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**Bose-Einstein Condensation of exciton polaritons**

Bose-Einstein condensation (BEC), predicted for a gas of non interacting bosons in 1924 by Einstein, has been demonstrated for the first time in 1995 in a dilute gas of rubidium atoms at temperatures below 10– 6 K. In this work, it is shown that BEC can be achieved at around 15 – 20 K in a solid state system by using microcavity polaritons, which are composite bosons of mass one billion times lighter than that of rubidium atoms.

People:

Robert Romestain^{†}, Régis André, Le Si Dang

Jacek Kasprzak, Maxime Richard

Bosons are integer spin particles, which can undergo BEC when their thermal de Broglie wavelength becomes comparable to their average separation. Then a large fraction of the bosons condense in the lowest quantum state, resulting in the appearance of macroscopic coherence. Since this de Broglie wavelength scales as the inverse of the square root of the particle mass and the temperature, the BEC criterion is most easily satisfied at high temperature for bosons with a light mass.

For solid state systems, excitons in semiconductors have long been considered as a promising candidate for BEC. Excitons are pairs of electrons and holes bound by the Coulomb interaction. Although electrons and holes are fermions, excitons are bosons. Moreover their light mass, of the order of the electron mass, would permit BEC at temperatures of a few Kelvin, reachable by standard cryogenic techniques. However, in spite of intense research efforts over the past three decades, no convincing evidence of exciton condensation has ever been firmly established.

In fact, BEC has been demonstrated for the first time in a dilute gas of rubidium atoms. Because of the heavy atom mass (about five orders of magnitude larger than the electron mass), sophisticated cooling techniques were needed to lower the atomic gas temperature down to the micro-Kelvin range to achieve condensation (more details).

Recently semiconductor microcavities with embedded quantum wells have attracted attention for BEC studies. In such devices, very similar to VCSELs (Vertical Cavity Surface Emitting Lasers), the light-matter interaction between excitons confined in quantum wells and optical modes confined in the microcavity can be optimized to achieve the so-called strong coupling regime. The resulting eigenstates of the microcavity system are mixed exciton-photon states called polaritons. Thanks to their half photonic nature, polaritons possess an ultra light mass, of the order of 10– 5 the electron mass, which should favour BEC at high temperature (A. Kavokin and G. Malpuech, Cavity Polaritons, Elsevier, Amsterdam (2003)).

To demonstrate BEC, a CdTe-based microcavity embedding 16 quantum wells has been grown by Molecular Beam Epitaxy. Hot electron-hole pairs are injected in the microcavity by continuous wave laser pumping. Excitons are formed and relax through exciton-phonon and exciton-exciton scatterings. They strongly interact with the cavity photon modes to form polaritons. The distribution of these polaritons in the Energy-Momentum space (E, k) can be probed by measuring the microcavity far-field emission. Figure 1 shows 2D images of the polariton distribution measured at T = 5 K, for three pumping powers. At low pumping power (left panel), polaritons are smoothly distributed along their parabolic energy dispersion curve, over a broad range of E and k. However, above some critical power P0 (middle and right panels), condensation occurs, evidenced by the massive occupation of the k = 0 ground state, whereas the excited state occupation remains almost unchanged.

Data such as those shown in Figure 1 can be used to extract the occupation of polariton states as a function of their energy, and results are displayed in Figure 2 for various pumping powers. A bimodal distribution, typical of BEC at finite temperature, can be clearly observed when pumping above some threshold power Pthr: It consists of a massively occupied ground state (condensate) and a thermal cloud of excited polaritons, whose distribution can be fitted with a Maxwell-Boltzmann distribution and an effective temperature of T = 16 K.

The long range order expected for BEC has been investigated by measuring the first order spatial correlation function within the emitting spot, using a Michelson interferometer (Figure 3). For pumping below threshold, no spatial correlation can be found beyond the polariton de Broglie wavelength (about 3 µm at T = 20 K). Above threshold however, correlation extends across the entire emitting spot of 20 µm diameter, evidencing the long range spatial coherence of the condensate.

Outlook

A challenging objective is to realize BEC at room temperature. This could be achieved by using wider band gap semiconductors, such as GaN or ZnO, to increase the exciton stability under high pumping power at high temperature.

- - Quantum optics in 1D atoms
- - Cavity quantum electrodynamics in a solid by nonlinear spectroscopy
- - From Single Particle to Superfluid Excitations in a Dissipative Polariton Fluid
- - Strain-mediated coupling in a quantum dot–mechanical oscillator hybrid system
- - Single Photon : Manipulation
- - Single photon – Production
- - Photon Detection - superconducting detectors
- - Theory of Cavity Quantum Electrodynamics with solid-state emitters and cavities
- - Quantum optics with II-VI quantum dots
- - Single III-N quantum dot spectroscopy
- - Bose-Einstein Condensation of exciton polaritons

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