Section 7: Atom Cooling and Trapping
The discovery that laser light can cool atoms to less than a millionth of a degree above absolute zero opened a new world of quantum physics. Previously, the speeds of atoms due to their thermal energy were always so high that their de Broglie wavelengths were much smaller than the atoms themselves. This is the reason why gases often behave like classical particles rather than systems of quantum objects. At ultra-low temperatures, however, the de Broglie wavelength can actually exceed the distance between the atoms. In such a situation, the gas can abruptly undergo a quantum transformation to a state of matter called a Bose-Einstein condensate. The properties of this new state are described in Unit 6. In this section, we describe some of the techniques for cooling and trapping atoms that have opened up a new world of ultracold physics. The atom-cooling techniques enabled so much new science that the 1997 Nobel Prize was awarded to three of the pioneers: Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips.
Figure 26: Recipients of the 1997 Nobel Prize, for laser cooling and trapping of atoms.
Source: © Left: Steven Chu, Stanford University; Middle: Claude Cohen-Tannoudji, Jean-Francois DARS, Laboratoire Kastler Brossel; Right: William D. Phillips, NIST. More info
As we learned earlier, a photon carries energy and momentum. An atom that absorbs a photon recoils from the momentum kick, just as you experience recoil when you catch a ball. Laser cooling manages the momentum transfer so that it constantly slows the atom's motion, slowing it down. In absorbing a photon, the atom makes a transition from its ground state to a higher energy state. This requires that the photon has just the right energy. Fortunately, lasers can be tuned to precisely match the difference between energy levels in an atom. After absorbing a photon, an atom does not remain in the excited state but returns to the ground state by a process called spontaneous emission, emitting a photon in the process. At optical wavelengths, the process is quick, typically taking a few tens of nanoseconds. The atom recoils as it emits the photon, but this recoil, which is opposite to the direction of photon emission, can be in any direction. As the atom undergoes many cycles of absorbing photons from one direction followed by spontaneously emitting photons in random directions, the momentum absorbed from the laser beam accumulates while the momentum from spontaneous emission averages to zero.
Figure 27: Temperature scale in physics
This diagram of temperatures of interest in physics uses a scale of factors of 10 (a logarithmic scale). On this scale, the difference between the Sun's surface temperature and room temperature is a small fraction of the range of temperatures opened by the invention of laser cooling. Temperature is in the Kelvin scale at which absolute zero would describe particles in thermal equilibrium that are totally at rest. The lowest temperature measured so far by measuring the speeds of atoms is about 450 picokelvin (one picokelvin is 10-12 K). This was obtained by evaporating atoms in a Bose-Einstein condensate.
The process of photon absorption followed by spontaneous emission can heat the atoms just as easily as cool them. Cooling is made possible by a simple trick: Tune the laser so that its wavelength is slightly too long for the atoms to absorb. In this case, atoms at rest cannot absorb the light. However, for an atom moving toward the laser, against the direction of the laser beam, the wavelength appears to be slightly shortened due to the Doppler effect. The wavelength shift can be enough to permit the atom to absorb the light. The recoil slows the atom's motion. To slow motion in the opposite direction, away from the light source, one merely needs to employ a second laser beam, opposite to the first. These two beams slow atoms moving along a single axis. To slow atoms in three dimensions, six beams are needed (Figure 28). This is not as complicated as it may sound: All that is required is a single laser and mirrors.
Figure 28: Red-detuned lasers don't affect an atom at rest (left) but will slow an atom moving toward the light source (right).
Source: © Daniel Kleppner. More info
Laser light is so intense that an atom can be excited just as soon as it gets to the ground state. The resulting acceleration is enormous, about 10,000 times the acceleration of gravity. An atom moving with a typical speed in a room temperature gas, thousands of meters per second, can be brought to rest in a few milliseconds. With six laser beams shining on them, the atoms experience a strong resistive force no matter which way they move, as if they were moving in a sticky fluid. Such a situation is known as optical molasses.
As one might expect, laser cooling cannot bring atoms to absolute zero. The limit of Doppler cooling is actually set by the uncertainty principle, which tells us that the finite lifetime of the excited state due to spontaneous emission causes an uncertainty in its energy. This blurring of the energy level causes a spread in the frequency of the optical transition called the natural linewidth. When an atom moves so slowly that its Doppler shift is less than the natural linewidth, cooling comes to a halt. The temperature at which this occurs is known as the Doppler cooling limit. The theoretical predictions for this temperature are in the low millikelvin regime. However, by great good luck, it turned out that the actual temperature limit was lower than the theoretical prediction for the Doppler cooling limit. Sub-Doppler cooling, which depends on the polarization of the laser light and the spin of the atoms, lowers the temperature of atoms down into the microkelvin regime.
Like all matter, ultracold atoms fall in a gravitational field. Even optical molasses falls, though slowly. To make atoms useful for experiments, a strategy is needed to support and confine them. Devices for confining and supporting isolated atoms are called "atom traps." Ultracold atoms cannot be confined by material walls because the lowest temperature walls might just as well be red hot compared to the temperature of the atoms. Instead, the atoms are trapped by force fields. Magnetic fields are commonly used, but optical fields are also employed.
