Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers

Abstract

We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.

Bose–Einstein condensation of photons in an erbium–ytterbium co-doped fiber cavity

“…In this work, we experimentally observed BEC in a one-dimensional (1D) photon gas, in a standard, meters long, double-clad Er/Yb co-doped fiber (EYDF) cavity. Double-clad EYDFs that are commonly used as amplifiers for communication at the 1550 nm wavelength regime give similar thermalization behavior to what we obtained in EDF 22 , as we show below, but allow relatively uniform pumping along the fiber. Double-clad EYDFs have several advantages compared to the core EDF pumping: They give a relatively uniform upper levels population that stays in our experiments below an overall inversion along the whole fiber 22 .…”

“…Double-clad EYDFs that are commonly used as amplifiers for communication at the 1550 nm wavelength regime give similar thermalization behavior to what we obtained in EDF 22 , as we show below, but allow relatively uniform pumping along the fiber. Double-clad EYDFs have several advantages compared to the core EDF pumping: They give a relatively uniform upper levels population that stays in our experiments below an overall inversion along the whole fiber 22 . The uniform pumping also eliminates hysteresis and bistability 22,23 .…”

“…(2) Adequate light-modes density of states (DOS) in a 1D cavity, as discussed below. (3) Low loss rates of photons in the cavity that distinguishes the quantum BE-BEC regime from lasers 15,18 , fulfilled in our EYDF cavities, despite the relatively low finesse (~18) and the strong spontaneous emission loss in the fiber (~98% is lost) 22 . The low loss rate guarantees many absorption-emission cycles needed for thermalization 22 .…”

“…Double-clad EYDFs have several advantages compared to the core EDF pumping: They give a relatively uniform upper levels population that stays in our experiments below an overall inversion along the whole fiber 22 . The uniform pumping also eliminates hysteresis and bistability 22,23 . We give in the Supplementary Notes 1 and 2 more details on the rate equations model and figures that show the differences between the cases of core and cladding pumping.…”

“…Photons in optical cavities and lasers that have losses were not thought to be in thermal equilibrium or show BEC. However, our recent demonstration of thermal equilibrium of a photon gas in standard erbium-doped fibers (EDF) 22 opens the way to BEC in these simple fibers at a room temperature. We demonstrated thermalization and Bose–Einstein (BE) spectral distribution of photons in EDF in a broad spectral range up to ~200 nm at the 1550 nm wavelength regime 22 .…”