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arXiv:1812.05194 · Journal of Statistical Mechanics Theory and Experiment

Non-classical critical exponents at Bose–Einstein condensation

I. Reyes-Ayala, Freddy Jackson Poveda-Cuevas, Vı́ctor Romero-Rochı́n

Published Nov 1, 2019• 2 citations
arXivHTMLPDF

Abstract

Abstract We show that ideal Bose–Einstein condensation (BEC) in d = 3 dimensions is a non-classical critical second order phase transition with exponents , , , , and , obeying all the scaling equalities. These results are found with no approximations or assumptions. The previous exponents are a critical universality class on its own, different from the so-far accepted notion that BEC belongs to the spherical model universality class.

DOI
10.1088/1742-5468/ab4984

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Abstract We show that ideal Bose–Einstein condensation (BEC) in d = 3 dimensions is a non-classical critical second order phase transition with exponents , , , , and , obeying all the scaling equalities. These results are found with no approximations or assumptions. The previous exponents are a critical universality class on its own, different from the so-far accepted notion that BEC belongs to the spherical model universality class.
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Abstract The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.
The condensation of photons in a dye-filled optical microcavity represents a landmark achievement in macroscopic quantum phenomena, bridging quantum optics and statistical mechanics. While ordinary Bose-Einstein condensation (BEC) of massive particles is governed by well-established critical exponents, photon condensation occurs in an open, dissipative system where thermalization is mediated through repeated absorption and re-emission cycles by dye molecules. In this paper, we systematically investigate whether photon condensation exhibits independent critical exponents. We define the scaling of the condensed photon density as n_gamma proportional to |T - T_c|^(beta_gamma) and examine whether the critical exponent beta_gamma deviates significantly from the classical values associated with standard three-dimensional or trapped two-dimensional Bose systems. Through a rigorous theoretical formulation based on master equations, grand canonical statistical mechanics, and renormalization group techniques, we explore the universal properties of this light-matter phase transition. Establishing a distinct set of critical exponents for photon condensation could lay the foundational stone for a new universal class of non-equilibrium quantum phase transitions, offering profound implications for fundamental physics and advanced quantum technologies.
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional trapped quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be ν=0.52(4)ν= 0.52(4)ν=0.52(4). Our results constitute a first experimental test of the long-standing scaling predictions for the Bose gas universality class.
The analytical theory of Bose–Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose–Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose–Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose–Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose–Einstein condensation has been given.