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Science

Watching Excitons Condense

Jelena Stajic

Published May 17, 2012• 0 citations
Publisher

Abstract

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).

DOI
10.1126/science.336.6083.780-c

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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).
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.
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.
The realization of Bose-Einstein Condensation (BEC) in dilute gases of ultracold atoms has revolutionized quantum physics by offering an unprecedented platform to study quantum phenomena on macroscopic scales. Ultracold atomic systems, cooled to temperatures near absolute zero, exhibit collective behaviors governed by quantum statistics, coherence, and interactions. This article discusses the theoretical and experimental frameworks underpinning the formation of BECs, focusing on the trapping, cooling, and coherence properties of ultracold bosonic gases. Further, we delve into the role of quantum phase transitions, atom-atom interactions, and external field manipulation in controlling condensate dynamics. The implications of BECs extend into precision measurements, quantum simulation, and quantum computing, positioning them as a cornerstone in modern atomic and condensed matter physics.
A Bose-Einstein condensate (BEC), the first of which was shown experimentally 22 years ago, isn’t your garden variety state of matter. It formed at a fraction above absolute zero and only in atoms that act like bosons, one of two types of fundamental particles. Bosons don’t follow the Pauli exclusion principle, which prohibits two particles from existing in the same quantum state. When bosonic atoms are cooled to form a condensate, they can lose their individuality. They behave like one big collective superatom, analogous to how photons become indistinguishable in a laser beam. But it’s even weirder than that. This velocity-distribution data for a gas of rubidium atoms confirmed the discovery of the Bose–Einstein condensate in 1995. In these three snapshots in time, atoms—cooled to near absolute zero—condensed from less dense areas on the left (red, yellow, and green) to very dense areas at the center and the right (blue and white). Image courtesy of NIST/JILA/CU-Boulder. “In a very good analogy, one can view a BEC as a bell, which begins to ring spontaneously when it is cooled below a certain temperature,” writes physicist Nick Proukakis at the Joint Quantum Centre Durham–Newcastle in the United Kingdom, in Universal Themes of Bose–Einstein Condensation , a forthcoming collection of research essays on progress in BECs (1). That behavior provides physicists with an extraordinary opportunity: to study bizarre quantum effects on a large scale, instead of having to probe individual particles. For the last two decades, physicists have treated BECs something like Play-Doh. They poke it, smash it, tickle it with lasers, and trap it in magnetic fields. They mix condensates together to see what happens, and use it to slow down light (2). They have observed strange behaviors that would have been impossible to predict even two decades ago: solids that flow …
Superfluidity and Bose-Einstein condensation (BEC) in ultracold atomic gases represent macroscopic quantum phenomena arising from collective particle behavior at near-zero temperatures. Experimental realizations of BEC in alkali gases have enabled the observation of quantized vortices, matter-wave interference, and nonclassical excitations. This article reviews theoretical frameworks including Gross-Pitaevskii and Bogoliubov models, experimental techniques such as evaporative cooling and optical trapping, and computational approaches for simulating condensate dynamics. Two graphical analyses illustrate the condensate density profile and vortex lattice formation. Understanding these phenomena has implications for quantum simulation, atom interferometry, and exploration of quantum hydrodynamics.
Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.