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Physical Review A

Simulation of laser cooling by the bichromatic force

Xiang Hua, Christopher Corder, Harold J. Metcalf

Published Jun 10, 2016• 4 citations
Publisher

Abstract

The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.

DOI
10.1103/physreva.93.063410

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The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.
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.
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.
The spontaneous decay rate $\ensuremath{\gamma}$ of excited atomic states limits the radiative force on atoms to $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2.$ This bottleneck in the dissipative exchange of momentum between atoms and light can be overcome by coherent control of the momentum exchange interactions. The bichromatic force provides such control by using stimulated instead of spontaneous emission to produce the force, while at the same time exploiting spontaneous emission to enable a dissipative interaction. It is implemented with two counterpropagating light beams, each containing two frequencies, whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
Optical forces using lasers allow precise control over the motion of atoms. The bichromatic optical force (BF) is unique in its large magnitude and velocity range, arising from the absorption and stimulated emission processes. These properties were used to transversely collimate a beam of metastable helium (He∗ ) using the 2^{3}S − 2^{3}P transition. The collimation created a very bright beam of He∗ , allowing experiments of neutral atom lithography. The He∗ beam was used to pattern material surfaces using a resist-based lithography technique, where the pattern was determined by either mechanical or optical masks. The optical masks produced features with a separation of half the wavelength of the light used. Patterning was successfully demonstrated with both IR and UV optical masks. The etched pattern resolution was ∼ 100 nm and limited by the material surface. Further experiments were performed studying the ability of the bichromatic force to cool. The finite velocity range of the BF allows estimation of a characteristic cooling time which is independent of the excited state lifetime, only depending on the atomic mass and optical transition energy. Past experiments, including the helium collimation used for neutral atom lithography, have demonstrated that the BF can collimate and longitudinally slow atomic beams, but required long interaction times that included many spontaneous emission (SE) events. The effect of SE can be mitigated, and is predicted to not be necessary for BF cooling. Since the BF cooling time is not related to the excited state lifetime, a transition can be chosen such that the cooling time is shorter than the SE cycle time, allowing direct laser cooling on atoms and molecules that do not have cycling transitions. Experiments using the helium 2^{3}S− 3^{3}P transition were chosen because the BF cooling time (285 ns) is on the order of the average SE cycle time (260 ns). Numerical simulations of the experimental system were run predicting compression of the atomic velocity distribution. Our experimental results demonstrate the stimulated nature of the force through many atomic recoils from the light in less than one SE cycle time. A large range of the atomic velocity distribution is accelerated and accumulates at the velocity limit of the force. This accumulation results in an increase in the velocity space density, demonstrating cooling. | 112 pages
For cold samples of laser-cooled atoms to be useful in emerging technologies such as compact atomic clocks and sensors, it is necessary to achieve small sample sizes while retaining a large number of cold atoms. Achieving large atom numbers in a small system is a major challenge for producing miniaturized laser-cooled atomic clocks, since the number of captured atoms in a vapor-cell magneto-optical trap (MOT) scales as the fourth power of the laser beam diameter. This strong dependence on size is fundamentally set by the maximum spontaneous light force ħkγ/2, where ħk is the photon momentum and γ/2 is the maximum spontaneous photon scatter rate of a saturated transition of linewidth γ. We are attempting to surmount the limit imposed by spontaneous emission by using bichromatic cooling - a technique that uses stimulated emission to slow the atoms. We have built a table-top experiment that uses stimulated-emission bichromatic cooling to pre-cool rubidium atoms and dramatically enhance the trappable atom number in a small MOT. The apparatus lets us test how bichromatic cooling scales with miniaturization. Here we report on our first experimental results of cooling a thermal beam of rubidium atoms down to MOT capture velocities.