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Raman Laser Cooling of Solids Journal of Luminescence 133 (2013) 10–14 Contents lists available at SciVerse ScienceDirect Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin Raman laser cooling of solids Stephen C. Rand n Division of Applied Physics, University of Michigan, Ann Arbor, Michigan, USA article info abstract Available online 5 February 2012 A new approach is proposed for 3-D laser cooling of solids. Stimulated Raman scattering on a Keywords: narrowband electronic transition is used in conjunction with 1-photon optical pumping on a broadband Optical refrigeration transition to provide a mechanism that cools all the vibrational modes of solids while conserving energy and momentum, photon by photon. The individual steps in the 2-photon Raman process are 4f–5d and 5d–4f transitions which are electric-dipole-allowed (broadband) transitions that form a L-system. By contrast, the 2-photon transition between the 4f states of the rare earth ion is 3þ narrowband. By considering examples of Ce ions in Y3Al5O12 and CeF3, elevated transition rates are predicted to offer substantial improvement over anti-Stokes fluorescence cooling when all 1-photon detunings exceed their corresponding Stokes shifts. & 2012 Elsevier B.V. All rights reserved. 1. Introduction The motivation to discover efficient new laser cooling methods for condensed matter is nevertheless strong. Potential applica- Optical refrigeration of gases is a relatively mature subject. In tions exist for ‘‘radiation-balanced’’ solid state lasers [11], the past, laser cooling of bosonic systems was systematically improved gravitational wave detection [12], compact frequency developed [1–3] to achieve Bose–Einstein Condensation (BEC) for references [13], refrigeration of infrared imagers below the the first time [4], and the continuing effort to refine techniques thermo-electric limit in space [14], and compact cooling systems that allow light to transport energy, momentum, and entropy out for super-conducting electronics. In the past, the axial vibrations of atomic systems has shown that fermionic atoms can similarly of mirrors in Fabry–Perot interferometers were reduced with all- condense into a single macroscopic quantum state [5]. These optical techniques to improve the sensitivity limits of gravita- advances have drawn the subjects of superconductivity and BEC tional observatories. However this opto-mechanical cooling of a closer together and promise a unified view of these basic physics single mode was not accompanied by an irreversible increase in topics in the future. Experimental techniques for laser cooling entropy of the optical field and therefore altered the (non- have relied heavily on one simple but important characteristic of equilibrium) distribution of phonons without cooling the solid atoms in gases, namely that the atoms comprising a gas are in as a whole. Parallel efforts with anti-Stokes cooling sought to cool motion. Moving atoms experience the Doppler effect in inelastic the entire distribution of internal vibrational modes of solids in collisions with photons, and can progressively be slowed down order to surpass the thermo-electric cooling limit that determines (cooled) while conserving energy and momentum in each and the signal-to-noise ratio of imaging arrays in space. Space-based every interaction, provided that the light field undergoes an infrared imagery is an example of an important technology that is increase of entropy. Hence, although other mechanisms such as hampered by detector noise, and could be greatly improved by evaporative cooling have been applied in combination with laser refrigeration below this limit (N 153) in the rarified environment cooling to attain the most extreme temperatures [4], it may be of space. Thermo-electric temperature limitations have now been said that the harnessing of Doppler interactions has provided the surpassed with anti-Stokes fluorescence cooling [14], but far more most powerful set of approaches for optical cooling [6–10]. effective methods are needed to reach temperatures of only a few Unfortunately in solids the Doppler effect is ostensibly absent. Kelvin starting from room temperature. There is also interest in This implies that the optical refrigeration of condensed matter the fundamental objective of cooling solids to their vibrational must rely on a drastically more limited set of cooling mechan- ground state, but higher cooling rates are needed for that too. isms, and dims the prospect of using condensed matter to form In this paper, a new method is outlined that accelerates new quantum states. cooling of the internal vibrations of solids by combining a fast, stimulated Raman process to annihilate specific phonons of the host medium in a resonant manner with rapid optical pumping n Tel.: þ734 763 6810. on an allowed fluorescent transition. The method avoids heating E-mail address: [email protected] due to multi-phonon emission by atoms with arbitrarily large 0022-2313/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2012.01.019 