1. Introduction

Cooling of solids by anti-Stokes fluorescence [1,2] has gathered great attention within the last decade. This is because cryogenic cooling is indispensable in many fields of science, e.g., to reduce the noise level of infrared and gamma-ray detectors [3,4]. In contrast to cryocoolers based on liquefied gases, anti-Stokes fluorescence cooling is intrinsically compact and vibration-free, which is relevant for example in space-borne applications [5]. The concept of anti-Stokes fluorescence cooling was introduced nearly 100 years ago: If the fluorescence photons have on average higher energy than the excitation photons, the fluorescence removes energy from the material, and hence reduces its temperature by annihilating phonons in each anti-Stokes cycle [6]. First cooling was demonstrated in an Yb³⁺-doped fluorozirconate glass in 1995 [7], and nowadays laser cooling to cryogenic temperatures, commonly defined to be below 123 K, is routinely achieved mainly using Yb³⁺-doped LiYF₄ (Yb:YLF) as the cooling medium [8–12]. In particular Yb-doped fluoride crystals and glasses have proven to be well-suited cooling materials mainly for two reasons: First, their low crystal field strength, resulting in a small Stark splitting of the energy multiplets, causes a strong overlap between emission and absorption spectra even at low temperatures. This enhances the absorption of photons with energies below the mean fluorescence energy. Second, the large energetic gap between the ground and excited state of Yb³⁺ suppresses non-radiative decay by multi-phonon relaxation, yielding high fluorescence quantum efficiencies close to unity. Meanwhile, several host crystals have been tested for laser cooling, including LiLuF₄ [8,13], KYF₄ [14], CaF₂ [15], SrF₂ [15] and BaY₂F₈ [16,17], but for most of them, except Yb:LiLuF₄, the cooling potential is not yet fully explored. Therefore, Yb:YLF is still a state-of-the-art material for laser cooling. The current record cooling temperature is 87 K [18,19], which is only 10 K above the boiling point of liquid nitrogen (LN) at 77 K.

Here, we investigate the potential of the cubic KY₃F₁₀ crystal doped with Yb³⁺ (Yb:KYF) as a laser cooling medium in comparison with Yb:YLF. We describe the Czochralski growth of Yb:KYF and Yb:YLF crystals and present temperature-dependent absorption and emission cross sections, as well as the temperature-dependent fluorescence lifetime of Yb:KYF. These data enable to compare Yb:KYF with Yb:YLF with respect to its potential for laser cooling. We find that Yb:KYF exhibits the potential for higher cooling efficiencies than Yb:YLF at temperatures below 200 K, and the laser cooling figure-of-merit for Yb:KYF becomes even eight times larger than that of Yb:YLF at 77 K. We demonstrate the first laser cooling of Yb:KYF and present the results of laser-induced thermal modulation spectroscopy (LITMoS) tests for a systematic comparison with Yb:YLF crystals. Our calculations predict that both Yb:KYF and Yb:YLF grown from raw materials of 99.99% – 99.999% (i.e., 4N – 5N) purity grade can be cooled down to ≈100 K, and even lower temperatures are achievable for Yb:KYF with only minor improvements of the crystal purity. Thus, we propose Yb:KYF as a promising laser cooling medium to reach the LN boiling point.

