Quasiparticles in quantum many-body systems have essential roles in modern physical problems. Bose–Einstein condensation (BEC) of excitons in semiconductors is one of the unobserved quantum statistical phenomena predicted in the photoexcited quasiparticles in many-body electrons. In particular, para-excitons in cuprous oxide have been studied for decades because the decoupling from the radiation field makes the coherent ensemble a purely matter-like wave. However, BEC has turned out to be hard to realize at superfluid liquid helium-4 temperatures due to a two-body inelastic collision process. It is therefore essential to set a lower critical density by further lowering the exciton temperature. Here we cool excitons to sub-Kelvin temperature and spatially confine them to realize the critical number for BEC. We show that BEC manifests itself as a relaxation explosion as has been discussed in atomic hydrogen. The results indicate that dilute excitons are purely bosonic and BEC indeed occurs. Bose–Einstein condensation of excitons in thermal equilibrium is a predicted quantum statistical phenomenon that has been difficult to observe. Yoshiokaet al. cool trapped excitons to sub-Kelvin temperatures and show that condensation manifests itself as a relaxation explosion as has been observed for atomic hydrogen.
Quasiparticles in quantum many-body systems have essential roles in modern physical problems. Bose–Einstein condensation (BEC) of excitons in semiconductors is one of the unobserved quantum statistical phenomena predicted in the photoexcited quasiparticles in many-body electrons. In particular, para-excitons in cuprous oxide have been studied for decades because the decoupling from the radiation field makes the coherent ensemble a purely matter-like wave. However, BEC has turned out to be hard to realize at superfluid liquid helium-4 temperatures due to a two-body inelastic collision process. It is therefore essential to set a lower critical density by further lowering the exciton temperature. Here we cool excitons to sub-Kelvin temperature and spatially confine them to realize the critical number for BEC. We show that BEC manifests itself as a relaxation explosion as has been discussed in atomic hydrogen. The results indicate that dilute excitons are purely bosonic and BEC indeed occurs. Bose–Einstein condensation of excitons in thermal equilibrium is a predicted quantum statistical phenomenon that has been difficult to observe. Yoshiokaet al. cool trapped excitons to sub-Kelvin temperatures and show that condensation manifests itself as a relaxation explosion as has been observed for atomic hydrogen.
We present our recent experimental studies on anomalous luminescence and its connection to Bose–Einstein condensation (BEC) transition of dark excitons in a bulk semiconductor. Our sensitive and quantitative detection of this nonluminous quasi-particle using hydrogen-like internal transitions allows obtaining continuous spectra of dark excitons using a quantum cascade laser. According to quantitative measurements on the two-body inelastic collision cross section of excitons, the system needs to be cooled to sub-Kelvin temperatures. We discuss in detail our recent observation of an explosive phenomenon when the BEC criterion is satisfied (Yoshioka et al 2011 Nature Commun . 2 328) for trapped excitons using a helium-3 refrigerator, and outline a plausible scenario when the BEC transition occurs in an inelastic environment. We also discuss how to increase the condensate fraction in order to study the unique ground state of many-body electric excitations in solids.
Abstract An unambiguous observation of the Bose-Einstein condensation (BEC) of excitons in a photoexcited bulk semiconductor and elucidation of its inherent nature have been longstanding problems in condensed matter physics. Here, we observe the quantum phase transition and a Bose-Einstein condensate appearing in a trapped gas of 1s paraexcitons in bulk Cu2O below 400 mK, by directly visualizing the exciton cloud in real space using mid-infrared induced absorption imaging that we realized in a dilution refrigerator. Our study shows that the paraexciton condensate is undetectable by conventional luminescence spectroscopy. We find an unconventionally small condensate fraction of 0.016 with the spatial profile of the condensate well described by mean-field theory. Our discovery of this new type of BEC in the purely matter-like exciton system interacting with a cold phonon bath could pave the way for the classification of its long-range order, and for essential understanding of quantum statistical mechanics of non-equilibrium open systems.
Summary form only given. In the dilute limit excitons behave as weakly interacting Bose particles and are expected to undergo the Bose-Einstein condensation (BEC). Because the exciton mass is very small at experimentally accessible exciton densities the critical temperature for exciton BEC should reach several Kelvins, i.e., about six orders of magnitude higher than the T/sub c/ for atom BEC. To create degenerate Bose-gas of excitons we propose quasi-2D gas of indirect excitons in coupled quantum wells (CQWs) which have two primary advantages for realizing a quantum degenerate exciton gas and, ultimately, the BEC-like phase transition: (i) the long lifetime of indirect excitons and (ii) the short exciton cooling time.
Physics
A fascinating property of the quantum world is that particles come equipped with a dual, wavelike nature, which becomes apparent at low temperatures and high densities. For a certain type of particle, bosons, this results in the formation of a giant wave, a Bose-Einstein condensate (BEC). BECs have been realized in laser-trapped ultracold gases of alkali elements, but bosons that exist elsewhere in nature are also expected to condense. An exciton is a composite boson consisting of an electron and a hole (a missing electron) in a semiconductor. High et al. take a page out of the atomic physicists' book and demonstrate the condensation of excitons in a trap. A spatially varying electric field traps the excitons' dipole moments, which are nonzero because of the spatial separation of electrons and holes in a GaAs/AlGaAs coupled quantum well (such so-called indirect excitons also have the advantage of a long lifetime necessary for cooling). When the temperature is lowered below ~2 K, the excitons collect at the trap center, and the entire trap volume becomes coherent, signifying the onset of a BEC. The realization of a BEC in a trapped semiconductor system is expected to enable explorations complementary to those possible with ultracold atomic gases.
Nano Lett. 12 , 10.1021/nl300983n (2012).
Bose–Einstein condensation is a phenomenon, first proved by Einstein, in which a gas of bosons condenses into the lowest quantum state below a certain critical temperature. It occurs due to the symmetry, under particle exchange, of the boson wave function. The chapter discusses temperature, the Kelvin scale, the concept of absolute zero, and how laser cooling can reach ultralow temperatures. The property of bosons in which they often prefer to be in the same state is seen to apply to lasers, superfluid liquid helium, and to dilute nearly ideal gases. The latter are trapped in magnetic or optical potential wells where the condensation can be observed directly. These large condensate matter waves show quantum interference in a variety of possible experiments.
As was shown by Einstein in 1924, Bose-Einstein statistics gives rise to a phase transition in which a macroscopic part of a gaseous state condenses into a phase with ground state properties, offering a unique view on the behavior of matter at zero temperature. From the very start the nature of Bose-Einstein condensation (BEC) has provoked statements concerning its relation with respect to superconductivity in electron gases (Einstein 1925) and the superfluidity of liquid helium (London 1938), but this connection is not easily grasped experimentally. Remarkably, although the concept of BEC appears routinely in very different contexts, ranging from excitons in semiconductors to nuclear matter, it had never been observed in its pure form, i.e., in a gaseous phase, until in 1995 BEC in ultracold Rb vapor was reported by Cornell and Wieman. Bose-Einstein condensation is probably the most exciting phenomenon currently under experimental investigation in ultracold atomic gases. In the tutorial the physics will be addressed which is at the roots of the current interest of BEC in atomic gases.