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Physical Review A

Entropy exchange in laser cooling

Harold J. Metcalf

Published Jun 3, 2008• 28 citations
Publisher

Abstract

It is usually presumed that spontaneous emission is necessary to remove the entropy lost by laser-cooled atoms. Here we show that the changes in the laser beams themselves constitute a sufficiently large reservoir of $N$ states accessible to the system that their entropy $S={k}_{B}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(N)$ is sufficient to absorb the entropy lost by the atoms in the cooling process. Proper choice of laser parameters could possibly produce cooling of atoms or molecules over a wide range of temperatures without spontaneous emission.

DOI
10.1103/physreva.77.061401

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It is usually presumed that spontaneous emission is necessary to remove the entropy lost by laser-cooled atoms. Here we show that the changes in the laser beams themselves constitute a sufficiently large reservoir of NNN states accessible to the system that their entropy S=kBln(N)S={k}_{B}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(N)S=kB​ln(N) is sufficient to absorb the entropy lost by the atoms in the cooling process. Proper choice of laser parameters could possibly produce cooling of atoms or molecules over a wide range of temperatures without spontaneous emission.
It is usually presumed that spontaneous emission is necessary to remove the entropy lost by laser-cooled atoms. Here we show that the changes in the laser beams themselves constitute a sufficiently large reservoir of N states accessible to the system that their entropy S=kB ln N is sufficient to absorb the entropy lost by the atoms in the cooling process. Proper choice of laser parameters could possibly produce cooling of atoms or molecules over a wide range of temperatures without spontaneous emission.
It is widely believed that spontaneous emission (SE) is necessary to remove entropy from an atomic sample during laser cooling. In fact, SE is needed for energy removal when laser cooling is done with single-frequency light, but with more than one frequency, both energy and entropy can be removed using only stimulated processes. Our experimental demonstration of this phenomenon works by restricting the atom–light interaction to a time short compared to a cycle of absorption followed by natural decay [Phys. Rev. Lett.114, 043002 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.043002]. We present here additional information on these results, in particular, simulations of the motion of atoms under the bichromatic force that compare well with our data. This accomplishment is of interest to direct laser cooling of molecules or in experiments where working space or time is limited.
It is widely believed that spontaneous emission (SE) is necessary to remove entropy from an atomic sample during laser cooling. In fact, SE is needed for energy removal when laser cooling is done with single-frequency light, but with more than one frequency, both energy and entropy can be removed using only stimulated processes. Our experimental demonstration of this phenomenon works by restricting the atom–light interaction to a time short compared to a cycle of absorption followed by natural decay [Phys. Rev. Lett.114, 043002 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.043002]. We present here additional information on these results, in particular, simulations of the motion of atoms under the bichromatic force that compare well with our data. This accomplishment is of interest to direct laser cooling of molecules or in experiments where working space or time is limited.
We propose a laser cooling concept for the translational motion of molecules which does not require repeated spontaneous emission by each molecule. The cooling works by repetition of three main steps; velocity selection of a narrow momentum width, deceleration of velocity selected molecules by repeated STIRAP and accumulation of decelerated molecules via one time spontaneous emission. We use single spontaneous emission for irreversible accumulation of narrow velocity selected and decelerated populations. We develop an analytical model to describe the evolution of the molecular gas system, internal subsystem and external (center of mass) subsystem density matrices and entropies. Simulation results show cooling from an arbitrary momentum width towards final width of about hbark\\hbar khbark. The external entropy is reduced while the internal entropy is increased. The external entropy is shown to decrease during coherent laser interactions, a possibility of translational cooling via unitary evolution. The system entropy increases in consistency with the Araki-Lieb inequality.
This Letter reports the demonstration of laser cooling without spontaneous emission, and thereby addresses a significant controversy. It works by restricting the atom-light interaction to a time short compared to a cycle of absorption followed by natural decay. It is achieved by using the bichromatic force on an atomic transition with a relatively long excited state lifetime and a relatively short cooling time so that spontaneous emission effects are minimized. The observed width of the one-dimensional velocity distribution is reduced by ×2 thereby reducing the "temperature" by ×4. Moreover, our results comprise a compression in phase space because the spatial expansion of the atomic sample is limited. This accomplishment is of interest to direct laser cooling of molecules or in experiments where working space or time is limited.
Cooling of internal atomic and molecular states via optical pumping and laser cooling of the atomic velocity distribution, rely on spontaneous emission. The outstanding success of such examples, taken together with general arguments, has led to the widely held notion that radiative cooling requires spontaneous emission. We here show by specific examples and direct calculation, based primarily on breaking emission-absorption symmetry as in lasing without inversion, that cooling of internal states by external coherent control fields is possible. We also show that such coherent schemes allow us to practically reach absolute zero in a finite number of steps, in contrast to some statements of the third law of thermodynamics.