2. Crystal growth

We grew two Yb:KYF crystals by the Czochralski method. The raw materials were KF powder (Fox Chemicals GmbH) with 4N purity, YbF₃ powder (AC Materials, Inc.) with 5N purity, and two different YF₃ powders. For the first crystal (Yb:KYF-1) we used YF₃ (Alfa Aesar) with 4N purity, and for the second crystal (Yb:KYF-2) we used YF₃ (Projector GmbH) with 99.9995% (5N5) purity. In all growth experiments presented here, prior to the growth, the starting powders were fluorinated by purging them with a mixture of Ar and HF gas for 4 h at 800°C to reduce the amount of trace oxygen, oxyfluoride, and moisture [20]. Since KYF is congruently melting, both crystals were grown from a stoichiometric melt with a target Yb doping level of 3% corresponding to a composition of K(Y_0.97Yb_0.03)₃F₁₀. For Yb:KYF-1 we used a graphite crucible coated with pyrolytic carbon (SGL Carbon SE), while for Yb:KYF-2 a glassy carbon crucible (HTW Hochtemperatur-Werkstoffe GmbH) was used. Both crystals were seeded with an undoped KYF crystal and grown along the crystallographic [100]-direction in a growth atmosphere of Ar mixed with 5 vol.% CF₄ to prevent the formation of Yb²⁺ [21]. The size of both as-grown boules was 20  mm in diameter and ≈80 mm in length. The crystals contained light-scattering centers visualized by an irradiation of a HeNe laser, and their bottom part exhibited whitish inclusions. These are possibly due to residual oxides in the raw materials [22], in particular in the hygroscopic KF. The Yb doping level in the grown crystals was determined to be 2.7 ± 0.1% using an X-ray fluorescence (XRF) spectrometer (Bruker, M4 TORNADO). The inclusions in the bottom part did not show any detectable change in the X-ray fluorescence signal, so they could be composed of elements lighter than sodium, which is the lightest element detectable by the spectrometer, e.g. oxygen containing phases.

Besides the Yb:KYF crystals, we also grew three Yb:YLF crystals by the Czochralski method. These were grown from different raw materials of various purity. The first and second crystals (Yb:YLF-1 and Yb:YLF-2) were grown from identical raw materials, 4N purity LiF (Auer Remy GmbH) and 5N5 purity YF₃ (Projector GmbH). Yb:YLF-1 was grown from a pyrolytic-carbon-coated graphite crucible (SGL Carbon SE) along the [001]-direction. Instabilities during its growth process caused by dirt on the melt surface, considered to be organic residue, led to many small-angle grain boundaries as well as scattering centers. Yb:YLF-2 grown from a platinum crucible along the [110]-direction showed no scattering centers. The third crystal (Yb:YLF-3) was grown from LiF and YF₃ converted respectively from 5N purity Li₂CO₃ (Acros Organics B.V.B.A.) and Y₂O₃ (Lehmann & Voss & Co KG) by the fluorination using HF gas. It was grown from a platinum crucible and did not show any scattering centers. For all the Yb:YLF crystals, the powders were weighed for a target Yb doping level of 5%. To avoid the precipitation of YF₃ due to the peritectic reaction reported for melts containing more than 49 mol.% YF₃ [23], these crystals were grown from a non-stoichiometric composition with 2 mol.% excess of LiF. The Yb doping level in the grown crystals was determined to be between 4.5 and 4.8% by XRF spectroscopy.

The parameters and conditions of the growth of the Yb:KYF and Yb:YLF crystals are summarized in Tab. 1. We chose the lower doping level of 3% for Yb:KYF (4.7 × 10²⁰cm^-3) rather than 5% as in Yb:YLF (7.0 × 10²⁰cm⁻³) because we anticipated a stronger influence of fluorescence reabsorption in Yb:KYF than in Yb:YLF from the spectroscopic data in the literature [24]. Note that we used the identical YbF₃ (AC Materials, Inc., 5N purity) for all five crystals, so possible variations of the foreign rare-earth impurity level should arise from the purity of the YF₃ starting materials.

Table 1. Growth conditions and parameters of Yb:KYF and Yb:YLF crystals.

