Laser cooling of ytterbium-doped silica glass

Laser cooling of a solid is achieved when a coherent laser illuminates the material in the red tail of its absorption spectrum, and the heat is carried out by anti-Stokes fluorescence of the blue-shifted photons. Solid-state laser cooling has been successfully demonstrated in several materials, including rare-earth-doped crystals and glasses. Here we show the net cooling of high-purity Yb-doped silica glass samples that are fabricated with low impurities to reduce their parasitic background loss for fiber laser applications. The non-radiative decay rate of the excited state in Yb ions is very small in these glasses due to the low level of impurities, resulting in near-unity quantum efficiency. We report the measurement of the cooling efficiency as a function of the laser wavelength, from which the quantum efficiency of the Yb-doped silica is calculated. Laser cooling of rare-earth-doped silica may provide a route to vibration-free refrigeration of integrated photonic circuits and quantum sensors to reduce the thermal noise. Here, cooling of high-purity Yb-doped silica to 0.7 K below ambient temperature is demonstrated using sub-optimal laser parameters, and in spite of a substantial extra thermal load.

I n solid-state laser cooling, anti-Stokes fluorescence removes heat from the material, resulting in net refrigeration. Pringsheim 1 first proposed anti-Stokes fluorescence cooling in 1929 and Epstein et al. 2 reported the first experimental confirmation of solid-state laser cooling in Yb-doped ZBLANP (ZrF 4 -BaF 2 -LaF 3 -AlF 3 -NaF-PbF 2 ) in 1995. Multiple experiments have since confirmed solid-state laser cooling; they have focused on two broad classes of solids: rare-earth-doped (REdoped) crystals and glasses, and semiconductors. Laser cooling of RE-doped crystals has been the most successful so far [3][4][5] ; the record cooling to 91 K of a 10 mol% Yb-doped YLiF 4 (Yb:YLF) crystal was reported at the University of New Mexico in 2016 (ref. 6 ). The only reported laser cooling of semiconductors is that of a CdS nanobelt in 2013 (ref. 7 ), but the validity of their results has been questioned recently 8 . Several RE-doped glasses have been successfully cooled [9][10][11][12][13][14][15] since the first experimental report by Epstein et al. 2 . However, attempts to cool silica glass, which is arguably the most versatile optical material, have been unsuccessful 16,17 until very recently 18,19 . Here, we report laser cooling of Yb-doped silica glass.
The perennial failure in the laser cooling of RE-doped silica glass made one wonder whether it would ever be possible for the Yb-doped silica glass to have a sufficiently small non-radiative decay rate of the Yb excited-state population to achieve a nearunity internal quantum efficiency. This was examined recently in a spectroscopic study of the Yb-doped silica glass and by looking into the potential decay channels of the Yb excited-state population; it was concluded that there is no a priori reason to reject the possibility of laser cooling for the high-purity Yb-doped silica glass 16 . The background absorption of 5-15 dB km −1 is commonly achieved in high-purity Yb-doped silica glass used in fiber lasers and amplifiers 17 and is small enough not to be an obstacle to laser cooling. However, it was predicted that for adequate laser cooling, the glass host must be co-doped with modifiers such as Al to mitigate the quenching-induced non-radiative decay for sufficiently high concentrations of Yb ions in silica glass 20,21 .
Advancements in solid-state laser cooling may eventually lead to all-optical compact and vibration-free cryocoolers that can reduce the thermal noise in semiconductor-based single-photon detectors or quantum information processing circuits 5 . Another important application is for radiation-balanced fiber lasers (RBFLs), where the cooling from anti-Stokes fluorescence offsets the waste heat generation in the laser [22][23][24][25][26][27] . RE-doped crystals like Yb:YLF have proven to be the best materials of choice for laser cooling because they have a small inhomogeneous broadening of the absorption lines and a high ion solubility that leads to a higher cooling efficiency 3,5 . RE-doped ZBLAN glass is another successful cooling-grade material, but its low mechanical and chemical stability limits its application for integrated photonics or RBFLs. On the other hand, Yb-doped silica glass is the material of choice for fiber lasers and is commonly used as the substrate in silicon photonics [28][29][30][31] . Therefore, potential applications, especially for RBFLs in the near-term and photonic-device cooling in the long-run, are strong motivations for the laser cooling of REdoped silica glass beside the scientific curiosity.
The primary focus of this paper is to investigate the laser cooling of Yb-doped silica glass. In particular, we will determine the wavelength dependence of the cooling efficiency of our Ybdoped silica glass samples as a function of the pump laser wavelength to observe their transition from the heating to cooling regime.

