Precise determination of minimum achievable temperature for solid-state optical refrigeration
Highlights
► Laser cooling model for optical refrigeration is reviewed in this article. ► Importance of crystalline host for cryogenic operation is explained and verified. ► Novel differential spectroscopy is used for sensitive temperature measurements. ► Minimum achievable temperature of 110 K in Yb:YLF is measured at E4–E5 transition. ► Measurements and model predictions are in excellent agreement.
Introduction
The physical principle of optical refrigeration is based on a phonon-assisted anti-Stokes fluorescence. Spectrally narrow-band low-energy excitation photons produce energetically upshifted incoherent fluorescence emission, extracting heat away from the lattice in the process and resulting in cooling of the latter [1]. Optical refrigeration was first postulated by Pringsheim in 1929 [2], put on a solid thermodynamic footing by Landau in 1946 [3] and finally demonstrated in solids by Epstein and co-workers in 1995 [4]. First observation consisted of bulk cooling of an ytterbium-doped fluorozirconate glass (Yb:ZBLAN) by 0.3 K, starting from the room temperature. Cooling of this material system has progressed over the years and culminated with demonstration of cooling to 208 K by Thiede et al. in 2005 [5]. In parallel with these results, other trivalent ions of Tm and Er were cooled on various transitions and in a wide variety of hosts (see Refs. [6], [7] for recent reviews of this field). Interesting applications of optical refrigeration have also been proposed, including solid-state cryogenic refrigerators [8], [9], [1] and radiationally-balanced lasers [10]. Advancing toward realization of the former, laser cooling to 155 K (from room temperature) was recently demonstrated [11], followed by cooling a semiconductor payload to 165 K [12], utilizing 5 mol% ytterbium doped yttrium lithium fluoride crystal (Yb:YLF). These bulk cooling results provided the proof-of-principle demonstration of operation of all solid-state optical refrigerator at temperatures below what conventional Peltier devices can achieve.
In this paper we discuss rate-equation based cooling efficiency model [13], [6] along with the predictions of minimum achievable temperature (MAT) of 110 K at 1020 nm [11], corresponding to E4–E5 Stark manifold transition in Yb:YLF. In order to make these predictions, model is supplemented with experimentally determined quantities, details of which are discussed below. To verify these model predictions, we developed a highly sensitive differential spectroscopic technique that allows us to fully characterize cooling sample performance. Below we discuss several implementations and details of this technique along with recent results on Yb:YLF verifying MAT of 110±5 K at 1020 nm, in excellent agreement with the model.
Section snippets
Model
The cooling efficiency is defined as the ratio of the cooling power (Pcool) to the absorbed laser power (Pabs), is given by [13]where λf(T) is a temperature-dependent external mean fluorescence wavelength (i.e. including fluorescence trapping and reabsorption). The term p(λ,T) is a probability of the conversion of a low-energy excitation photon into an escaped fluorescence photon:where ηext is the external quantum efficiency (EQE)
Experimental results and discussion
Before we discuss direct measurements of MAT(λ), we point out that predictive capabilities of the cooling efficiency model (Eq. (1)) can be gained only if its individual components are well characterized, namely: ηext, αb, α(λ,T) and λf(T).
Conclusions
Using temperature-dependent spectroscopic data, we constructed accurate two-dimensional maps of the cooling efficiency ηc(λ,T) of Yb-doped YLF and ZBLAN using standard cooling model. From this, we predicted minimum achievable temperature (MAT) of current Yb:YLF crystals at 110 K and typical Yb:ZBLAN samples around 190 K. We presented highly-sensitive differential spectrum metrology technique, which enables us to verify the cooling efficiency spectra to high accuracy. Most importantly, these
Acknowledgments
We wish to acknowledge useful discussions with Dr. Markus Hehlen. We also thank Mr. Chengao Wang for GaAs sample preparation and Dr. Michael Hasselbeck for his assistance with LabView software. This work was supported by an AFOSR Multi-University Research Initiative Grant no. FA9550-04-1-0356 entitled Consortium for Laser Cooling in Solids, and a DARPA seedling grant. Research in part was performed while DVS held a National Research Council Research Associateship Award at Air Force Research
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