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.
BECs form when low temperatures cause nearly all particles to occupy the lowest quantum state.
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 particles obey the Bose–Einstein distribution and all occupy the ground state: The Bose gas can be considered in a harmonic trap,
, with the ground state occupancy fraction as a function of temperature: 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.
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.
[6] Experimental phenomenon were predicted leading to various pulsed laser searches that failed to produce evidence.
Excitons results from photons exciting electrons creating holes, which are then attracted and can form bound states.
Assuming a thermodynamic phase occurs when separation reaches the de Broglie wavelength(
[7] A potential well limits diffusion, damps exciton decay, and lowers the critical number, yielding an improved critical temperature versus the T3/2 scaling of free particles: In an ultrapure Cu2O crystal:
[8] More detailed calculations by J. Keldysh[9] and later by D. Snoke et al.[10] started a large number of experimental searches into the 1990s that failed to detect signs.
Helium cooling allows mili-kelvin setups and continuous wave optics improves on pulsed searches.
Relaxation explosion of a condensate at lattice temperature 354 mK was seen by Yoshioka et al. in 2011.
[14] Recent experiments by Stolz et al. using a potential trap have given more evidence at ultralow temperature 37 mK.
[7] In a parabolic trap with exciton temperature 200 mK and lifetime broadened to 650ns, the dependence of luminescence on laser intensity has a kink which indicates condensation.
Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible.
The condensate appears as the emission of monochromatic microwaves, which are tunable with the applied magnetic field.
In 2006, condensation in a ferromagnetic Yttrium-iron-garnet thin film was seen even at room temperature[17][18] with optical pumping.
[21] Semiconductor cavity polariton gases transition to ground state occupation at 19K.
[22] The signatures of BEC were observed at room temperature for the first time in 2013, in a large exciton energy semiconductor device [23][24] and in a polymer microcavity.
[25] BECs of plasmonic excitations (surface lattice resonances, SLRs) and their dye-coupled quasiparticles (plasmon-exciton polaritons) have been realized in periodic arrays of metal nanoparticles overlaid with dye molecules.
The first demonstration was achieved having the SLRs weakly coupled to dye molecules, facilitating thermalization by emission and re-absorption process.
Further increasing the molecule concentration led to the realization of BECs of strongly coupled exciton-polaritons, exhibiting ultrafast sub-picosecond thermalization dynamics[27] and long-range correlations[28].
Rotons, an elementary excitation in superfluid 4He introduced by Landau,[29] were discussed by Feynman[30] and others.
Experiments have been proposed and the expected spectrum has been studied,[32][33][34] but roton condensates have not been detected.