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Bulletin of the American Physical Society

Entropy Exchange in Laser Cooling

H. Metcalf

Published May 30, 2008• 2 citations
OpenAlex

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=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.

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Cambridge University Press eBooks•Dec 31, 2015•0 citations
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 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 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.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.