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Fluorescent refrigeration

Richard I. Epstein

Published Jan 23, 2023• 1 citation
OpenAlex

Abstract

Fluorescent refrigeration is based on selective radiative pumping, using substantially monochromatic radiation, of quantum excitations which are then endothermically redistributed to higher energies. Ultimately, the populated energy levels radiatively deexcite emitting, on the average, more radiant energy than was initially absorbed. The material utilized to accomplish the cooling must have dimensions such that the exciting radiation is strongly absorbed, but the fluorescence may exit the material through a significantly smaller optical pathlength. Optical fibers and mirrored glasses and crystals provide this requirement.

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Optical refrigeration using anti-Stokes photoluminescence is now well established, especially for rare-earth-doped solids where cooling to cryogenic temperatures has recently been achieved. The cooling efficiency of optical refrigeration is constrained by the requirement that the increase in entropy of the photon field must be greater than the decrease in entropy of the sample. Laser radiation has been used in all demonstrated cases of optical refrigeration with the intention of minimizing the entropy of the absorbed photons. In this presentation, I will show that as long as the incident radiation is unidirectional, the loss of coherence does not significantly affect the cooling efficiency. Using a general formulation of radiation entropy as the von Neumann entropy of the photon field, I will show how the cooling efficiency depends on the properties of the light source such as wavelength, coherence, and directionality. These results suggest that the laws of thermodynamics permit optical cooling of materials with incoherent sources such as light emitting diodes and filtered sunlight almost as efficiently as with lasers.

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This review discusses the progress and ongoing efforts in optical refrigeration. Optical refrigeration is a process in which phonons are removed from a solid by anti-Stokes fluorescence. The review first summarizes the history of optical refrigeration, noting the success in cooling rare-earth-doped solids to cryogenic temperatures. It then examines in detail a four-level model of rare-earth-based optical refrigeration. This model elucidates the essential roles that the various material parameters, such as the spacing of the energy levels and the radiative quantum efficiency, play in the process of optical refrigeration. The review then describes the experimental techniques for cryogenic optical refrigeration of rare-earth-doped solids employing non-resonant and resonant optical cavities. It then examines the work on laser cooling of semiconductors, emphasizing the differences between optical refrigeration of semiconductors and rare-earth-doped solids and the new challenges and advantages of semiconductors. It then describes the significant experimental results including the observed optical refrigeration of CdS nanostructures. The review concludes by discussing the engineering challenges to the development of practical optical refrigerators, and the potential advantages and uses of these refrigerators.

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Chapter 10 Fluoride Glasses and Fibers

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Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).

Pan Stanford Publishing eBooks•Aug 31, 2016•0 citations

Photoluminescent cooling with incoherent light

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Optical refrigeration using anti-Stokes photoluminescence is now well established, especially for rare-earth-doped solids where cooling to cryogenic temperatures has recently been achieved. The cooling efficiency of optical refrigeration is constrained by the requirement that the increase in the entropy of the photon field must be greater than the decrease in the entropy of the sample. Laser radiation has been used in all demonstrated cases of optical refrigeration with the intention of minimizing the entropy of the absorbed photons. Here, we show that as long as the incident radiation is unidirectional, the loss of coherence does not significantly affect the cooling efficiency. Using a general formulation of radiation entropy as the von Neumann entropy of the photon field, we show how the cooling efficiency depends on the properties of the light source, such as wavelength, coherence, and directionality. Our results suggest that the laws of thermodynamics permit optical cooling of materials with incoherent sources, such as light emitting diodes and filtered sunlight, almost as efficiently as with lasers. Our findings have significant and immediate implications for design of compact all-solid-state devices cooled via optical refrigeration.

arXiv:2306.17327•APL Photonics•Aug 1, 2024•2 citations

Purcell-enhanced optical refrigeration

Peng Ju, Kunhong Shen, Stefan Püschel +3 more

Optical refrigeration of solids with anti-Stokes fluorescence has been widely explored as a vibration-free cryogenic cooling technology. A minimum temperature of 87 K has been demonstrated with rare-earth-ion-doped crystals using optical refrigeration. However, the depletion of the upper-lying energy levels in the ground-state manifold hinders further cooling to below the liquid nitrogen ( LN 2 ) temperatures, restricting its applications. In this work, we introduce a Purcell-enhanced optical refrigeration method to circumvent this limitation. This approach enhances the emission of high-energy photons by coupling the emitters to an optical cavity, blueshifting the mean emission wavelength. Such Purcell-enhanced emission facilitates cooling starting from a lower-energy level in the ground-state manifold, which exhibits a higher occupation below the LN 2 temperatures. Using experimentally measured optical coefficients, our theoretical analysis predicts a minimum achievable internal temperature of about 38 K for a Yb 3 + : YLiF 4 nanocrystal near a cavity under realistic conditions. The proposed method is applicable to other rare-earth-ion-doped materials and semiconductors and will have applications in creating superconducting and other quantum devices through solid-state cooling.

