Quantum nonlinear mixing of thermal photons to surpass the blackbody limit

Abstract

Nearly all thermal radiation phenomena involving materials with linear response can be accurately described via semi-classical theories of light. Here, we go beyond these traditional paradigms to study a nonlinear system which, as we show, necessarily requires quantum theory of damping. Specifically, we analyze thermal radiation from a resonant system containing a χ (2) nonlinear medium and supporting resonances at frequencies ω1 and ω2 ≈ 2ω1, where both resonators are driven only by intrinsic thermal fluctuations. Within our quantum formalism, we reveal new possibilities for shaping the thermal radiation. We show that the resonantly enhanced nonlinear interaction allows frequency-selective enhancement of thermal emission through upconversion, surpassing the well-known blackbody limits associated with linear media. Surprisingly, we also find that the emitted thermal light exhibits non-trivial statistics (g (2) (0) = 2) and biphoton intensity correlations (at two distinct frequencies). We highlight that these features can be observed in the near future by heating a properly designed nonlinear system, without the need for any external signal. Our work motivates new interdisciplinary inquiries combining the fields of nonlinear photonics, quantum optics and thermal science.

Nonlinear thermal emission and visible thermometry

“…This process extends the emission spectrum into the visible band. Unlike prior works relying on self-nonlinear wave mixing of thermal photons, 29,30 here, the upconverted photons are determined by both the temperature and external pump laser, giving us a unique tool to regulate thermal emission besides traditional temperature control. Here, the nonlinear upconversion process inside the thermal emitter with second-order nonlinearity can be described as 32,33…”

“…29 However, the low conversion efficiency is the main issue halting the experimental realization of these theoretical proposals. Although many of these works have studied resonant enhancement techniques such as plasmonic antenna 30 and optical microresonator, 31 they have ignored the phase-matching condition, which is the critical factor to determine the nonlinear conversion efficiency. Such phasemismatching is due to the massive wavelength differences between thermal photons in far/mid-infrared and their converted ones like visible photons, hence greatly trimming the conversion efficiency.…”

Review on the Scientific and Technological Breakthroughs in Thermal Emission Engineering

“…Indeed, due to the resonant behavior of subwavelength emitters, ,− the absorption cross-section may largely exceed the geometrical cross-section of emitters, ,, resulting in an enhancement of the radiative heat transfer that appears to be super-Planckian. , Nonetheless, if we consider the absorption/emission cross-section as a suitable metric on which the thermal emission power is normalized (as customarily done in antenna theory), such an enhancement vanishes, and even subwavelength emitters are bounded by the usual upper limits imposed by Planck’s radiation law. Moreover, it is worth stressing that, due to the very low emitting power (on the order of nW), the experimental demonstration of super-Planckian emission in subwavelength emitters has turned out to be very challenging, and even though various orders of magnitude of enhancement in far-field radiation with respect to the blackbody spectrum have been claimed, − the highest experimental measurement of emissivity reported so far is still clearly below 1. − Yet, it is possible to overcome Planck’s radiation law just by disregarding each of the underlying constraints, namely, the near-field regime, or the conditions of thermal equilibrium. , In particular, a typical approach to deal with nonequilibrium systems relies on the use of nonlinear media. ,,,, Such is the case, for example, of a semiconductor externally biased either electrically or optically, which produces a redistribution of the energy of electrons and holes in different quasi-Fermi levels described by qV e and qV h , where q and Δ V = V e – V h stand, respectively, for the electron charge and the potential difference. This can be modeled by introducing a nonzero chemical potential, μ F = q Δ V , so that the spectral energy density of nonequilibrium thermal radiation is given by − I NE ( ω , T , μ F ) = ω 2 π 2 c 3 ℏ ...…”

“…In this sense, it is possible to overcome such fundamental laws just by disregarding each of those constraints, namely, undertaking the near-field regime or breaking down the conditions of thermal equilibrium or the reciprocity . Yet, it is worth noticing that the most typical approaches to break down nonequilibrium, mainly based either on the use of nonlinear materials ,,,, or on dynamic (time-dependent) systems, ,,− can also be used to break down the reciprocity, , which reveals such a close relationship between the notions of equilibrium and reciprocity.…”

“… 247 , 447 In particular, a typical approach to deal with nonequilibrium systems relies on the use of nonlinear media. 74 , 220 , 367 , 448 , 449 Such is the case, for example, of a semiconductor externally biased either electrically or optically, which produces a redistribution of the energy of electrons and holes in different quasi-Fermi levels described by qV e and qV h , where q and Δ V = V e – V h stand, respectively, for the electron charge and the potential difference. This can be modeled by introducing a nonzero chemical potential, μ F = q Δ V , so that the spectral energy density of nonequilibrium thermal radiation is given by 450 − 452 This expression, valid provided that ℏω ± μ F > k B T , slightly deviates from Planck’s law on account of ℏω ± μ F (compare with eq 4 ) and provides with an extra degree of freedom for controlling the frequency distribution of thermal radiation.…”