Results
Determination of the cooling efficiency. The cooling efficiency, η c , is defined as the net power density (per unit volume) extracted from the material (p net ) per unit total absorbed power density (p abs ): η c = net /p abs . The cooling efficiency can be expressed as 5,32 (see Supplementary Note 1 for the derivation) where λ f is the mean wavelength of the escaped fluorescence, λ p is the laser pump wavelength, η ext is the external quantum efficiency, and η abs is the absorption efficiency; they are defined as where W r , W nr , and W tot are radiative, non-radiative, and total decay rates of the excited state, respectively, and η e is the fluorescence extraction efficiency. α b is the background absorption coefficient and α r is the resonant absorption coefficient. In practice, both η ext and η abs must be very close to unity to observe laser cooling, because λ p cannot be much longer than λ f to keep α r (λ p ) sufficiently large for a near-unity value of η abs . It was recently shown by Mobini et al. 16 that it is possible for the Yb excited-state population to have a small non-radiative decay rate in a silica glass host, i.e. W nr ≪ W r ; therefore, the external quantum efficiency can be near unity. To revisit the arguments presented by Mobini et al. 16 , note that the nonradiative decay rate, W nr , can be divided into two separate parts: the multiphonon decay rate (W mp ) and the sum of other nonradiative decay rates (W i ) for those channels that are related to the concentration quenching effect, i.e., W nr = W mp + Σ i W i 16,33 . Using the energy-gap law, we showed that the multiphonon decay rate of silica glass is W silica mp % 10 À8 s À1 , while that of ZBLAN is W ZBLAN mp % 10 À4 s À1 ; therefore, as far as the multiphoton nonradiative decay rate is concerned, Yb-doped silica glass is a better material than ZBLAN for optical refrigeration 16 . Additional information is provided in Supplementary Note 2.
The non-radiative decay channels related to the concentration quenching are mainly due to the dipole-dipole interactions between Yb ions and impurities, which include OH − , transition metals, and undesirable RE ions, as well as Yb-Yb interactions in Yb ion clusters. Developing a high-purity Yb-doped silica glass is therefore required to avoid the interactions between the Yb ions and impurities 16 . Additionally, to ensure that Yb ion clustering is suppressed and to further mitigate Yb-impurity interactions, it is imperative for the Yb ion density to remain below the critical ion concentration 33 . It is known that the ion solubility of the silica glass is quite low, i.e., for pure silica glass the critical quenching concentration is N c ≈ 10 25 m −3 or lower 34 . However, by using modifiers such as Al and P, the quenching concentration of silica glass can be increased by an order of magnitude 20,21 . To prevent concentration quenching and achieve η ext ≈ 1, it is necessary to keep the Yb ion density below N c . Quite possibly, this issue has been one of the main reasons behind the previously failed attempts in laser cooling of the Yb-doped silica glass 17 . The Yb-doped silica glass samples that are studied in this paper are all high-purity and are doped with modifiers to increase the Yb ion solubility 35 . The parasitic background absorption (α b ) in these glasses is sufficiently low to ensure that η abs ≈ 1, as is required to achieve laser cooling.
For the laser cooling experiments, we used three different samples of Yb-doped silica glass optical fiber preforms (see "Methods"). We refer to these preforms as sample A, sample B, and sample C, respectively. These preforms are Yb-doped only in the core and their characteristics are listed in Table 1.
The background absorption coefficients were measured for large mode-area fibers drawn from the respective preform samples by means of the well known cut-back technique.
To investigate laser cooling and obtain the cooling efficiency, η c , of the Yb-doped silica glass preforms as a function of the laser pump wavelength, we perform the laser-induced thermal modulation spectroscopy (LITMoS) test on all three samples 5,36 (see Supplementary Notes 3 and 4 for additional information). The LITMoS test setup is shown in Fig. 1. The samples are held by a set of silica fibers inside a vacuum chamber with the pressure of 10 −6 Torr to minimize the conductive and convective heatloads on the samples, so the black body radiation remains the only source of heating from the environment. The samples are pumped by a wavelength-tunable continuous wave (CW) Ti-Sapphire laser (980 nm < λ p < 1070 nm) and the laser light passes through each sample twice using an external mirror.
