Bose–Einstein condensation can occur in quasiparticles, particles that are effective descriptions of collective excitations in materials. Some have integer spins and can be expected to obey Bose–Einstein statistics like traditional particles. Conditions for condensation of various quasiparticles have been predicted and observed. The topic continues to be an active field of study.
Contents
Properties
BECs form when low temperatures cause nearly all particles to occupy the lowest quantum state. Condensation of quasiparticles occurs in ultracold gases and materials. The lower masses of material quasiparticles relative to atoms lead to higher BEC temperatures. An ideal Bose gas has a phase transitions when inter-particle spacing approaches the thermal De-Broglie wavelength:
The Bose gas can be considered in a harmonic trap,
This can be achieved by cooling and magnetic or optical control of the system. Spectroscopy can detect shifts in peaks indicating thermodynamic phases with condensation. Quasiparticle BEC can be superfluids. Signs of such states include spatial and temporal coherence and polarization changes. Observation for excitons in solids was seen in 2005 and for magnons in materials and polaritons in microcavities in 2006. Graphene is another important solid state system for studies of condensed matter including quasi particles; It's a 2D electron gas, similar to other thin films.
Excitons
Excitons are electron-hole pairs. Similar to helium-4 superfluidity at the
Theory
Excitions results from photons exciting electrons creating holes, which are then attracted and can form bound states. The 1s paraexciton and orthoexciton are possible. The 1s triplet spin state, 12.1meV below the degenerate orthoexciton states(lifetime ~ns), is decoupled and has a long lifetime to an optical decay. Dilute gas densities (n~1014cm−3) are possible, but paraexcition generation scales poorly, so significant heating occurs in creating high densities(1017cm−3) preventing BECs. Assuming a thermodynamic phase occurs when separation reaches the de Broglie wavelength(
Where,
Experiments
In an ultrapure Cu2O crystal:
Magnons
Magnons, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic ordering is the analog of superfluidity. The condensate appears as the emission of monochromatic microwaves, which are tunable with the applied magnetic field.
In 1999 condensation was demonstrated in antiferromagnetic TlCuCl3, at temperatures as large as 14 K. The high transition temperature (relative to atomic gases) is due to the small mass (near an electron) and greater density. In 2006, condensation in a ferromagnetic Yttrium-iron-garnet thin film was seen even at room temperature with optical pumping. Condensation was reported in gadolinium in 2011. Magnon BECs have been considered as qubits for quantum computing.
Polaritons
Polaritons, caused by light coupling to excitons, occur in optical cavities and condensation of exciton-polaritons in a optical microcavity was first published in Nature in 2006. Semiconductor cavity polariton gases transition to ground state occupation at 19K. Bogoliubov excitations were seen polariton BECs in 2008. The signatures of BEC were observed at room temperature for the first time in 2013, in a large exciton energy semiconductor device and in a polymer microcavity.
Other quasiparticles
Rotons, an elementary excitation in superfluid 4He introduced by Landau, were discussed by Feynman and others. Rotons condense at low temperature. Experiments have been proposed and the expected spectrum has been studied, but roton condensates have not been detected. Phonons were first observed in a condensate in 2004 by ultrashort pulses in a bismuth crystal at 7K.