Observation of Laser-Induced Fluorescent Cooling of a SolidObservation of Laser-Induced Fluorescent Cooling of a Solid
Published as a Letter on page 500 of the October 12, 1995 edition of Nature.
Authors: R.I. Epstein, M.I. Buchwald, B.C. Edwards, T.R. Gosnell, and C.E. Mungan.
The possibility that an object might cool through its interaction with radiation was suggested as early as 1929 by Pringsheim [ 1]. After Landau [ 2] established the basic thermodynamic consistency of such a process, aspects of fluorescent cooling were vigorously pursued [ 3-11]. In particular, laser 'Doppler' cooling of gas-phase atoms and ions has today grown into a robust research area [ 12-15]. In contrast, attempts to cool solids with light have met with limited success; nonradiative heating effects tend to dominate, and fluorescent cooling has at best resulted in a reduction in overall heating rates [ 6]. Here, we report the first experimental realization of net cooling of a solid with radiation. The cooling efficiencies achieved (up to 2%) are at least 4 orders of magnitude larger than those observed in Doppler cooling of gases. By pumping a fluorescent cooling element with a high-efficiency diode laser, it should be possible to construct a compact, all-solid-state optical cryocooler; this would enable widespread deployment of cryogenic electronics and detectors in space and elsewhere [ 16].
The basic principles and requirements of fluorescent cooling are illustrated by the processes occurring in our experiments which use a heavy-metal-fluoride glass (ZBLANP) doped with trivalent ytterbium ions. Each Yb 3+ ion possesses only two groups of energy levels below the UV absorption edge of the host glass [ 17]. These groups are separated by an energy of 1.3 eV, corresponding to a wavelength of %7e1000 nm. The ground-state group is split into four levels and the excited-state group is split into three levels, as shown schematically in the inset of Fig. 1. The main part of this figure shows the measured absorption and fluorescence spectra of a sample of ZBLANP doped with 1 wt % Yb 3+. The mean energy of the fluorescent photons corresponds to a wavelength λ F = 995 nm, as indicated by the vertical line. Pumping this glass in the long-wavelength tail of the absorption spectrum moves excitations from the top of the ground-state group to the bottom of the excited-state group. The relative populations of the Stark levels within each group are thereby shifted slightly out of thermal equilibrium. That is, the populations of the lower levels in each group are larger than they would be in equilibrium. By absorbing thermal energy from the host material, thermal equilibrium within each group is restored. Radiative decays from the excited- to the ground-state groups produce photons that carry off the absorbed radiative and thermal energies.
Figure 1: Main plot — Absorption coefficient (dashed curve) and fluorescence spectrum (solid curve) at room temperature of ZBLANP (ZrF 4-BaF 2-LaF 3-AlF 3-NaF-PbF 2) doped with 1 wt % Yb 3+. The actual peak absorption coefficient is 1.1 cm -1 at 975 nm. The fluorescence spectrum was recorded using a one-meter spectrometer and an InGaAs detector in a 90 degree scattering geometry, and was corrected for the nonuniform responsivity of the system. The shape of the fluorescence spectrum is the same regardless of where one pumps in the Yb 3+ absorption band. The wavelength corresponding to the mean fluorescent-photon energy, λ F, is indicated by a vertical line. Inset plot—The schematic energy-level structure of ZBLANP:Yb 3+; the splittings within each group have been exaggerated for clarity. The arrows denote a typical cooling cycle: (1) laser pumping, (2) energy absorption from the thermal bath, (3) radiative decay, and (4) additional thermal-energy absorption.
Successful fluorescent cooling requires that a negligible fraction of the decays from the excited- to the ground-state groups occurs through nonradiative, heat-generating processes. Cooling is, at best, proportional to the energy spread of each group, whereas nonradiative decays generate heat in proportion to the much greater energy spacing between the groups. A high radiative quantum efficiency is thus required in order that nonradiative heating not overwhelm the fluorescent cooling. Kastler [ 3] suggested that rare-earth ions in transparent solids could be effective fluorescent coolers because of their large quantum efficiencies.
