NOVEL PHASES FOR BOSE GASES
Strongly correlated electronic systems, like superconductors, display remarkable electronic and magnetic properties, and are of considerable research interest. These systems are fermionic, meaning they are composed of a class of particle called a fermion. Bosonic systems, composed another family of particles called bosons, offer a level of control often not possible in solid state systems. Creating analogous states in bose gases is an excellent way to model the dynamics of these less tractable systems. This means engineering a gas that, when cooled down to a condensate, assumes a phase equivalent to its solid state counterpart.
JQI theorists Juraj Radic, Stefan Natu, and Victor Galitski have proposed a new magnetic phase for a bose gas. The transition to this phase is analogous to the formation of ferromagnetism in magnetic materials, like iron, and might give insight into the physics of strongly-correlated electronic systems.
“One of the basic motivations we had is: how can we frustrate Bose Condensation to produce more exotic bosonic states of matter?” explains Stefan Natu, a postdoctoral fellow at the JQI. Although this can be difficult to do in ultracold gases, creating new phases for other sorts of matter is part of everyday life, whether heating water to make soup or cooling a drink with ice. The shift from one phase to another, like water into steam, is called a phase transition.
Phase transitions happen all around us, as energy flows in and out of physical systems. For instance, water molecules assume different phases based on temperature and pressure.
Generically, phase transitions occur when there are competing elements in a system. As an ice cube warms up, competition between the kinetic energy of individual water molecules and weak hydrogen bonding between molecules determines whether the ice retains its crystalline structure or melts into a puddle.
Phase transitions between solid, liquid, and gas are perhaps the most familiar in day-to-day observations. These examples signify a change in the long-distance order. Other properties of a system can also change dramatically, resulting in different types of phases. For example, take a dilute gas of atoms. This gas behaves as a normal gas, like air, over a wider range of temperatures. However, at temperatures near absolute zero, the gas suddenly undergoes a phase transition to form of correlated quantum matter called a Bose-Einstein condensate (BEC). Really, a phase transition happens any time one stable physical description of a system is substituted for another.
One way of thinking about phases is that a system has a number of latent properties, and based on the external conditions one property or another will dominate and become apparent. One neat aspect of the particular example of the BEC and of many other systems is that lower temperatures in general can sort of freeze out thermal, non-quantum behavior, allowing physicists to explore the quantum world. Ultracold gases can achieve some remarkable phases, where quantum effects dominate, and are often in multiple phases simultaneously depending on the arrangement and composition of the gas.
Similiar but not identical to Bose-Einstein condensation, superfluidity is a state of matter where atoms flow without resistance, similiar to the movement of electrons in a superconductor. A superfluid can even defy gravity and flow upward out of a vessel that contains it.
A Bose-Einstein condensate forms when temperatures are cold enough that atoms in a bose gas assume the same lowest-energy quantum state. This happens just barely above absolute zero, the point where motion is arrested entirely.
A FEW PHASES of ULTRACOLD GASES
By focusing beams of light to form an optical lattice, researchers can coax a cold gas into a periodic pattern, emulating the crystal structure of a solid. In a really deep optical lattice, the condensate undergoes a transition from a superfluid to a Mott insulating phase, where the number of atoms residing in each well of the lattice is known to high precision.
These gases are extremely useful research tools, not only for exploring fundamental physics, but also for emulating the properties of other systems. Many solid state systems are difficult to probe experimentally, due to inherent noise. Complementary models composed of cold atoms offer a high level of control and in some cases tunable parameters that are often not accessible with electrons in solids.
These models depend on placing the gas into a phase analogous with that of the solid. So how did the researchers introduce new phases? As with the ice cube example, there needs to be competing terms in the system, which will lead to a phase transition when one term dominates over the other. In many experiments a BEC is composed of identical particles, and will transition into a normal gas that behaves similar to air when heated. In order to uncover more interesting transitions, the theorists introduced competing terms into the system by replacing a uniform bose gas with one composed of two different variations of an atom, spin-up and spin-down — here the spins interact differently depending on their orientation.
Spin refers to two distinct internal energy states of the atoms. Atomic spins act like little bar magnets, with spin-up corresponding to magnetic north pointing in one direction and spin-down corresponding to north pointing in the opposite direction.
Analogous to magnets, atoms with opposite spin orientations can either attract, moving towards each other, or repel and fly apart. The researchers found that the sign and strength of these interactions, as well as the temperature of the gas, determine the phase of the entire system.
When atoms with opposing spins attract with sufficient energy, they move towards each other. When this happens, the spin-up and spin-down atoms are in a superposition, represented in the graphic above by red and blue averaging to purple. This combined spin is oriented in the horizontal direction, an arrangement known as a transverse ferromagnet (TFM) since the gas is magnetized horizontal to the direction the spins are pointing.
When atoms with opposing spins repel with enough energy, they separate into regions of uniform spin, as depicted in the graphic above. Since in each region the spin bar magnets are all aligned in the same direction, there is some global magnetization for that region. This is analogous to what happens in a magnetizable metal like iron, where an applied magnetic field causes electron spins, which behave like little bar magnets, to become aligned to the magnetic field. Since spins are usually thought of as pointing “up” or “down”, this particular arrangement is known as a z-ferromagnet, since the polarization point upward along the z axis.
With the addition of the spin interactions described above, the system now has competing parameters: there are spin-dependant interactions between atoms, condensation (or lack thereof) due to temperature, density, etc. In whole, this is a mixture ripe for some interesting transitions. So what happens when temperature varies? “As the system is cooled, it has to make a decision: do I want to be a bose condensate, or a magnetized bose condensate, etc,” explains Natu. “Usually when a system is in this state of existential crisis, that is when it picks out new interesting phases."
“Usually when a system is in this state of existential crisis, that is when it picks out new interesting phases.”
The research group performed calculations to see just what descisions the gas would make. The result is a new phase diagram, illustrating the various states and transitions of the system. A phase diagram is a map of sorts for scientists, an extremely useful tool for navigating through the universe of possible states a system can assume.
The calculated phase diagram of the two-component bose gas. The vertical direction is temperature and the horizontal spin interaction strength. Each labeled region represents a different phase, with phase transitions occurring at the black boundary lines. Click below to view the regions.
For zero to small repulsive interaction strength, the bose gas is a normal gas, like air. This means that the atoms are mixed more or less uniformly (no spin separation) and have not condensed into a single state.
At sufficiently low temperatures, the gas condenses into a Bose-Einstein condensate. The bottom of the diagram (lowest temperature displayed) is the critical temperature for a BEC: below this temperature the gas is entirely in a condensed state, regardless of inter-spin interactions.
At the right combinations of temperature and attractive interaction, opposing spins are drawn towards each other. This forms regions of magnetization in the horizontal direction, called transverse ferromagnetism. The gas is now a magnetized bose gas.
Similarly, repulsive interactions of sufficient strength results in spin separation and spin-polarized regions. This means that the bose gas is now magnetized in the z-direction, known as a z-ferromagnet.