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arXiv:2606.24568 · Physical Review A

Optical spectroscopy of Bose-Einstein condensates at finite temperature

R. M. F. Andersen, Laurits Nikolaj Stokholm, I. Zebergs, N. R. Neubert, Adam S. Chatterley, N. Kjærgaard, J. Arlt

Published Oct 21, 2026• 0 citations
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Abstract

We report on optical spectroscopic measurements of ultracold and partially condensed 87Rb gases, which show distinct spectral features due to the thermal and the Bose condensed components in the frequency domain. These features are detected in-situ by using a dark-field configuration with single-photon sensitivity and a frequency-agile laser system. To interpret the observed spectra, we develop a model for light propagation through an inhomogeneous atomic cloud. This model enables the extraction of temperature and atom number, which we benchmark against conventional time-of-flight absorption imaging. The spectroscopically obtained cloud parameters show enhanced sensitivity to small thermal fractions in nearly pure condensates. We further compare the spectroscopy in dark-field and bright-field configurations, demonstrating the superior performance of the former. Our results reveal previously unexplored spectral structure in optically dense ultracold gases and establish spectroscopy as a tool for characterizing ultracold systems at very low temperatures.

DOI
10.1103/t5zd-3qd4

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We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight and to measure reliably temperatures as low as 0.2Tc00.2{T}_{c}^{0}0.2Tc0​ and thermal fractions as low as 10%. Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.
Phase contrast imaging is used to observe Bose-Einstein condensates at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two-relevant-parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and the thermal atoms is taken into account to various degrees.
We present a novel imaging system for ultracold quantum gases in expansion. After release from a confining potential, atoms fall through a sheet of resonant excitation laser light and the emitted fluorescence photons are imaged onto an amplified CCD camera using a high numerical aperture optical system. The imaging system reaches an extraordinary dynamic range, not attainable with conventional absorption imaging. We demonstrate single-atom detection for dilute atomic clouds with high efficiency where at the same time dense Bose-Einstein condensates can be imaged without saturation or distortion. The spatial resolution can reach the sampling limit as given by the 8 μm pixel size in object space. Pulsed operation of the detector allows for slice images, a first step toward a 3D tomography of the measured object. The scheme can easily be implemented for any atomic species and all optical components are situated outside the vacuum system. As a first application we perform thermometry on rubidium Bose-Einstein condensates created on an atom chip.
Phase contrast imaging is used to observe Bose-Einstein condensates (BECs) at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two relevant parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and thermal atoms is taken into account to various degrees.
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Abstract The investigation of atom number fluctuations in quantum gases at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, the microcanonical nature of atom number fluctuations in weakly interacting Bose–Einstein condensates was observed. This motivates an investigation of the thermal component of partially condensed Bose gases, due to the conservation of the total atom number. Here, we present a combined analysis of both components, including a comprehensive analysis of the uncertainties in the preparation and parameter extraction of partially condensed quantum gases. This enables a complementary observation of the thermal atom number fluctuations and yields and improved value of the peak BEC atom number fluctuations Δ N p , 0 2 = ( 3.7 ± 7 ) × 10 5 close to the critical temperature. This corresponds to a reduction by 41% with respect to previous analysis and corroborates the microcanonical nature of the fluctuations. The analysis of noise contributions due to the preparation and evaluation of partially condensed Bose gases is based on Monte Carlo simulations of optical density profiles. Importantly, this allows for an estimation of the technical noise contributions to the atom number and temperature, which is generally applicable in the field of ultracold atoms.