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Einstein condensation of atomic hydrogen

Wattana Lim, Virulh Sa-yakanit

Published Jan 1, 2001• 0 citations
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Abstract

We study the ground state properties of Bose-Einstein condensation of atomic hydrogen in the Ioffe-Pritchard magnetic trap using many-body Feynman Path Integral theory, which leads to the calculation of the ground state energy and the wave function. We also calculate the size, peak condensate density and the value of the ground state energy, which are in fair agreement with the experimental results obtained by laser spectroscopy of 1S-2S transition.

DOI
10.58837/chula.the.2001.1073

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We study the ground state properties of Bose-Einstein condensation of atomic hydrogen in the Ioffe-Pritchard magnetic trap using many-body Feynman Path Integral theory, which leads to the calculation of the ground state energy and the wave function. We also calculate the size, peak condensate density and the value of the ground state energy, which are in fair agreement with the experimental results obtained by laser spectroscopy of 1S-2S transition.
Atomic hydrogen has been loaded into a 1-K deep magnetic trap through the use of a dilution refrigerator. Evaporative cooling has been used to cool the trapped hydrogen into the submillikelvin temperature regime. These techniques have produced a sample with density of 8 × 1013 cm-3 at a temperature of 100 μK. At this density a transition to a Bose-Einstein condensate is predicted to occur at a temperature of 30 μK. These results have been obtained with a magnetic trap that has been constructed to accommodate upcoming experiments based on laser spectroscopy of the 1S-2S two photon transition in the trapped hydrogen. A frequency doubled narrow linewidth cw dye laser system has been constructed to excite the 1S-2S transition. The excitation will be detected by the observation of electric field-induced Lyman-alpha fluorescence. The optical detection system should yield improved sample density and temperature diagnostic capabilities that will facilitate a closer approach to the quantum degenerate regime. Additionally the cold, confined hydrogen gas offers the possibility of improving the level of resolution of Doppler-free hydrogen 1S-2S laser spectroscopy by several orders of magnitude.
We report observation of Bose-Einstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the 1S1S1S- 2S2S2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is $4.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$, corresponding to a condensate population of 109{10}^{9}109 atoms. The BEC transition occurs at about $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}50\ensuremath{\mu}\mathrm{K}$ and $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\ifmmode\times\else\texttimes\fi{}{10}^{14}{\mathrm{cm}}^{\ensuremath{-}3}$.
A modeled Bose system consisting of N particles with two-body interaction confined within volume V under the inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l . The inhomogeneity of the system or the porosity can be represented as density with interacting strength b and correlation length L . The mean-field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground-state energy and the condensate density which are in agreement with that from Bugoliubov's approach.
Abstract. New developments of optical trapping techniques make it possible to confine atoms independently of their spin orientation in experiments and thus result in spinor condensates. As a continuation of our previous work [M. Li, X. Luo, J. Wei, and M. Zhen, SIAM J. Math. Anal., 56 (2024), pp. 4375–4414], we investigate physical states as well as qualitative properties describing the aggregation and extinction of atoms, of spin-1 Bose–Einstein condensate in an Ioffe–Pritchard magnetic field, through two conserved quantities, the number of atoms and the total magnetization. Unlike the related free case which is well studied in [Y. Z. Kong, Q. X. Wang, and D. Zhao, Calc. Var. Partial Differential Equations, 60 (2021), 152] and our previous work, the presence of the Ioffe–Pritchard magnetic field, which competes dramatically with the harmonic trapping, requires new ideas to capture the physical states and analyze their qualitative properties. Based on the ferromagnetic or antiferromagnetic characterization of spin-1 Bose–Einstein condensate, our results support some experimental observations in [T. Ho and S. Yip, Phys. Rev. Lett., 84 (2000), pp. 4031–4034; C. Law, H. Pu, and N. Bigelow, Phys. Rev. Lett., 81 (1998), pp. 5257–5261] and some numerical analysis on ground states reported in [W. Bao, I. Chern, and Y. Zhang, J. Comput. Phys., 253 (2013), pp. 189–208; W. Bao and F. Lim, SIAM J. Sci. Comput., 30 (2008), pp. 1925–1948; W. Bao and H. Wang, SIAM J. Numer. Anal., 45 (2007), pp. 2177–2200].
A modeled Bose system consisting of N particles with two-body interaction confined within volume V under inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l. The inhomogeneity of the system or the porosity can be represented as density [Formula: see text] with interacting strength b and correlation length L. The mean field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground state energy which is in agreement with that from Bugoliubov's approach.