arXiv:2404.19142•Physical Review Research•Mar 21, 2026•2 citations
Fluorescent refrigeration is based on selective radiative pumping, using substantially monochromatic radiation, of quantum excitations which are then endothermically redistributed to higher energies. Ultimately, the populated energy levels radiatively deexcite emitting, on the average, more radiant energy than was initially absorbed. The material utilized to accomplish the cooling must have dimensions such that the exciting radiation is strongly absorbed, but the fluorescence may exit the material through a significantly smaller optical pathlength. Optical fibers and mirrored glasses and crystals provide this requirement.
Optical refrigeration using anti-Stokes photoluminescence is now well established, especially for rare-earth-doped solids where cooling to cryogenic temperatures has recently been achieved. The cooling efficiency of optical refrigeration is constrained by the requirement that the increase in entropy of the photon field must be greater than the decrease in entropy of the sample. Laser radiation has been used in all demonstrated cases of optical refrigeration with the intention of minimizing the entropy of the absorbed photons. In this presentation, I will show that as long as the incident radiation is unidirectional, the loss of coherence does not significantly affect the cooling efficiency. Using a general formulation of radiation entropy as the von Neumann entropy of the photon field, I will show how the cooling efficiency depends on the properties of the light source such as wavelength, coherence, and directionality. These results suggest that the laws of thermodynamics permit optical cooling of materials with incoherent sources such as light emitting diodes and filtered sunlight almost as efficiently as with lasers.
This review discusses the progress and ongoing efforts in optical refrigeration. Optical refrigeration is a process in which phonons are removed from a solid by anti-Stokes fluorescence. The review first summarizes the history of optical refrigeration, noting the success in cooling rare-earth-doped solids to cryogenic temperatures. It then examines in detail a four-level model of rare-earth-based optical refrigeration. This model elucidates the essential roles that the various material parameters, such as the spacing of the energy levels and the radiative quantum efficiency, play in the process of optical refrigeration. The review then describes the experimental techniques for cryogenic optical refrigeration of rare-earth-doped solids employing non-resonant and resonant optical cavities. It then examines the work on laser cooling of semiconductors, emphasizing the differences between optical refrigeration of semiconductors and rare-earth-doped solids and the new challenges and advantages of semiconductors. It then describes the significant experimental results including the observed optical refrigeration of CdS nanostructures. The review concludes by discussing the engineering challenges to the development of practical optical refrigerators, and the potential advantages and uses of these refrigerators.
Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).
Optical refrigeration using anti-Stokes photoluminescence is now well established, especially for rare-earth-doped solids where cooling to cryogenic temperatures has recently been achieved. The cooling efficiency of optical refrigeration is constrained by the requirement that the increase in the entropy of the photon field must be greater than the decrease in the entropy of the sample. Laser radiation has been used in all demonstrated cases of optical refrigeration with the intention of minimizing the entropy of the absorbed photons. Here, we show that as long as the incident radiation is unidirectional, the loss of coherence does not significantly affect the cooling efficiency. Using a general formulation of radiation entropy as the von Neumann entropy of the photon field, we show how the cooling efficiency depends on the properties of the light source, such as wavelength, coherence, and directionality. Our results suggest that the laws of thermodynamics permit optical cooling of materials with incoherent sources, such as light emitting diodes and filtered sunlight, almost as efficiently as with lasers. Our findings have significant and immediate implications for design of compact all-solid-state devices cooled via optical refrigeration.
Optical refrigeration of solids with anti-Stokes fluorescence has been widely explored as a vibration-free cryogenic cooling technology. A minimum temperature of 87 K has been demonstrated with rare-earth-ion-doped crystals using optical refrigeration. However, the depletion of the upper-lying energy levels in the ground-state manifold hinders further cooling to below the liquid nitrogen ( LN 2 ) temperatures, restricting its applications. In this work, we introduce a Purcell-enhanced optical refrigeration method to circumvent this limitation. This approach enhances the emission of high-energy photons by coupling the emitters to an optical cavity, blueshifting the mean emission wavelength. Such Purcell-enhanced emission facilitates cooling starting from a lower-energy level in the ground-state manifold, which exhibits a higher occupation below the LN 2 temperatures. Using experimentally measured optical coefficients, our theoretical analysis predicts a minimum achievable internal temperature of about 38 K for a Yb 3 + : YLiF 4 nanocrystal near a cavity under realistic conditions. The proposed method is applicable to other rare-earth-ion-doped materials and semiconductors and will have applications in creating superconducting and other quantum devices through solid-state cooling.