Magnetic traps depend on the intrinsic magnetism that many atoms have. If an atom has a magnetic moment, meaning that it acts as a tiny magnet, its energy is altered when it is put in a magnetic field. The change in energy was first discovered by examining the spectra of atoms in magnetic fields and is called the Zeeman effect after its discoverer, the Dutch physicist Pieter Zeeman.
Because of the Zeeman effect, the ground state of alkali metal atoms, the most common atoms for ultracold atom research, is split into two states by a magnetic field. The energy of one state increases with the field, and the energy of the other decreases. Systems tend toward the configuration with the lowest accessible energy. Consequently, atoms in one state are repelled by a magnetic field, and atoms in the other state are attracted. These energy shifts can be used to confine the atoms in space.
Figure 29: Atoms trapped in a MOT.
Source: © Martin Zwierlein. More info
The magneto-optical trap, or MOT, is the workhorse trap for cold atom research. In the MOT, a pair of coils with currents in opposite direction creates a magnetic field that vanishes at the center. The field points inward along the z-axis but outward along the x- and y-axes. Atoms in a vapor are cooled by laser beams in the same configuration as optical molasses, centered on the midpoint of the system. The arrangement by itself could not trap atoms because, if they were pushed inward along one axis, they would be pushed outward along another. However, by employing a trick with the laser polarization, it turns out that the atoms can be kept in a state that is pushed inward from every direction. Atoms that drift into the MOT are rapidly cooled and trapped, forming a small cloud near the center.
To measure the temperature of ultracold atoms, one turns off the trap, letting the small cloud of atoms drop. The speeds of the atoms can be found by taking photographs of the ball and measuring how rapidly it expands as it falls. Knowing the distribution of speeds gives the temperature. It was in similar experiments that atoms were sometimes found to have temperatures below the Doppler cooling limit, not in the millikelvin regime, but in the microkelvin regime. The reason turned out to be an intricate interplay of the polarization of the light with the Zeeman states of the atom causing a situation known as the Sisyphus effect. The experimental discovery and the theoretical explanation of the "Sisyphus effect" were the basis of the Nobel Prize to Chu, Cohen-Tannoudji, and Phillips in 1997.
When the limit of laser cooling is reached, the old-fashioned process of evaporation can cool a gas further. In thermal equilibrium, atoms in a gas have a broad range of speeds. At any instant, some atoms have speeds much higher than the average, and some are much slower. Atoms that are energetic enough to fly out of the trap escape from the system, carrying away their kinetic energy. As the remaining atoms collide and readjust their speeds, the temperature drops slightly. If the trap is slowly adjusted so that it gets weaker and weaker, the process continues and the temperature falls. This process has been used to reach the lowest kinetic temperatures yet achieved, a few hundred picokelvin. Evaporative cooling cannot take place in a MOT because the constant interaction between the atoms and laser beams keeps the temperature roughly constant. To use this process to reach temperatures less than a billionth of a degree above absolute zero, the atoms are typically transferred into a trap that is made purely of magnetic fields.
Atoms in light beams experience forces even if they don't actually absorb or radiate photons. The forces are attractive or repulsive depending on whether the laser frequency is below or above the transition frequency. These forces are much weaker than photon recoil forces, but if the atoms are cold enough, they can be large enough to confine them. For instance, if an intense light beam is turned on along the axis of a MOT that holds a cloud of cold atoms, the MOT can be turned off, leaving the atoms trapped in the light beam. Unperturbed by magnetic fields or by photon recoil, for many purposes, the environment is close to ideal. This kind of trap is called an optical dipole trap.
Figure 30: Atoms trapped in an optical lattice.
Source: © NIST. More info
If the laser beam is reflected back on itself to create a standing wave of laser light, the standing wave pattern creates a regular array of areas where the optical field is strong and weak known as an optical lattice. Atoms are trapped in the regions of the strong field. If the atoms are tightly confined in a strong lattice and the lattice is gradually made weaker, the atoms start to tunnel from one site to another. At some point the atoms move freely between the sites. The situation is similar to the phase transition in a material that abruptly turns from an insulator into a conductor. This is but one of many effects that are well known in materials and can now be studied using ultracold atoms that can be controlled and manipulated with a precision totally different from anything possible in the past.
Why the excitement?
The reason that ultracold atoms have generated enormous scientific excitement is that they make it possible to study basic properties of matter with almost unbelievable clarity and control. These include phase transitions to exotic states of matter such as superfluidity and superconductivity that we will learn about in Unit 8, and theories of quantum information and communication that are covered in Unit 7. There are methods for controlling the interactions between ultracold atoms so that they can repel or attract each other, causing quantum changes of state at will. These techniques offer new inroads to quantum entanglement—a fundamental behavior that lies beyond this discussion—and new possibilities for quantum computation. They are also finding applications in metrology, including atomic clocks.