Each fluorescent photon carries off, on average, thermal energy equal to the difference between the pump-photon and the mean fluorescent-photon energies. In the ideal case where there are no nonradiative relaxations from the excited- to the ground-state groups, the cooling power, P cool, is proportional to the absorbed pump power, P abs, and to the average difference in the photon energies of the pump and fluorescence radiation. In terms of wavelength λ of the pump radiation, the cooling power is thus
P cool = P abs(λ - λ F) / λ F.
Experimental Results and Analysis
In our work, two different experimental arrangements are used to investigate the fluorescent cooling of ZBLANP:Yb 3+. In the first of these, photothermal-deflection spectroscopy [ 18-19] is employed to measure the local temperature gradients induced by the pump laser in the interior of a sample. The pump beam from a c.w. titanium-sapphire laser is focused into the sample. A helium-neon laser probe beam, coaligned with and slightly displaced from the pump beam, passes through the sample in the opposite direction. Angular deflections of this probe beam, which are caused by thermally-induced refractive-index gradients in the pumped volume of the sample, are measured with a position-sensitive photodetector. An optical chopper placed in the path of the pump beam modulates the photothermal-deflection signal.
Figure 2: (a) Photothermal-deflection waveforms recorded on an averaging oscilloscope for pump-laser wavelengths of 980 and 1010 nm, at a chopping period of 1.8 s. This period is long compared to the relevant atomic and thermal relaxation time scales of the sample. The corresponding laser powers are 1.03 and 0.70 W, respectively, with a focused beam diameter of ~50 mm. The sample length is 2.7 cm. The ~50 ms rise and fall times depend upon the lateral separation between the pump and probe beams. (b) Amplitudes (filled circles) of the photothermal-deflection waveforms normalized by the incident laser power as a function of pump-laser wavelength. The solid curve is a plot of Eq. (1), scaled by an arbitrary temperature-to-deflection conversion factor.
Two examples of raw photothermal-deflection data recorded on an averaging oscilloscope are shown in Fig. 2(a). This panel presents deflection waveforms synchronous with the chopper for pump wavelengths of 980 and 1010 nm, respectively 15 nm below and above λ F. The unmistakable 180 degree phase difference between the two waveforms indicates that the positive temperature gradient observed at 980 nm becomes a negative temperature gradient at 1010 nm. Evidently, the probed volume of the sample is cooling at the longer wavelength.
A more systematic investigation of the photothermal-deflection spectra appears in Fig. 2(b). In this figure, the filled circles specify the measured deflection amplitudes normalized with respect to the incident pump-laser power. A clear transition from the heating to the cooling regime is observed as the pump wavelength is tuned to values larger than λ F, indicated by the vertical line.
In the second experimental arrangement, the equilibrium temperatures reached by a bulk 2.5 mm by 2.5 mm by 6.9 mm sample are measured when the sample is continuously pumped by a titanium-sapphire laser beam. The sample is positioned at the center of a vacuum chamber and rests on two thin, vertical glass slides that thermally insulate the sample from the chamber. The inner wall of the chamber is painted black to absorb stray pump radiation as well as the fluorescence emitted by the sample. The pump-laser beam is directed along the long axis of the sample. The dimensions of the sample transverse to the optical axis are small enough that self-absorption of the fluorescence is minimal. The temperature of the sample is monitored with a liquid-nitrogen-cooled InSb infrared camera which is sensitive in the 3-5 µm range but blind to the ~1 µm laser and fluorescence radiation. Because ZBLANP is transparent at wavelengths shorter than 5 µm, a 1 mm 2 square of gold foil painted black on its outer face is attached to the sample to enhance the emissivity at the detection wavelengths. The outer surface of the foil emits thermal radiation characteristic of the temperature of the sample, while the polished inner surface reflects most of the fluorescent radiation. To account for the changes in the sample temperature arising from temperature drifts of the chamber, a reference sample with an identical gold foil is positioned ~1 cm away from the test sample, outside the pump-beam path but on the same glass supports in the chamber. Temperature differences of 0.02 K between the pumped and reference samples can be resolved. When the test sample is exposed to the pump laser, we find that the sample temperature equilibrates in about 15 min.
