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Physical Review A

Laser-noise-induced heating in far-off resonance optical traps

T. A. Savard, Kenneth M. O’Hara, John E. Thomas

Published Aug 1, 1997• 348 citations
Publisher

Abstract

Using a simple model, we calculate the heating rates arising from laser intensity noise and beam-pointing fluctuations in far-off resonance optical traps. Intensity noise causes exponential heating, while beam-pointing noise causes heating at a constant rate. The achievement of heating time constants well beyond 10 sec imposes stringent requirements on the laser noise power spectra. Noise spectra are measured for a commercial argon-ion laser to illustrate the expected time scales.

DOI
10.1103/physreva.56.r1095

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Using a simple model, we calculate the heating rates arising from laser intensity noise and beam-pointing fluctuations in far-off resonance optical traps. Intensity noise causes exponential heating, while beam-pointing noise causes heating at a constant rate. The achievement of heating time constants well beyond 10 sec imposes stringent requirements on the laser noise power spectra. Noise spectra are measured for a commercial argon-ion laser to illustrate the expected time scales.
We solve a stochastic master equation based on the theory of Savard et al. [T. A. Savard, K. M. O'Hara, and J. E. Thomas, Phys. Rev. A 56, R1095 (1997)] for heating arising from fluctuations in the trapping laser intensity. We compare with recent experiments of Ye et al. [J. Ye, D. W. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999)], and find good agreement with the experimental measurements of the distribution of trap occupancy times. The major cause of trap loss arises from the broadening of the energy distribution of the trapped atom, rather than the mean heating rate, which is a very much smaller effect.
A Fokker-Planck equation is derived for the energy distribution of atoms in a three-dimensional harmonic trap with fluctuations in the spring constant and the equilibrium position. Using this model, we predict trap lifetimes based on the measurable noise spectra of the fluctuations. The energy distributions evolve into a single eigenmode where the apparent temperature of the distribution remains constant while the population decays as a consequence of the energy input. The method of analysis and the corresponding results are applicable to any optical, magnetic, or ion trap that is approximately harmonic, and offer useful insights into both noise-induced and optical heating processes.
We have investigated motional heating of laser-cooled 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes. The results show that heating is due to electric-field noise from the trap electrodes that exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.
We experimentally and theoretically study the origin of heating in optical lattices by disentangling the respective roles of intensity and phase noise depending on the lattice parameters. While intensity noise is widely identified as a major limiting factor, we show that phase noise can become the dominant heating source, especially for light atoms and deep optical lattices. We provide a simple theoretical framework to predict the phase-noise-induced heating from the power spectral density of the laser phase noise, which can be measured experimentally. We show that such predictions can accurately reproduce the measured heating rates of lithium-6 atoms in a triangular lattice. Our approach is readily generalized to other lattice geometries and atomic species.
We discuss heating and decoherence in traps for ions and neutral particles close to metallic surfaces. We focus on simple trap geometries and compute noise spectra of thermally excited electromagnetic fields. If the trap is located in the near field of the substrate, the field fluctuations are largely increased compared to the level of the blackbody field, leading to much shorter coherence and life times of the trapped atoms. The corresponding time constants are computed for ion traps and magnetic traps. Analytical estimates for the size dependence of the noise spectrum are given. We finally discuss prospects for the coherent transport of matter waves in integrated surface waveguides.