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arXiv:1806.06906 · Physical Review A

Phase-space-density limitation in laser cooling without spontaneous emission

T. Chanelière, D. Comparat, Hans Lignier

Published Dec 27, 2018• 6 citations
arXivHTMLPDF

Abstract

We study the possibility to enhance the phase-space density of noninteracting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semiclassical description, which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase-space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase-space density can only increase by a factor $M$ for $M$-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.

DOI
10.1103/physreva.98.063432

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We study the possibility to enhance the phase-space density of noninteracting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semiclassical description, which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase-space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase-space density can only increase by a factor MMM for MMM-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.
We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling-time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling-time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally, it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.
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We study the dynamics of laser-cooled two-level atoms in a time-dependent standing wave. In the absence of spontaneous emission, our model reduces to the much studied quantum standard mapping. For a sample of atoms initially cooled to the Doppler limit, the momentum variance increases linearly with interaction time. A sample of atoms initially cooled to the recoil limit will display momentum diffusion at a rate that is determined by two numbers: the classical chaos parameter and a dimensionless Planck parameter. This diffusion ceases after the quantum-mechanical break time. Spontaneous emission will modify the diffusion rate of both Doppler- and recoil-cooled atoms. We show that one component of the new diffusion constant is due to spontaneous recoil and that there is a correction to the deterministic diffusion rate due to the destruction of correlations in the stroboscopic position. Spontaneous emission will destroy the dynamic localization of atoms cooled to the recoil limit. The new momentum diffusion constant can be related to the quasistationary state-decoherence rate. \textcopyright{} 1996 The American Physical Society.
Theoretical progress in the cooling of internal degrees of freedom of molecules using shaped laser pulses is reported. The emphasis is on general concepts and universal constraints. Several alternative definitions of cooling are considered, including reduction of the von Neumann entropy, −tr{ρ̂logρ̂} and increase of the Renyi entropy, tr{ρ̂2}. A distinction between intensive and extensive considerations is used to analyse the cooling process in open systems. It is shown that the Renyi entropy increase is consistent with an increase in the system phase space density and an increase in the absolute population in the ground state. The limitations on cooling processes imposed by Hamiltonian generated unitary transformations are analyzed. For a single mode system with a ground and excited electronic surfaces driven by an external field it is shown that it is impossible to increase the ground state population beyond its initial value. A numerical example based on optimal control theory demonstrates this result. For this model only intensive cooling is possible which can be classified as evaporative cooling. To overcome this constraint, a single bath degree of freedom is added to the model. This allows a heat pump mechanism in which entropy is pumped by the radiation from the primary degree of freedom to the bath mode, resulting in extensive cooling.
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.
The emergence of classical behavior in quantum theory is often ascribed to the interaction of a quantum system with its environment, which can be interpreted as environmental monitoring of the system. As a result, off-diagonal elements of the density matrix of the system are damped in the basis of a preferred observable, often taken to be the position, leading to the phenomenon of decoherence. This effect can be modeled dynamically in terms of a Lindblad equation driven by the position operator. Here the question of decoherence resulting from a monitoring of position and momentum, i.e., a phase-space measurement, by the environment is addressed. There is no standard quantum observable corresponding to the detection of phase-space points, which is forbidden by Heisenberg's uncertainty principle. This issue is addressed by use of a coherent-state-based positive operator-valued measure for modeling phase-space monitoring by the environment. In this scheme, decoherence in phase space implies the diagonalization of the density matrix in both position and momentum representations. This is shown to be linked to a Lindblad equation where position and momentum appear as two independent Lindblad operators.