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3. Spectroscopic characterization of Yb:KYF

In contrast to the tetragonal YLF, KYF is a cubic crystal. It has been used successfully as a laser host material for trivalent rare-earth ions such as Pr³⁺ [25], Nd³⁺ [26,27], or Tm³⁺ [28]. KYF crystallizes in a superstructure of fluorite with eight formula units. The structure can be described as an undulating combination of [KY₃F₈]²⁺ and [KY₃F₁₂]^2- clusters [29]. In KYF, the coordination polyhedra of the Y³⁺-sites, substituted by rare-earth ions, are antiprisms with local symmetry axes parallel to the crystallographic <100>-axes. As a result, despite the cubic structure, rare-earth ions doped in KYF may differently interact with linearly polarized light depending on the symmetry axes of the substitution sites. This causes polarization effects in the fluorescence spectrum of Pr:KYF [30], but we did not observe this effect in a < 100>-cut Yb:KYF crystal. The maximum phonon energy of 495 cm⁻¹ of KYF [31] is slightly higher than that of YLF (450 cm^-1 [32]), but still sufficiently low to fully inhibit multi-phonon relaxation bridging the ≈10,000 cm^-1 energy gap between the excited and the ground states of Yb³⁺. KYF may also be a useful crystalline host for laser cooling based on Tm³⁺ or Ho³⁺, in which the energetic position of the first excited states are lower than in Yb³⁺, according to the internal quantum efficiency criterion for laser cooling (the energy separation between the ground- and first excited-states should be more than eight times larger than the maximum phonon energy) [33].

Similar to the spectroscopy of Yb:YLF described in [34], we performed temperature-dependent transmission and fluorescence spectroscopy as well as fluorescence lifetime measurements for Yb:KYF. We investigated our samples prepared from the crystal Yb:KYF-1 in a temperature range between 15 K and 300 K using a closed-cycle helium cryostat. We used a high-resolution monochromator (HORIBA, M1000) with a photomultiplier tube (Hamamatsu, R5108) as a detector. For transmission spectroscopy, a tungsten-halogen lamp was utilized as a broadband light source. To avoid reabsorption effects affecting the detected fluorescence spectral shape, a 200 µm thin sample was used in the corresponding experiments. Figure 1(a) shows the absorption and emission cross section spectra of Yb:KYF at room temperature. The measured fluorescence intensity spectra were corrected for the sensitivity of the measurement setup. The emission cross section spectrum was calculated by the Füchtbauer-Ladenburg formula [35] using the experimentally determined radiative lifetime of 1.86 ms described below. The absorption cross section spectrum was calculated from the transmission spectrum by the Beer-Lambert law using the Yb concentration determined by XRF spectroscopy, and also calculated via the reciprocity relation [36] from the emission cross section spectrum. The agreement of the two absorption cross section spectra shown in Fig. 1(a) evidences that due to the use of a thin sample the measured fluorescence spectrum was unaffected by reabsorption, despite the large overlap of the absorption and emission spectra at room temperature. To resolve all features of the absorption spectrum at 15 K, the 200 µm thin sample was used for wavelengths above 960 nm and a thick sample of 12 mm was used to resolve the significantly weaker features at shorter wavelengths.

 

Fig. 1. (a) Absorption and emission cross section spectra of Yb:KYF at room temperature. The emission cross sections were calculated by the Füchtbauer-Ladenburg (F-L) formula. The absorption cross sections were obtained from the transmission spectrum with the Yb concentration determined by XRF spectroscopy and in addition calculated using the reciprocity relation from the emission cross section spectrum with a radiative lifetime of 1.86 ms (presented below). (b) Absorption coefficients and fluorescence spectra at 15 K. The assigned resonant transitions between Stark levels are marked by *. The other peaks are considered to be phonon replicas [24]. To resolve the weak features in the short (< 960 nm) wavelength part of the absorption, a different, 12 mm thick sample was used for this range. For better visibility, the y-axis is enhanced by a factor of 25 in this range. The fluorescence spectra were recorded with the same sample (200 µm) throughout the whole range, but for better visibility, the y-axis is enhanced by a factor of three for wavelengths > 980 nm.