The spectral features of the samples are captured by a spectrometer through a thermally transparent KCl salt window mounted in the chamber. Similarly, the thermal images are recorded by a thermal camera through the KCl salt window and the images are post-processed to determine the changes in the sample temperatures. To calculate the mean fluorescence wavelength, the samples are initially pumped at λ p = 1030 nm. The fluorescence emission then is captured with an optical spectrum analyzer. The calculated mean fluorescence wavelengths of the samples A, B, and C are found to be λ A f = 1010 nm, λ B f = 1008 nm, and λ C f = 1008 nm, respectively 16   In each subfigure corresponding to the particular sample A, B, or C, the pump laser wavelength is gradually increased; once it becomes longer than approximately the mean fluorescence wavelength, the anti-Stokes fluorescence begins to extract heat from the sample until the cooling efficiency becomes positive, indicating the net laser cooling. As can be seen in Fig. 2, all three samples have been laser cooled. By fitting Eq. (1) to the experimental results and using the values of α b reported in Table 1, we can find the external quantum efficiency, η ext , of the samples, which are summarized in Table 2. Note that the blue lines in Fig. 2 are the results of the one-parameter fitting-we could have used the fitting procedure to determine the values of α b as well. However, the lack of experimental data for η c at wavelengths above 1070 nm results in large uncertainties in α b ; therefore, we have chosen to use the directly measured values in The Yb2O3 concentration is measured via electron probe micro-analysis. The Yb density is calculated from the measured Yb2O3 concentration. The given error for the Yb2O3 concentration is related to the uncertainty of the used method in this concentration range. OH − concentration and parasitic background absorption (αb) are measured by cut-back method, for which the errors represent the repeatability of the measurement setup.   Table 1, which appear to conform well to our measurements. We note that α b in Table 1 is measured at 1200 nm wavelength to ensure that the resonant absorption is very small; as such, we are implicitly assuming that α b does not change significantly down tõ 1035 nm wavelength.
Power cooling experiment. The results of the LITMoS tests prove laser cooling in all the Yb-doped silica glass preforms. However, because in the LITMoS test setup, the maximum power of our Ti:Sapphire laser in the cooling wavelength range is less than 900 mW, the signal-to-noise ratio, as can be seen from the error-bars in Fig. 2, is large. Therefore, to enhance and further confirm the laser cooling of our samples, we pumped the preforms with a 10.4 W Nd-doped YLiF 4 (Nd:YLF) laser, the wavelength of which at 1053 nm resides in the cooling spectral range of the samples (see Fig. 2). We have shown in Supplementary Note 6 that the optimum wavelength for laser cooling is around 1035 nm in the low absorbance (α r l ≪ 1) regime. Our use of the Nd:YLF laser operating at 1053 nm was mainly due to the availability of a high-power source in our laboratory. With multipass pump geometries where N p α r l ≫ 1 (N p is the number of passes), optimum cooling wavelength will increase in accordance with the maximum cooling efficiencies shown in Fig. 2. Similar to the LITMoS test, the samples were double-pass pumped by the Nd:YLF laser inside the vacuum chamber and the changes of the temperature were recorded by the thermal camera as a function of the exposure time. Figure 3 shows the thermal images of sample A (a) before and (b) after the exposure to the laser light. Figure 3b was taken after the laser was turned on and the sample temperature was stabilized (~40 min). Note that the heat extraction occurs only in the core of each sample, but the entire sample cools almost uniformly in less than a minute. The cooling is easily recognizable by unaided human eye when the thermal camera image become darker after the exposure to the Nd:YLF laser. The bright regions in the thermal image of the sample in Fig. 3 can be misleading; the reason for these bright regions is that silica glass is not transparent in the thermal window and the bright regions on the sample originate from reflections of the thermal radiation from the side walls of the chamber onto our sample's cylindrical surface and eventually into the thermal camera. Figure 4 shows the evolution of the temperature of the samples over time while being exposed to the 10.4 W Nd:YLF laser. In each case, the temperature drop can be fitted to the exponential function where we use the following definitions: where P abs is the absorbed power, ϵ = 0.85 is the emissivity of the implemented Yb-doped silica glass fiber preforms, σ = 5.67 × 10 −8 W m −2 K −4 is the Stefan-Boltzmann constant, T 0 is the ambient temperature, l is the sample length, A is the surface area of the sample, V is the volume of the sample, ρ = 2.2 × 10 3 kg m −3 is the silica glass mass density, and c v = 741 J kg −1 K −1 is the specific heat of the silica glass 37,38 .
Equations (4) and (5) can be derived by noting that in the vacuum chamber, the convective and conductive heat transfers are negligible; therefore, the temporal behavior of the temperature obeys the following differential equation 39 (see Supplementary Note 3 for additional information): where the absorbed power in the double-pass experiment is given by ΔT = T s − T 0 , where T s is the sample temperature. α r (λ p ) is the resonant absorption coefficient of the pump laser. We also have T ¼ T w T l T g , where T w = 0.92 is the transmission of the vacuum chamber windows, T l = 0.998 is the transmission of the lenses, T g = 0.96 is the transmission of the preforms' facets, and Results of the fitting procedures related to the laser-induced thermal modulation spectroscopy (LITMoS) tests presented in Fig. 2 with Eq. (1), and the temporal evolution curves of the temperatureexposed to the high-power 1053 nm laser presented in the power cooling experiment. The errors in ηext signify the range of acceptable values from the fitting of the theoretical curves to the experimental data with error bars in Fig. 2. Fig. 3 Thermal camera images before and after cooling. Panel a shows the thermal image of samples A before it is exposed to the laser light, and b shows its thermal image after nearly 1 h of being cooled by the high-power 105 nm laser. The regions that are used in calculating the temperature changes are marked by the dashed lines in the left column.  Table 2.
