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Chinese Physics B

Temperature dependence of the energy-level shift induced by the Bose—Einstein condensation of photons

Jian-Jun Zhang, Ze Cheng, Jianhui Yuan, Junpei Zhang

Published Sep 1, 2012• 0 citations
Publisher

Abstract

We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose—Einstein condensation of photons. It is found that below the critical temperature T c , the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.

DOI
10.1088/1674-1056/21/9/090502

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We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose—Einstein condensation of photons. It is found that below the critical temperature T c , the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.
We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose-Einstein condensation of photons. It is found that below the critical temperature T c , the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T . Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.
Abstract A quantum system consisting of a single-mode microcavity and a two-level quantum dot or atom placed inside this microcavity, the interaction of monoenergetic photons in the microcavity with the electron in the two-level quantum dot or atom being the allowed electrical dipole transition between two energy levels, is a basic element of prospective devices for quantum information processing. Its time evolution is governed by cavity quantum electrodynamics (CQED). The photon–electron coupling induces the shifts of energy levels of the electron in the two-level quantum dot or atom. If there is no photon in the microcavity, then the shift of electron energy levels is induced by the radiative corrections and it is called the Lamb shift. The presence of photons in the microcavity induces another type of electron energy level shift—the ac Stark shift. In this paper, we present the exact derivation of the formulae for the Lamb and ac Stark shifts of electron energy levels in the two-level quantum dot or atom placed inside a single-mode microcavity.
Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a "white-wall" photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.
The dynamic Stark shift of a high-lying atom in a system of Bose Einstein condensation (BEC) of photons is discussed within the framework of nonrelativistic quantum electrodynamics (QED) theory. It is found that the Stark shift of an atom in BEC of photons is modified by a temperature dependent factor, compared to that in a normal two-dimensional photonic fluid. In photonic BEC, the value of Stark shift is always greater than that in two-dimensional free space. Physical origin of the phenomenon is presented and potential application is also discussed.
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.