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From the spectra shown in Fig. 1(b) we determined the energetic positions of the ground- and excited-state Stark levels of Yb³⁺ in KYF. Figure 2(a) shows the resulting Stark energy level diagram. Our spectra are in good agreement with previous data [24,37] which, however, differently determined the position of the levels E4 and E7. We assign the peak around 1028  nm in Fig. 1(b) to the transition E5→E4 in agreement with [24]. This is consistent with the temperature-dependent emission cross sections presented below [cf. Figure 4(a)]. Among the three main absorption peaks at wavelengths shorter than 960 nm, the peak at 945.1 nm is assigned to the transition E1→E7 owing to its narrowest feature. Figure 2(b) shows the fractional occupancy of each Stark level calculated by the Boltzmann distribution function using the determined energetic position for a temperature range of 0–300 K. These graphs also show that the actual assignment of E4 and E7 has little influence on the partition functions required in the reciprocity method.

 

Fig. 2. (a) Energy diagram of Yb³⁺ in KY₃F₁₀ with the Stark level positions and corresponding wavelengths of the resonant absorption and emission transitions. (b) Fractional occupancy of the ground-state (²F_7/2) and excited-state (²F_5/2) Stark levels as a function of temperature according to the Boltzmann distribution.

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For a precise determination of the temperature-dependent emission cross sections, the knowledge of the temperature-dependent radiative lifetime is essential. To this end, we measured the fluorescence decay of a sample prepared from the crystal Yb:KYF-1 at various temperatures. To minimize the influence of radiation trapping on the measured fluorescence lifetime, the pinhole method [38] was applied for room temperature measurements where pinholes of different diameters are placed in front of the sample to vary the excited volume. Figure 3(a) shows the measured fluorescence lifetimes with respect to the pinhole diameter. A linear extrapolation to a 0-mm pinhole diameter yields the intrinsic fluorescence lifetime, free of radiation trapping, to be τ_rad = 1.86 ± 0.07 ms. This agrees with the previously reported value of 1.77 ms for Yb(0.5%):KYF [39] and the value of 1.87 ms proposed in [40]. For lower temperatures, we used the ≈200 µm thin sample which had been proven to effectively suppress reabsorption in the fluorescence measurements as illustrated in Fig. 1(a). Figure 3(b) shows the fluorescence lifetime of Yb:KYF versus temperature. The result of the pinhole method indicated as a red square symbol agrees with the value obtained with the thin sample (blue circles). Considering the decreasing influence of reabsorption with decreasing temperature, this indicates a successful suppression of radiation trapping in all temperature-dependent fluorescence lifetime measurements performed without using the pinhole method. We observed an increase of the fluorescence lifetime up to 3.2  ms with decreased temperatures down to 15 K. For Yb³⁺ ions in the trigonal host KYF₄, a similar trend was observed and attributed to a temperature-dependent energy transfer from Yb³⁺ to Er³⁺ and Ho³⁺ impurities which quench the lifetime of Yb³⁺ [41]. Such effect would be extremely detrimental for laser cooling. In contrast, we previously attributed the strong temperature dependence of the radiative lifetime to the population distribution of excited Yb³⁺ in the three upper Stark levels having individual radiative lifetimes in Yb:YLF [34]. A corresponding fit considering the fractional occupancies of the levels E5, E6, and E7 as seen in Fig. 2(b) yields individual lifetimes for the lower two Stark levels of the upper ²F_5/2 manifold of the Yb³⁺ ion (E5 and E6) of τ_E5 = 3.2 ms and τ_E6 = 1.1 ms. The small fractional occupancy of the highest level E7 leads to a significant fit-error for τ_E7 which is thus roughly estimated to be longer than 4  ms; a more accurate determination would require further measurements at elevated temperatures.

 

Fig. 3. (a) Fluorescence decay time of Yb(3%):KYF measured with a variety of pinhole diameters. (b) Temperature-dependent fluorescence lifetimes. The measured values are shown as blue circles. The value at room temperature determined by the pinhole method is shown as a red square. The dashed line is the result of a fitting with the equation shown in the graph, yielding the individual lifetimes of the upper Stark levels denoted in the graph, too.