R m = 0.998 is the reflection of the mirror. Note that the absorption coefficients of samples A, B, and C were measured to be α r (λ p ) = 0.43, 0.52, and 0.50 m −1 , respectively. The exponential form presented in Eq. (4) is a direct solution to Eq. (6); by fitting Eq. (4) to the measurements in Fig. 4, the values of the two fitting parameters for each sample, i.e., ΔT max and η ext (via τ c ) are extracted and reported in Table 2. We note that the slope of the ΔT(t) curve at t = 0 in Eq. (4) gives us the value of the cooling efficiency at 1053 nm wavelength, i.e., η c = −(ρVc v / P abs )∂ t ΔT| t=0 . For each sample, we also calculate the value of η c using the two fitted coefficients, and present the results in Table 2; these values all agree well, within the error bars, with the plots of η c in Fig. 2 obtained using the LITMoS tests. Video clips of the cooling evolution of the samples are presented in Supplementary Note 7.2.

Discussion
In conclusion, we have demonstrated laser cooling in three separate bulk samples of Yb-doped silica glass optical fiber preform. Each sample has a different Yb ion concentration and each is co-doped with one or more of Al, P, F, and Ce elements. We performed an LITMoS test on each sample and extracted its cooling efficiency and showed that each sample is cooled over a certain laser pump wavelength range. Separately, we exposed each sample to a high-power Nd:YLF laser at 1053 nm wavelength and monitored the temporal evolution of its temperature. The independently extracted cooling efficiencies all agree with those from the LITMoS tests, indicating a maximum cooling of the three samples by 0.6, 0.7, and 0.56 K, respectively, at 1053 nm laser pump wavelength. Because of the geometry of the samples, the temperature variation within each sample is negligible; therefore, the reported temperature drop is nearly uniform in the entire volume of each sample 29 . We emphasize that the added dopants in silica glass results in an increase in the critical quenching concentration of Yb atoms; therefore, the preforms can be sufficiently doped with Yb to observe laser cooling, while keeping the external quantum efficiencies near unity. The experiments allowed us to extract the external quantum efficiency of each sample. We note that this is, to the best of our knowledge, the first reported measurement of the external quantum efficiency of Yb-doped silica glass, the determination of which is critical to laser cooling experiments. Last but not least, we would like to emphasize that the heat extraction occurs only in the core of each sample. Each sample is surrounded by the undoped (no Yb-doping) silica glass cladding region, which provides a significant thermal load. The cooling in our experiments has been achieved in spite of this large thermal load. We anticipate that in future experiments, we can achieve a larger temperature drop by geometrical optimization 40,41 , reducing the thermal load, and using a high-power pump laser at the optimum wavelength for laser cooling at around 1035 nm.
While this paper was under review in another Nature Research journal, we became aware of the successful report of laser cooling of silica fiber by Knall et al. 42 , where they report temperature changes up to −50 mK in a fiber with a 21 μm diameter core doped with 2.06 wt% Yb 3+ , and co-doped with Al 2 O 3 and F − to increase the critical quenching concentration by a factor of 16 over the largest reported values for the Yb-doped silica.

Methods
Fabrication of silica glass preforms. The high-purity glasses were fabricated by a modified chemical vapor deposition technique. Yb doping was performed by either the all-solution doping technique (sample A) 43 or the gas-phase doping technique (samples B and C) 35 . As stated above, Al codoping was used to ensure a good solubility of the Yb, employing an Al/Yb ratio of greater than 7:1. Codoping with P or Ce, as well as the gas-phase doping technique, reduced the photodarkening loss of the material (samples B and C). For sample C, a Ce/Yb ratio of about 0.3 was used, which is known to reduce photodarkening substantially 44 .
These glasses were developed for single-mode, high-power fiber lasers, so controlling the core-cladding refractive index step was essential; for this reason, codoping with phosphorus 43 or fluorine was used to decrease the refractive index of the material. Fiber lasers using these types of glasses have been used to achieve CW output powers of greater than 4 kW, while maintaining good beam quality 45,46 . Output powers like these can only be accomplished with, among others, high-purity core materials with low background absorption. The background losses of these glasses are listed in Table 1 and are ≤10 dB km −1 measured at 1200 nm wavelength. At this wavelength, the main contributions to loss are from Fe 2+ impurities and Rayleigh scattering. Assuming that Fe 2+ impurity is the only loss channel, its concentration can be estimated to be around 15 ppb 47 ; if scattering losses are also considered, the Fe 2+ concentration would be even lower. The OH-induced quenching is negligible because the OH concentration in these glasses is very low (see Table 1); similar investigations on Yb-doped aluminosilicate glasses support this 48 .

Data availability
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.