Figure 3: Equilibrated temperature differences (filled circles) of a laser-pumped 0.69-cm-long bulk sample relative to an identical reference sample. Measurements are made with an infrared camera thermometrically calibrated by comparison to a type-T thermocouple. Temperature changes are normalized by the incident laser power. The values between 1008 and 1030 nm are less than zero, corresponding to cooling. The solid curve is a plot of the expected temperature changes from Eq. (2), reduced by 20% to allow for laser radiation which misses the sample. The differences in the data near the peak at 975 nm, compared to those of Fig. 2(b), are due to differences in sample lengths and hence optical depths.
The filled circles in Fig. 3 show the steady-state temperatures of the test sample relative to the reference sample as a function of the pump wavelength per watt of incident laser power. Note that negative temperature differences as large as 0.3 K are obtained at long pump wavelengths. These results definitively demonstrate, for the first time, the absolute cooling of a solid by laser-induced anti-Stokes fluorescence.
The equilibrium temperature, T S, of the sample is established by a balance between the laser-induced fluorescent cooling and the heat load from the environment. In our setup, the dominant heat load is from the radiative coupling between the walls of the vacuum chamber at ambient temperature T C and the sample. If the sample radiates as a blackbody, then
P cool = σ A( T C 4 - T S 4)
where σ is the Stefan-Boltzmann constant and A = 0.82 cm 2 is the surface area of the sample. For small temperature changes, Eq. (2) implies
Δ T = T C - T S ≈ - P cool / (4σ AT C 3) ≅ -2.0 K ( P cool / 1 mW)
with P cool given by Eq. (1). This prediction is plotted as the solid curve in Fig. 3, scaled vertically by 0.8. The small discrepancies between theory and experiment in the cooling region can be reconciled if the radiative quantum efficiency equals ~0.997 and if ~0.1% of the laser power directly heats the sample. The results of the two types of experiments are in good agreement with each other, as can be seen in Fig. 4, where the data from Figs. 2(b) and 3 have been normalized by the corresponding absorptivities and plotted together for comparison. This normalization gives the cooling efficiency, defined as the ratio of the cooling power to the absorbed laser power. In agreement with Eq. (1), most of the data lie on a straight line. If the quantum efficiency were unity, the zero crossing would occur at λ F = 995 nm. Experimentally, the zero crossing agrees with this prediction to within 3 nm, indicating that the radiative quantum efficiency is at least 0.997. The deviations from linearity for λ ≥ 1020 nm may be explainable in terms of parasitic heating in our sample or experimental artifacts. The experimental cooling efficiency in Fig. 4 is ~2% at a pump wavelength of 1015 nm.
Figure 4: Cooling efficiencies measured in the photothermal-deflection (filled circles) and bulk-cooling (open squares) experiments. Negative efficiencies correspond to heating. The amplitudes of the two data curves have been adjusted using the scaling factors from Figs. 2(b) and 3. The solid curve is a plot of P cool / P abs from Eq. (1).
A computer model of the excitations and radiative transfer in the ZBLANP:Yb 3+ system predicts that similar efficiencies should be achievable down to a temperature of 60 K. By pumping a fluorescent cooling material with an efficient diode laser, an all-solid-state cryocooler could be developed that operates with an efficiency comparable to commercial mechanical coolers [ 16]. This type of cryocooler would be functional in the temperature range useful for high-T C superconductors, infrared detectors, and other cooled electronic devices and would be well-suited for space-based applications.
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We thank D.E. Casperson, C. Edwards, C. Ho, N. Kurnit, S. Lloyd, A.V. Olinto, W.C. Priedhorsky, W.R. Scarlett, and P. Xie for helpful discussions and comments. A.J. Gibbs and J. Fajardo are appreciated for help in preparing the glass samples. This work was carried out under the auspices of the U.S. Department of Energy.