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With these lifetime data, we were able to determine the temperature-dependent cross sections of Yb:KYF as shown in Fig. 4. The emission cross section spectra in Fig. 4(a) were calculated by the Füchtbauer-Ladenburg formula. Figure 4(b) shows the temperature-dependent absorption cross sections and absorption coefficients.

 

Fig. 4. (a) Emission cross section spectra of Yb:KYF at various temperatures. Resonant transitions between Stark levels are labeled. (b) Temperature-dependent absorption spectra of Yb:KYF for wavelengths longer than 980 nm. The colored lines were derived from the measured transmission spectra, and the black dashed lines were calculated from the emission cross section spectra using the reciprocity relation.

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Even using an Yb:KYF sample as thick as 14.3 mm, we were not able to reliably measure absorption coefficients below values of 10⁻² cm⁻¹. To get access to the precise absorption in spectral regions with lower absorption coefficients, we calculated the absorption coefficients from the absorption cross sections derived using the reciprocity relation and the Yb³⁺ density (n_Yb = 4.7·10²⁰ cm³). In this way, we retrieved even two orders of magnitude lower absorption coefficients down to ≈10⁻⁴ cm⁻¹. The good agreement with the measured absorption coefficients for values above 10⁻² cm^-1 confirms the reliability of this method. Thus, the absorption coefficients retrieved from the emission measurements were used for the calculations in the following Sections 4 and 5.

4. Laser cooling potential of Yb:KYF

The laser cooling efficiency by anti-Stokes fluorescence at a temperature T [42] is given as

Here I_f(λ,T) is the fluorescence intensity at a wavelength λ and a temperature T. From Eq. (1), one can immediately see that the excitation wavelength λ_ex has to be longer than the mean fluorescence wavelength λ_f to enable cooling, but with increasing excitation wavelength α_r decreases strongly [cf. Figure 4(b)] and the influence of background absorption becomes significant. Hence, there is an optimum wavelength maximizing η_c. Note that the fluorescence intensity spectrum I_f only considers emitted photons leaving the laser cooling medium. However, in Yb³⁺-doped gain media, a part of the emitted fluorescence is reabsorbed. Thus, the measured mean fluorescence wavelength λ_f is red-shifted from the intrinsic value λ_f0 calculated from the reabsorption-free fluorescence spectra. Consequently, the actual values of λ_f depend on the geometry of the cooling medium as well as of the excitation. Therefore, to discuss the intrinsic potential of Yb:KYF as a laser cooling medium, all the following calculations are based on λ_f0. Figure 5(a) shows the temperature dependence of the intrinsic mean fluorescence wavelength λ_f0 for Yb:KYF. For comparison, the values for Yb:YLF [34] are also plotted.

 

Fig. 5. (a) Intrinsic mean fluorescence wavelength of Yb:KYF and Yb:YLF versus temperature. The values for Yb:YLF are from [34]. (b) Material figure-of-merit for laser cooling F_cool of Yb:KYF for excitation transitions E3→E5 and E4→E5 compared with Yb:YLF (for π-polarized excitation) at the excitation wavelength indicated in brackets versus temperature. Note that the excitation transition E3→E4 will lead to negative values for Yb:YLF, as the corresponding excitation wavelength of 995.1 nm is shorter than the mean fluorescence wavelength at room temperature of 995.8 nm.

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For all Yb³⁺-doped materials, the mean fluorescence wavelength undergoes a red-shift towards lower temperatures, as the transitions from the upper Stark levels E6 and E7 gradually vanish owing to their decreasing fractional occupancies as seen in Fig. 2(b). At all temperatures, the intrinsic mean fluorescence wavelength λ_f0 of Yb:KYF is about 10 nm shorter than that of Yb:YLF, even though the barycenters of both lower and upper Stark manifolds differ only by ≈10  cm^-1 between the two crystals [24]. This is because, as seen in Fig. 4(a), for Yb:KYF the highest energy emission transitions terminating at E1 are stronger than those terminating in the other lower Stark levels. In contrast, for Yb:YLF the strongest emission transitions are E5→E2 and E5→E3 [34]. The higher radiative decay rate from the level E6 than from E5, evidenced by their individual radiative lifetimes (τ_E5 = 3.2 ms, τ_E6 = 1.1 ms), also contributes to the shorter mean fluorescence wavelength compared with Yb:YLF.

