Spatial Chaos of Bose-Einstein Condensates in a Cigar-Shaped Trap

The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied. For a system with a steady current, we construct the general solution of the 1st-order equation. From the boundedness condition of the general solution, we obtain the Melnikov function predicting the onset of chaos. The unpredictability of the system's distribution of atom density is also theoretically analyzed. For a 23Na system meeting the perturbation condition, numerical simulations show the existence of chaos, which is in accordance with our analytical results. Numerical simulations of a 87 Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system. The case without a current is also investigated.     

Parallel numerical simulations for quantized vortices in Bose--Einstein condensates

We employ the parallel computing technology to study numerically the three-dimensional structure of quantized vortices of Bose--Einstein condensates. For anisotropic cases, the bending process of vortices is described in detail by the decrease of Gross--Pitaevskii energy. A completely straight vortex and the steady and symmetrical multiple-vortex configurations are obtained. We analyse the effect of initial conditions and angular velocity on the number and shape of vortices.     

双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为

考虑玻色-爱因斯坦凝聚体局限于周期性的双色光晶格势阱中,研究其中的Bloch能带结构、第一能隙和第二能隙的Landau-Zener隧穿行为.结果表明,随着双色光晶格势阱的主、次晶格相位差从0增加到π,Bloch能带中第一能隙宽度逐渐增加,而第二能隙宽度逐渐减小.同时发现,双色光晶格势阱的主、次晶格深度及其相位差对第一能隙和第二能隙的Landau-Zener隧穿性质有重要的影响.     

Rotational and rovibrational transitions in the a 1Δ2 and b 1Σ+0+ states of sulfur monoxide radical

ABSTRACT

Sulfur monoxide radical has widely been detected in outer space using ground-state spectroscopy. The a ¹Δ₂ and b ¹Σ⁺₀₊ states of this radical have low excitation energies, and they possibly exist in outer space. In this work, the potential energy curves and dipole moment functions of the two states were evaluated using the complete active space self- consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The transition line positions, oscillator strengths, band transition dipole matrix elements, Einstein A coefficients, and Franck–Condon factors of all transitions were calculated for lower vibrational levels at rotational angular momentum quantum number J up to 150. The transition line positions calculated in this study are in good agreement with the experimental results. The rovibrational transition became noticeably weak at Δυ > 5. Comparing the results of a ¹Δ₂ and b ¹Σ⁺₀₊ states reported in this paper with the previous values, we conclude that these results are the most accurate and complete to date.     

Are Words the Quanta of Human Language? Extending the Domain of Quantum Cognition

In previous research, we showed that ‘texts that tell a story’ exhibit a statistical structure that is not Maxwell–Boltzmann but Bose–Einstein. Our explanation is that this is due to the presence of ‘indistinguishability’ in human language as a result of the same words in different parts of the story being indistinguishable from one another, in much the same way that ’indistinguishability’ occurs in quantum mechanics, also there leading to the presence of Bose–Einstein rather than Maxwell–Boltzmann as a statistical structure. In the current article, we set out to provide an explanation for this Bose–Einstein statistics in human language. We show that it is the presence of ‘meaning’ in ‘texts that tell a story’ that gives rise to the lack of independence characteristic of Bose–Einstein, and provides conclusive evidence that ‘words can be considered the quanta of human language’, structurally similar to how ‘photons are the quanta of electromagnetic radiation’. Using several studies on entanglement from our Brussels research group, we also show, by introducing the von Neumann entropy for human language, that it is also the presence of ‘meaning’ in texts that makes the entropy of a total text smaller relative to the entropy of the words composing it. We explain how the new insights in this article fit in with the research domain called ‘quantum cognition’, where quantum probability models and quantum vector spaces are used in human cognition, and are also relevant to the use of quantum structures in information retrieval and natural language processing, and how they introduce ‘quantization’ and ‘Bose–Einstein statistics’ as relevant quantum effects there. Inspired by the conceptuality interpretation of quantum mechanics, and relying on the new insights, we put forward hypotheses about the nature of physical reality. In doing so, we note how this new type of decrease in entropy, and its explanation, may be important for the development of quantum thermodynamics. We likewise note how it can also give rise to an original explanatory picture of the nature of physical reality on the surface of planet Earth, in which human culture emerges as a reinforcing continuation of life.     

Decoherence effects in Bose–Einstein condensate interferometry I. General theory

The present paper outlines a basic theoretical treatment of decoherence and dephasing effects in interferometry based on single component Bose–Einstein condensates in double potential wells, where two condensate modes may be involved. Results for both two mode condensates and the simpler single mode condensate case are presented. The approach involves a hybrid phase space distribution functional method where the condensate modes are described via a truncated Wigner representation, whilst the basically unoccupied non-condensate modes are described via a positive P representation. The Hamiltonian for the system is described in terms of quantum field operators for the condensate and non-condensate modes. The functional Fokker–Planck equation for the double phase space distribution functional is derived. Equivalent Ito stochastic equations for the condensate and non-condensate fields that replace the field operators are obtained, and stochastic averages of products of these fields give the quantum correlation functions that can be used to interpret interferometry experiments. The stochastic field equations are the sum of a deterministic term obtained from the drift vector in the functional Fokker–Planck equation, and a noise field whose stochastic properties are determined from the diffusion matrix in the functional Fokker–Planck equation. The stochastic properties of the noise field terms are similar to those for Gaussian–Markov processes in that the stochastic averages of odd numbers of noise fields are zero and those for even numbers of noise field terms are the sums of products of stochastic averages associated with pairs of noise fields. However each pair is represented by an element of the diffusion matrix rather than products of the noise fields themselves, as in the case of Gaussian–Markov processes. The treatment starts from a generalised mean field theory for two condensate modes, where generalised coupled Gross–Pitaevskii equations are obtained for the modes and matrix mechanics equations are derived for the amplitudes describing possible fragmentations of the condensate between the two modes. These self-consistent sets of equations are derived via the Dirac–Frenkel variational principle. Numerical studies for interferometry experiments would involve using the solutions from the generalised mean field theory in calculations for the stochastic fields from the Ito stochastic field equations.