evolve unitarily according to pure Hamiltonian dynamics and can be viewed as unstable limit cycles of the general nonlinear dynamics.
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy states it reduces to standard unitary QM. The nonlinear dynamical group of QT is construed so that the second law emerges as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituents. It implements two fundamental ansatzs. The first is that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated system admits also states that must be described by non-idempotent density operators (nonzero entropy). The second is that for such additional states the law of causal evolution is determined by the simultaneous action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituents, and (in forward time) drives any density operator, no matter how far from TE, in the 'direction' of steepest entropy ascent (maximal entropy increase). The equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also backwards in time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates.