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Optics Express

Bose-Einstein condensation of photons in a long fiber cavity

Rafi Weill, Alexander M. Bekker, Boris Levit, Baruch Fischer

Published Jul 26, 2021• 6 citations
Publisher

Abstract

We demonstrate photon Bose-Einstein condensation (photon-BEC) at a broad temperature range that is valid also in the long 1D fiber cavity limit. It is done with an erbium-ytterbium co-doped fiber (EYDF) cavity by overcoming the challenging requirement of sublinear light dispersion for BEC in 1D using a chirped-gratings Fabry-Perot. We experimentally show with a square-root mode-dispersion, a quadratic temperature dependence of the critical power for condensation (compared to a linear dependence in finite regular fiber-cavities) between 90 K and 382 K, as the theory predicts.

DOI
10.1364/oe.430406

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We demonstrate photon Bose-Einstein condensation (photon-BEC) at a broad temperature range that is valid also in the long 1D fiber cavity limit. It is done with an erbium-ytterbium co-doped fiber (EYDF) cavity by overcoming the challenging requirement of sublinear light dispersion for BEC in 1D using a chirped-gratings Fabry-Perot. We experimentally show with a square-root mode-dispersion, a quadratic temperature dependence of the critical power for condensation (compared to a linear dependence in finite regular fiber-cavities) between 90 K and 382 K, as the theory predicts.
Abstract Bose–Einstein condensation (BEC) is a special many-boson phenomenon that was observed in atomic particles at ultra-low temperatures. Later, BEC was also shown for non-atomic bosons, such as photons. Those experiments were usually done in micron-size cavities, where the power (particle number) was varied, and not the temperature, until condensation was reached. Here we demonstrate BEC of photons in a few-meters-long one-dimensional (1D) erbium–ytterbium co-doped fiber cavity at, below and above room temperature, between 100 K and 415 K. The experiments were done at about the 1550 nm wavelength regime having a few to tens of μW intra-cavity light power (107−108 photons). By varying the power and also the temperature, we found linear dependence of the condensation on power for various temperatures and of the critical power (for condensation) on temperature. These findings agree, functionally and quantitatively, with the theoretical BEC prediction without any adjustable parameter.
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.
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 lasing without an overall inversion. The experimental results are supported by a theoretical analysis based on the rate equations.
A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.
Contrary to what is commonly accepted in lasers, we show that photons in standard erbium-doped fibers (edf) and lasers can be in thermal equilibrium and show lasing without an overall population inversion. The thermalization with Bose-Einstein spectra is found in edf cavities and even in open fibers in a broad spectral range up to ~200nm at the 1550nm wavelength regime. We also find in the edf cavities coexistence of thermal-equilibrium with oscillation without an overall inversion that can be attributed to lasing or Bose-Einstein condensation (BEC). The experimental results are supported by a theoretical analysis based on the rate equations.
The interesting question if and how can Bose-Einstein condensation (BEC) occur with photons has received a boost by a recent experiment that reported on the observation of photon-BEC condensation in an optical microcavity [1]. Here we present a different laser light condensation (LC) phenomenon [2], while discussing and questioning the meaning and the possibility to observe thermal photon-BEC in laser cavities. LC is a classical condensation effect that is based on very different grounds than the regular BEC. Its “energy” levels are measured in a loss-gain scale inherent in laser cavities, where the “ground-state” is the lowest-loss mode, and noise has the role of temperature. The loss scale gives a power occupation hierarchy and power spectra similar to Bose-Einstein statistics with an effective chemical potential parameter and eventually laser light-condensation (LC) which is formally very similar to BEC in a potential-well [3].