To quantify the suitability of a given material for laser cooling based on its spectroscopic properties, we introduce a material figure-of-merit F_cool, extended from the one introduced by Bowman [43] to consider the dependency on the excitation wavelength and temperature, as follows:

5. LITMoS test: laser cooling characterization of Yb:KYF

F_cool indicates the general suitability of an idealized sample of a material to be cooled by anti-Stokes fluorescence. Nevertheless, the actual laser cooling performance of a given sample depends on the purity of the material. For laser cooling using rare-earth-doped solids, foreign rare-earth ions [44,45] and transition-metal ions [46,47] have been identified to be the main detrimental impurities. Foreign rare-earth ions can deexcite neighboring laser-cooling ions by energy transfer, which reduces the quantum efficiency and causes parasitic heating by non-radiative processes. Transition-metal ions have been considered the primary cause of background absorption [46]. In addition, oxides and hydroxides in fluoride crystals are also detrimental, because these impurities create high-energy phonon modes and cause multi-phonon relaxation [47]. The LITMoS test [12] is a useful method to reveal the quality of a specific laser cooling medium. It is used to quantify the values of η_ext and α_b from Eq. (1) which are sample-specific and reduce the maximum cooling efficiency from its ideal cooling efficiency.

Due to the difficulties in the accurate determination of the actual mean fluorescence wavelength λ_f mentioned above we propose to instead use the intrinsic mean fluorescence wavelength λ_f0 and to modify Eq. (1) as follows:

We performed LITMoS tests for our crystals to evaluate their sample-specific parameters η_ext/β and α_b. To this end, we prepared a cuboid-shaped sample from each of the two Yb:KYF and three Yb:YLF crystals. All six facets were polished to optical grade. The dimensions of the samples are summarized in Tab. 2. The crystallographic c-axis of the uniaxial Yb:YLF crystals was oriented perpendicular to the laser direction, yielding π-polarized excitation for all samples. A schematic of the LITMoS setup is shown in Fig. 6. The sample is placed on two optical glass fibers of 125  µm in diameter suspended over a copper block in a vacuum chamber to minimize the conductive heat from the supports. The chamber is evacuated to below 10⁻⁶ mbar by a turbo-molecular pump to reduce the convective heat exchange with the surroundings. A thin-disk laser based on Yb:Lu₃Al₅O₁₂ as the active medium is used as an excitation source. The laser is tunable between 990 nm and 1084 nm and excited the sample through an anti-reflection-coated glass window with a maximum incident power of 4 W at 1030 nm. The laser-induced temperature modulation ΔT was detected by a thermal camera (FLIR, SC645), and the power absorbed by the sample P_abs was determined using two thermal power meters (Ophir, 10A). In thermal equilibrium, we can assume the cooling efficiency η_c to be proportional to the induced temperature change per absorbed power ΔT·P_abs⁻¹. This proportionality was experimentally verified in our setup for ΔT up to, at least, ± 25 K around room temperature.

 

Fig. 6. Schematic of the LITMoS setup for (a) single-beam-pass and (b) triple-beam-pass configuration.

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Table 2. LITMoS test results and calculated global MAT with corresponding excitation wavelength.

