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Traitement du signal

03 - Refroidissement laser et marches au hasard anormales

Cohen-Tannoudji

Published Jan 1, 1998• 0 citations
OpenAlex

Abstract

Laser cooling allows now the velocity spread of an ensemble of atoms to be reduced below the value corresponding to the recoi l \nvelocity of an atom emitting or absorbing a single photon (subrecoil cooling) . This is achieved by using a random walk in velocit y \nspace with a jump rate which vanisches at zero velocity . We will review a few possible theoretical descriptions of such a coolin g \nmechanism . The anomalous character of the corresponding random walk will be analysed using Lvy statistical distributions an d \ncertain nonergodic features of the atomic evolution will be emphasized . Recent experimental developments will be also described . \nThey have allowed temperatures of a few nanokelvins to be reached and measured .

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We establish here the correspondence between the statistical models introduced in Chapter 3 and the quantum evolution of atoms undergoing subrecoil laser cooling. This enables us to establish analytical expressions connecting the parameters of the statistical models (τ 0 , p 0 , p D , Δ p , p max , τ b and) to atomic and laser parameters relevant to subrecoil laser cooling. Such a ‘dictionary’ is useful for the numerical estimation of the results derived in this book (see Chapter 8). It also leads to analytical relations between τ b and, which are used for cooling optimization (see Chapter 9). We first treat in detail Velocity Selective Coherent Population Trapping in Section A.1. Analytical expressions are given for the statistical parameters. Special attention is given to the p -dependences of the jump rates both for small p and for large p , because they control the asymptotic behaviours of the trapping and recycling times. It is thus important to include these p -dependences correctly in the simplified jump rates in order to ensure the validity of the statistical model. Raman cooling is then briefly treated in Section A.2. We only consider here the limit of small laser intensities (and a null detuning for VSCPT) but it is clear that the calculations can easily be generalized if needed. Velocity Selective Coherent Population Trapping We first present the quantum optics treatment of one-dimensional σ + /σ − VSCPT (Section A.1.1).

Cambridge University Press eBooks•Jul 2, 2010•0 citations
Laser cooling allows now the velocity spread of an ensemble of atoms to be reduced below the value corresponding to the recoi l \nvelocity of an atom emitting or absorbing a single photon (subrecoil cooling) . This is achieved by using a random walk in velocit y \nspace with a jump rate which vanisches at zero velocity . We will review a few possible theoretical descriptions of such a coolin g \nmechanism . The anomalous character of the corresponding random walk will be analysed using Lvy statistical distributions an d \ncertain nonergodic features of the atomic evolution will be emphasized . Recent experimental developments will be also described . \nThey have allowed temperatures of a few nanokelvins to be reached and measured .
Atoms can now be laser cooled, in one, two and three dimensions, below the limit corresponding to the recoil energy of an atom absorbing or emitting a single photon. Recent works have shown that all subrecoil cooling schemes are based on an anomalous random walk of the atom in momentum space which does not obey the central limit theorem and which introduces a fundamental non–ergodicity in the cooling process. Lévy statistics turn out to be very useful for analysing such a situation since they provide quantitative results for the long time limit of the momentum distribution. In this paper, we briefly review these theoretical works and we give a few references where more details can be found. We also mention a few recent experiments which have been stimulated by these theoretical developments.
In this chapter, we first recall (in Section 2.1) a few properties of the most usual laser cooling schemes, which involve a friction force. In such standard situations, the motion of the atom in momentum space is a Brownian motion which reaches a steady-state, and the recoil momentum of an atom absorbing or emitting a single photon appears as a natural limit for laser cooling. We then describe in Section 2.2 some completely different laser cooling schemes, based on inhomogeneous random walks in momentum space. These schemes, which are investigated in the present study, allow the ‘recoil limit’ to be overcome. They are associated with non-ergodic statistical processes which never reach a steady-state. Section 2.3 is devoted to a brief survey of various quantum descriptions of subrecoil laser cooling, which become necessary when the ‘recoil limit’ is reached or overcome. The most fruitful one, in the context of this work, is the ‘quantum jump description’ which will allow us in Section 2.4 to replace the microscopic quantum description of subrecoil cooling by a statistical study of a related classical random walk in momentum space. It is this simpler approach that will be used in the subsequent chapters to derive some quantitative analytical predictions, in cases where the quantum microscopic approach is unable to yield precise results, in particular in the limit of very long interaction times, and/or for a momentum space of dimension D higher than 1.
We report the first observation of subrecoil laser cooling in two dimensions by velocity selective coherent population trapping. We have compressed the momentum distribution of a cloud of trapped metastable helium atoms along two orthogonal axes to $\ensuremath{\delta}p=\frac{\ensuremath{\hbar}k}{4}$, where $\ensuremath{\hbar}k$ is the photon momentum. The corresponding temperature, 16 times below the single-photon recoil temperature, is 250 nK. Atoms are pumped into a nonabsorbing state exhibiting four well-resolved momentum peaks with subrecoil widths. The momentum space density in the peaks is significantly greater than that in the uncooled distribution.
Laser cooling of atomic motion enables advances in quantum information and precision metrology. However, the spatial spreading of subrecoil-laser-cooled atoms-crucial for understanding cooling mechanisms and atomic confinement-remains largely unexplored. Here, we analyze anomalous diffusion in subrecoil-laser-cooled atoms, where a velocity-dependent fluorescence rate R(v)∝|v|^{α} governs transport properties. By tuning α, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at α=3/2, diffusion is minimized, leading to optimal atomic confinement. We further identify a conceptual link between subrecoil laser cooling and the Pomeau-Manneville map from nonlinear dynamics, revealing that anomalous diffusion can generically exhibit a nontrivial minimum in spatial spreading-even across seemingly unrelated physical systems.
We establish here the correspondence between the statistical models introduced in Chapter 3 and the quantum evolution of atoms undergoing subrecoil laser cooling. This enables us to establish analytical expressions connecting the parameters of the statistical models (τ 0 , p 0 , p D , Δ p , p max , τ b and) to atomic and laser parameters relevant to subrecoil laser cooling. Such a ‘dictionary’ is useful for the numerical estimation of the results derived in this book (see Chapter 8). It also leads to analytical relations between τ b and, which are used for cooling optimization (see Chapter 9). We first treat in detail Velocity Selective Coherent Population Trapping in Section A.1. Analytical expressions are given for the statistical parameters. Special attention is given to the p -dependences of the jump rates both for small p and for large p , because they control the asymptotic behaviours of the trapping and recycling times. It is thus important to include these p -dependences correctly in the simplified jump rates in order to ensure the validity of the statistical model. Raman cooling is then briefly treated in Section A.2. We only consider here the limit of small laser intensities (and a null detuning for VSCPT) but it is clear that the calculations can easily be generalized if needed. Velocity Selective Coherent Population Trapping We first present the quantum optics treatment of one-dimensional σ + /σ − VSCPT (Section A.1.1).