Laser Cooling

Starting in about 1985 with the work of Steven Chu and others, the use of lasers to achieve extremely low temperatures has advanced to the point that temperatures of 10^-9 K have been reached. If an atom is traveling toward a laser beam and absorbs a photon from the laser, it will be slowed by the fact that the photon has momentum p = E/c = h/λ. If we take a sodium atom as an example, and assume that a number of sodium atoms are freely moving in a vacuum chamber at 300K, the rms velocity of a sodium atom from the Maxwell speed distribution would be about 570 m/s. Then if a laser is tuned just below one of the sodium d-lines (589.0 and 589.6 nm, about 2.1 eV), a sodium atom traveling toward the laser and absorbing a laser photon would have its momentum reduced by the amount of the momentum of the photon. It would take a large number of such absorptions to cool the sodium atoms to near 0K since one absorption would slow a sodium atom by only about 3 cm/s out of a speed of 570 m/s. A straight projection requires almost 20,000 photons to reduce the sodium atom momentum to zero. The change in speed from the absorption of one photon can be calculated from

大约从1985年开始，Steven Chu等人工作的开始，利用激光实现极低温的技术已经发展到可以达到10⁻⁹ K的温度。如果一个原子正对着激光束运动并吸收一个激光光子，它会因为光子具有动量p = E/c = h/λ而减速。以钠原子为例，假设一些钠原子在真空腔内自由运动，温度为300K，根据麦克斯韦速度分布，钠原子的均方根速度约为570 m/s。如果激光调谐到钠的一个D线（589.0和589.6 nm，约2.1 eV）之下，一个向激光运动并吸收激光光子的钠原子，其动量将减少光子动量的量。要将钠原子冷却到接近0K，需要大量的此类吸收，因为一次吸收只会使钠原子速度减少约3 cm/s，而其速度为570 m/s。要使钠原子动量减少到零，几乎需要20,000个这样的吸收。一次光子吸收导致的速度变化可以从

Δp/p = p photon /mv = Δv/v Δv = p photon /m（专名或术语）

That seems like a lot of photons, but according to Chu, a laser can induce on the order of 10⁷ absorptions per second so that an atom could be stopped in a matter of milliseconds.

那似乎有很多光子，但根据楚的说法，激光每秒可以引起约10⁷次吸收，因此一个原子可以在毫秒内被停止。

A conceptual problem is that an absorption can also speed up an atom if it catches it from behind, so it is necessary to have more absorptions from head-on photons if your goal is to slow down the atoms. This is accomplished in practice by tuning the laser slightly below the resonance absorption of a stationary sodium atom. From the atom's perspective, the headon photon is seen as Doppler shifted upward toward its resonant frequency and it therefore more strongly absorbed than a photon traveling in the opposite direction which is Doppler shifted away from the resonance. In the case of our room temperature sodium atom above, the incoming photon would be Doppler shifted up 0.97 GHz, so to get the head on photon to match the resonant frequency would require that the laser be tuned below the resonant peak by that amount. This method of cooling sodium atoms was proposed by Theodore Hansch and Arthur Schawlow at Stanford University in 1975 and achieved by Chu at AT&T Bell Labs in 1985. Sodium atoms were cooled from a thermal beam at 500K to about 240 mK. The experimental technique involved directing laser beams from opposite directions upon the sample, linearly polarized at 90° with respect to each other. Six lasers could then provide a pair of beams along each coordinate axis. The effectively "viscous" effect of the laser beams in slowing down the atoms was dubbed "optical molasses" by Chu.

一个概念性的问题是，如果一个光子从后面捕捉到原子，它也能加快原子的速率。因此，如果你的目标是减慢原子，就需要有更多来自正面碰撞的光子吸收。这在实践中是通过将激光略微调谐到静止钠原子的共振吸收频率以下来实现的。从原子的角度来看，正面碰撞的光子会被多普勒上移，接近其共振频率，因此比从相反方向来的光子（其多普勒频移远离共振频率）更容易被吸收。在我们上面提到的室温钠原子情况下，入射光子会被多普勒上移0.97 GHz，因此要让正面碰撞的光子与共振频率匹配，就需要将激光调谐到共振峰以下这个量。这种冷却钠原子的方法于1975年由斯坦福大学的Theodore Hansch和Arthur Schawlow提出，并于1985年由Chu在AT&T Bell Labs实现。钠原子从热束中被冷却至约240 mK。实验技术涉及将激光束从相反方向照射到样品上，两束激光线性极化，相互垂直。六束激光可以分别提供沿每个坐标轴的两束光。激光束对原子的“粘滞”效应被Chu称为“光学粘滞”或“光学粘液”。

Continuing to cool the sodium atoms by this method requires the tuning of the laser upward in frequency toward the atomic resonant frequency because the Doppler shift will be smaller. This places a practical limit on how much cooling can be achieved, because the differential cooling rate is reduced and at a certain point the cooling mechanism is foiled by heating due to the random absorption and reemission of photons. This practical limit is characterized by 2kT = E_{resonant photon}, which at the low temperature of 240 mK would correspond to photon energies around 4 x 10^-8 eV. Such energies can characterize the Zeeman split energy levels of the atoms in the magnetic fields produced by the laser photons.

继续通过这种方法冷却钠原子，需要将激光频率调谐向上，接近原子共振频率，因为多普勒效应会减小。这在实际中限制了可以实现的冷却程度，因为冷却速率的差异减小，并且在某个点，由于光子的随机吸收和再发射导致加热，冷却机制被破坏。这个实际限制由 2kT = E resonant photon 表征，而在 240 mK 的低温下，这对应于光子能量约为 4 x 10 -8 eV。这样的能量可以表征由激光光子产生的磁场中原子的塞曼分裂能级。

It was found that the splittings which limited the original laser cooling processes could be exploited to lower the ultimate temperatures below these limits. With the opposing laser beams with perpendicular linear polarization, atoms could be selectively driven or "optically pumped" into the lower energy levels. These lasers create a small region of space about a quarter wavelength in extent where the atoms can drift to a region where their energy is relatively higher, only to be pumped downward to a lower energy again. This was dubbed "Sisyphus cooling" after the legendary tormented man who was condemned to perpetually roll a rock up a hill, only to have it roll down again. With the "optical molasses" and the polarization gradient in the region of opposing laser beams, temperatures as low as 35 mK for sodium and 3 mK for cesium were obtained.

发现限制原始激光冷却过程的分裂可以被利用以将最终温度降低到这些限制以下。使用相互垂直线偏振的反向激光束，原子可以被选择性地驱动或‘光学泵’到较低的能量水平。这些激光在大约四分之一波长的区域内创造一个小空间，原子可以漂移到一个能量相对较高的区域，然后再被泵回较低的能量水平。这一现象被称作‘西西弗斯冷却’，这是向传说中永无止境地推滚岩石上山的受苦者西西弗斯致敬。借助‘光学糖浆’和反向激光束区域中的偏振梯度，可以达到钠原子35 mK和铯原子3 mK的极低温。