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Both Yb:KYF samples showed cooling in the LITMoS tests. The maximum temperature decrease was 2.5 K at λ_ex = 1016.9 nm with an absorbed power of 470 mW for Yb:KYF-1 and 2.7 K at λ_ex = 1018.2 nm with an absorbed power of 230 mW for Yb:KYF-2. Figure 7(a) shows ΔT·P_abs⁻¹ versus the excitation wavelength, hereafter simply named LITMoS result, for both Yb:KYF samples obtained in the single-beam-pass configuration shown in Fig. 6(a). Each LITMoS result exhibits two zero-crossing wavelengths λ_X1 and λ_X2 (λ_X1 < λ_X2) at which neither heating nor cooling is observed. The shorter zero-crossing wavelength λ_X1 is mainly influenced by η_ext/β, since the resonant absorption coefficient α_r in this wavelength range is by orders of magnitude higher than the background absorption coefficient α_b, thus α_r(λ_X1)/[α_r(λ_X1) + α_b] ≈ 1 in Eq. (4). On the other hand, the longer zero-crossing wavelength λ_X2 is sensitive to α_b, since the parasitic heating by impurities balances with the low cooling power due to low Yb³⁺ absorption at this wavelength. For the results shown in Fig. 7 (a), the least mean square fittings with Eq. (4) to the LITMoS results were not precise with respect to the parameter α_b. This is caused by the uncertainty in the precise determination of the longer zero-crossing wavelength λ_X2 resulting from the small absorbed power P_abs and hence the small temperature change at long excitation wavelengths. To refine λ_X2, we thus modified the setup to the triple-beam-pass configuration shown in Fig. 6(b) to increase P_abs and ΔT. In this way, we determined the long-wavelength zero-crossing wavelengths λ_X2 to be 1058.3 nm and 1066.5 nm for Yb:KYF-1 and Yb:KYF-2 and accordingly retrieved the background absorption coefficients to be (1.2 ± 0.3)·10⁻⁴ cm^-1 and (0.7 ± 0.3)·10⁻⁴ cm⁻¹, respectively. The best-fitting results, shown as the blue solid lines in Fig. 7(a), correspond to the values of η_ext/β and α_b denoted in the figure.

 

Fig. 7. (a) LITMoS test results of Yb:KYF-1 and Yb:KYF-2. The blue solid lines show the best fits using Eq. (1). (b) Temperature-dependent cooling efficiency of Yb:KYF-2 with an estimated global minimal achievable temperature (MAT) of 105 K at an excitation wavelength of 1013 nm. The excitation wavelength of 1007 nm maximizing F_cool for the ideal case is shown as the grey dashed vertical line corresponding to the transition E3→E5.

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Table 2 summarizes the LITMoS results for all five Yb:YLF and Yb:KYF samples. The sample-specific external quantum efficiency η_ext/β for Yb:KYF-2 is lower than for Yb:YLF-2, even though identical YF₃ and YbF₃ starting materials were used for these crystals. There are three explanations for this result:

Despite using identical starting materials for Yb:YLF-1 and Yb:YLF-2, the background absorption coefficient α_b in Yb:YLF-1 is more than six times larger than in Yb:YLF-2. This can be due to transition-metal impurities introduced by the graphite crucible used for the growth of Yb:YLF-1 with the possible insufficient pre-cleaning process, as a platinum crucible pre-cleaned by HCl was used to grow Yb:YLF-2. The difference in the LITMoS results between Yb:YLF-2 and Yb:YLF-3 is attributed to the different LiF and YF₃ starting materials (see Tab. 1). Interestingly, the background absorption in Yb:KYF is lower than in Yb:YLF. Yb:KYF-1 exhibits a background absorption coefficient comparable with Yb:YLF-2 and -3, although the nominal purity of the used YF₃ is lower for Yb:KYF-1 (cf. Table 1). The background absorption α_b of Yb:KYF-2 below 10⁻⁴ cm⁻¹ is among the lowest ever reported for Yb³⁺-doped fluoride crystals. Even though further investigations on the reason for this observation are needed, our experimental results show the advantage of Yb:KYF to achieve lower background absorption compared with Yb:YLF.