S.C. Rand / Journal of Luminescence 133 (2013) 10–14 11 Stokes shifts (and high transition rates) and furnishes the neces- Conduction sary increase in entropy of the radiation field [15] to cool the Band entire solid. n-1 n 4f n-5d-4fn-1 5d -4f -4f absorption emission 2. ‘‘Doppler’’ cooling principle for solids Δ Stokes The vibrations of atoms or molecules in a solid constitute the motion that determines its kinetic temperature. This motion may Δ Laser be analyzed as phonons, and phonons undergo ‘‘collisions’’ during their interactions with light. As a consequence, incident photons of frequency and wavevector (o1,k1) experience Doppler-like interactions with phonons of frequency and wavevector (O,q)to produce scattered light. The scattered field has a frequency and 1 2 3 wavevector described by (o2,k2), and the conditions o2¼o17O and k2 ¼ k1 7q must be met to conserve energy and momentum when phonons are annihilated or created (upper or lower sign, respectively). Doppler analogies are commonplace in acousto- δ optics [10], but they take on special significance in the context of laser cooling of solids where they can guide the adaptation of 2 Doppler-shifted atom-field interactions to phonon-field interac- F7/2 tions in condensed matter. Δ Here we propose an approach to cool rare earth ions in solids F based on a coherent 2-photon interaction [16–18] that destroys 2 phonons and an incoherent step that adds entropy, completing a F5/2 repetitive cooling cycle that exploits fast fluorescence of impurity Fig. 2. Stimulated Raman cooling of Ce3 þ . Fields 1 and 2 are applied simulta- or host ions. The method uses counter-propagating laser beams neously to cause the absorption of a phonon of wavevector qffi2k and frequency whose difference frequency is slightly lower than the transition O¼d. The bold vertical arrow (repump field 3 at o3) provides an optical pumping 2 frequency to a long-lived excited electronic state. A phonon is to avoid population buildup in the F7/2 state that would reverse the 2-photon annihilated during each electronic Raman transition to the latter process. This field also ensures that entropy increases in the overall interaction [4]. ‘‘shelving’’ state, when detuning is to the long wavelength (‘‘red’’) side of the 2-photon 4fn–4fn transition. Subsequently, the excited ion is returned to its ground state via fast optical pumping on a Phonon annihilation cannot be sustained indefinitely using spontaneous 4fnÀ1 5d24fn transition which raises the entropy of stimulated Raman scattering with continuous-wave radiation. the field. This last step makes the cooling irreversible. Through Because the net Raman transition rate is proportional to the 2 2 rapid repetition of this phonon annihilation and optical pumping population difference between the F5/2 and F7/2 levels, forward cycle, cooling can proceed at a high rate. and backward transitions are balanced at high intensity in steady- Fig. 1 illustrates the basic geometry of inelastic light scattering state. Under continuous excitation, the excited state population by phonons. In spontaneous 1-photon interactions, the scattered accumulates until it equals that of the ground state. Forward light has a higher or a lower optical frequency and wavevector (cooling) and backward (heating) transition rates then become (o7O, k7q) depending on whether the specific phonon that equal. To ensure that only the forward process takes place, the 2 conserves energy and momentum at scattering angle y is Raman interaction should be pulsed and the F7/2 state must be 2 absorbed or emitted. Consequently, both upshifted and down- emptied periodically. Depletion of the F7/2 state can be accom- shifted components are observed in the spontaneous light scat- plished with an intense ‘‘repump’’ field E3 of an appropriate tering spectrum. In scattering with two input fields however, wavelength, as depicted in Fig. 2. interaction with a specific phonon may be made more selective, The repump interaction at o3, as well as all other possible through the involvement of an excited state resonance. For 1-photon transitions in the overall cooling cycle (namely those at example, counter-propagating beams with a positive 2-photon o1 or o2), must avoid generating phonons originating from 3þ relaxation in either the ground or excited state. Transitions detuning of dDF À(o1Ào2)¼O in Ce (with respect to the 2 2 consistent with zero heating (or net cooling) require detuning F5/2(n)- F7/2(n) transition, as shown in Fig. 2) can produce only phonon annihilation at frequency O through the vibronic transi- to the red by an amount equal to or greater than the Stokes shift 2 2 of the longest wavelength 4fnÀ1 5d24fn transition. For Ce3þ this tion F5/2(n)- F7/2(nÀ1). If the fields E1 and E2 are interchanged, a phonon of the same frequency propagating in the opposite means, direction can be annihilated. However no phonons are created by DLaser ZDStokes þDF ð1Þ this process in either direction on average.
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