For each sample, we calculated the cooling efficiency as a function of excitation wavelength and temperature using Eq. (4) based on the temperature-dependent spectroscopic data and the parameters η_ext/β and α_b listed in Tab. 2. Figure 7(b) shows the result for Yb:KYF-2 calculated with the sample-specific parameters denoted in the figure. This model calculation reveals minimum achievable temperatures (MATs), defined as the lowest temperature at which the cooling efficiency is still positive, at a given excitation wavelength λ_ex. The global MAT, the lowest MAT, of each sample with the corresponding excitation wavelength is also listed in Tab. 2. Note that this calculation does not consider the temperature dependency in η_ext/β and α_b. While the reabsorption eventually vanishes for Yb:YLF at lower temperatures [34], Yb:KYF still shows an overlap of its absorption and emission spectra even at 15 K [cf. Figure 1(b)] and thus reabsorption. Consequently, the temperature dependency in β is expected to be smaller in Yb:KYF than in Yb:YLF. Note that the background absorption α_b can also decrease by an order of magnitude in Yb:YLF when cooled from 300 K to 100 K [19]. Therefore, the actual MATs are expected to be lower than the calculated values. Nevertheless, this simplified estimation is still useful to discuss the potential of materials for all-solid-state optical cryocoolers.

From Tab. 2 it is evident that the calculated wavelengths required to reach the global MAT in Yb:KYF-1 and Yb:KYF-2 are longer than the excitation wavelength of 1007 nm at which F_cool is maximized. However, for Yb:KYF-2 even a minor increase of η_ext/β by only 0.2% shifts the optimum excitation wavelength from 1013 nm to 1007 nm with a reduced global MAT of 92 K. Such small changes may not even require improved crystal quality, but could e.g. be achieved by reducing the crystal dimensions and thus β. In contrast, for all three Yb:YLF samples the global MAT was found at 1019 nm regardless of their η_ext/β and α_b, and the effect of improving η_ext/β was found to be much less pronounced.

6. Conclusion

We presented a detailed characterization of Yb:KYF and Yb:YLF crystals with respect to their potential for laser cooling by anti-Stokes fluorescence. For the first time, we experimentally demonstrate laser cooling in the cubic fluoride crystal Yb:KYF. Our temperature-dependent spectroscopic investigations revealed the cooling potential of Yb:KYF to be even higher than Yb:YLF at temperatures below 200 K. Even though the excitation transition from the uppermost ground-state Stark level E4 is known to be best-suited for cryogenic cooling in Yb:YLF, Yb:KYF shows its optimum excitation from the second-highest Stark level E3 owing to its mean fluorescence wavelength still shorter than the corresponding excitation wavelength. This feature allows the eight times larger maximum of figure-of-merit F_cool of Yb:KYF than Yb:YLF at the boiling point of LN. Therefore, Yb:KYF has the potential to reach temperatures lower than those achieved by the state-of-the-art material Yb:YLF (<87 K) [18,19]. The Czochralski-grown Yb(3%):KYF crystals yielded sample-specific values η_ext/β of up to 98.6% which are only slightly below the values observed in our Yb:YLF samples and partly caused by the larger red-shift of mean fluorescence wavelength β by reabsorption in Yb:KYF. Our growth and LITMoS results indicate that Yb:KYF exhibits lower background absorption than Yb:YLF even though a comparable amount of transition-metal impurities is expected in the raw materials. The obtained background absorption coefficient as low as (0.7 ± 0.3)·10⁻⁴ cm⁻¹ is the lowest ever reported for Yb³⁺-doped fluoride crystals. Note that imperfections of the grown Yb:KYF crystals attributed to the strong hygroscopicity of KF as well as the limited purity (4N) of the used KF powder leave room for further improvement. From the LITMoS test results of our Yb(3%):KYF and Yb(5%):YLF grown using the identical 5N YF₃ and YbF₃ starting materials (Yb:KYF-2 and Yb:YLF-2), we estimated their global MATs to be ≈100 K for both samples. Even a minor increase in η_ext/β, e.g., by improving the sample geometry to mitigate reabsorption, can significantly reduce the global MAT of Yb:KYF. We thus conclude that Yb:KYF crystals have the potential to exceed Yb:YLF in regards to laser cooling and to be used in all-solid-state optical cryocoolers to replace LN cryostats in various applications.