Spinor Bose–Einstein condensates

An overview of the physics of spinor and dipolar Bose–Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor–dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.     

Spontaneous U（1） symmetry breaking and Bose-Einstein condensation

Based on Bogoliubov's truncated Hamiltonian H_B for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a₀+\lambda^*a₀⁺) to H_B, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.     

Quantum phases of Bose gases on a lattice with pair-tunneling

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling.The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate.The various possible quantum phases,such as the Mott-insulator phase(MI),the superfluid phase(SF) of an individual atom,the charge density wave phase(CDW),the supersolid phase(SS),the pair-superfluid(PSF) phase,and the pair-supersolid phase(PSS) are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.     

Condensation of N interacting bosons: a hybrid approach to condensate fluctuations

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.     

Electromagnetically-Induced Transparency in Optomechanical Systems with Bose–Einstein Condensate

We study theoretically electromagnetically-induced transparency (EIT) in an optomechanical system that consists of a Bose–Einstein condensate (BEC) trapped inside a Fabry–Perot cavity driven by the laser field. The quantized laser field interacts with the collective density excitations (Bogoliubov mode) of the condensate. The phenomenon of electromagnetically-induced transparency is observed in the output of the probe laser field. We show that the probe laser field can efficiently be amplified or attenuated depending on the interaction of the BEC with the pump laser field. Furthermore, we explain the effect of atom–atom interaction on the transparency window and show that for increasing atom–atom interaction the transparency window increases.     

The Bogoliubov model of weakly imperfect Bose gas

We present a systematic account of known rigorous results about the Bogoliubov model of weakly imperfect Bose gas (WIBG). This model is a basis of the celebrated Bogoliubov theory of superfluidity, although the physical phenomenon is, of course, more complicated than the model. The theory is based on two Bogoliubov's ansätze: the first truncates the full Hamiltonian of the interacting bosons to produce the WIBG, whereas the second substitutes some operators by c-numbers (the Bogoliubov approximation). After some historical remarks, and physical and mathematical motivations of this Bogoliubov treatment of the WIBG, we turn to revision of the Bogoliubov's ansätze from the point of view of rigorous quantum statistical mechanics. Since the exact calculation of the pressure and the behaviour of the Bose condensate in the WIBG are available, we review these results stressing the difference between them and the Bogliubov theory. One of the main features of the mathematical analysis of the WIBG is that it takes into account quantum fluctuations ignored by the second Bogoliubov ansatz. It is these fluctuations which are responsible for indirect attraction between bosons in the fundamental mode. The latter is the origin of a nonconventional Bose condensation in this mode, which has a dynamical nature. A (generalized) conventional Bose–Einstein condensation appears in the WIBG only in the second stage as a result of the standard mechanism of the total particle density saturation. It coexists with the nonconventional condensation. We give also a review of some models related to the WIBG and to the Bogoliubov theory, where a similar two-stage Bose condensation may take place. They indicate possibilities to go beyond the Bogoliubov theory and the Hamiltonian for the WIBG.     

Interacting bosons in an optical lattice

A strongly interacting Bose gas in an optical lattice is studied using a hard‐core interaction. Two different approaches are introduced, one is based on a spin‐1/2 Fermi gas with attractive interaction, the other one on a functional integral with an additional constraint (slave‐boson approach). The relation between fermions and hard‐core bosons is briefly discussed for the case of a one‐dimensional Bose gas. For a three‐dimensional gas we identify the order parameter of the Bose‐Einstein condensate through a Hubbard‐Stratonovich transformation and treat the corresponding theories within a mean‐field approximation and with Gaussian fluctuations. This allows us to evaluate the phase diagram, including the Bose‐Einstein condensate and the Mott insulator, the density‐density correlation function, the static structure factor, and the quasiparticle excitation spectrum. The role of quantum and thermal fluctuations are studied in detail for both approaches, where we find good agreement with the Gross‐Pitaevskii equation and with the Bogoliubov approach in the dilute regime. In the dense regime, which is characterized by the phase transition between the Bose‐Einstein condensate and the Mott insulator, we discuss a renormalized Gross‐Pitaevskii equation. This equation can describe the macroscopic wave function of the Bose‐Einstein condensate in the dilute regime as well as close to the transition to the Mott insulator. Finally, we compare the results of the attractive spin‐1/2 Fermi gas and those of the slave‐boson approach and find good agreement for all physical quantities.     

原子间相互作用对双模原子激光压缩性质的影响

研究了由单模压缩相干态光场与Ξ型三能级原子玻色爱因斯坦凝聚体(BEC)相互作用系统中耦合输出的双模原子激光的压缩特性,重点讨论了玻色爱因斯坦凝聚体原子间相互作用对原子激光压缩性质的影响,并讨论了原子激光压缩对光场初始压缩因子的依赖关系。结果表明:由光场诱导的双模原子激光呈现周期性的压缩,原子间的相互作用和光场初始压缩因子对原子的压缩性质具有重要影响。原子间的相互作用影响原子激光压缩的振荡频率而不会影响其压缩深度,而初始光场的压缩因子则对原子激光压缩深度产生调制作用,且初始光场的压缩因子越大,则原子激光压缩的时间越短。     

相互作用原子玻色-爱因斯坦凝聚体诱导的光场压缩效应

给出了光场与二能级原子玻色-爱因斯坦凝聚体(BEC)相互作用系统的哈密顿量，研究了原子 间相互作用对压缩相干态光场与原子BEC相互作用系统中光场正交压缩特性的影响.结果表明 ：光场两正交分量的涨落均随时间按余弦规律周期性地变化，其压缩性质依赖于光场的初始 压缩因子和压缩方向角，而原子间的相互作用影响光场正交分量的涨落随时间变化的幅度和 周期. 关键词： 玻色-爱因斯坦凝聚 压缩相干态 光场的正交压缩     

Generations of dark hollow beams and their applications in laser cooling of atoms and all optical-type Bose－Einstein condensation

We report on a new experimental result to generate dark hollow beams by using a geometric optical method. We propose two new methods to produce focused and localized hollow laser beams by using π-phase plates. Using Monte-Carlo simulations, we have studied the Sisyphus cooling of alkali atoms in pyramidal hollow beam gravito-optical traps. We discuss some potential applications of the dark hollow beams in atom optics and the preparation of an all optically-cooled and optically-trapped atomic Bose－Einstein condensation (BEC). Our research shows that an ultracold atomic sample with a temperature of ～ 2μK can be obtained in the pyramidal hollow beam dipole trap and an all optical-type BEC may be realized in a far blue-detuned, hollow beam trap.     

Dilute Bose gas: short-range particle correlations and ultraviolet divergence

The modified Bogoliubov model where the primordial interaction is replaced by the t matrix is reinvestigated. It is shown to provide a negative value of the kinetic energy for a strongly interacting dilute Bose gas, contrary to the original Bogoliubov model. To clear up the origin of this failure, the correct values of the kinetic and interaction energies of a dilute Bose gas are calculated. It is demonstrated that both the problem of the negative kinetic energy and the ultraviolet divergence, dating back to the well-known paper of Lee, Yang and Huang, is connected with an inadequate picture of the short-range boson correlations. These correlations are reconsidered within the thermodynamically consistent model proposed earlier by the present authors. Found results are in absolute agreement with the data of the Monte-Carlo calculations for the hard-sphere Bose gas. Received 10 February 2000 and Received in final form 28 November 2000     

Critical point of an interacting two-dimensional atomic Bose gas

We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.     

Controlling Decoherence Speed Limit of a Single Impurity Atom in a Bose–Einstein‐Condensate Reservoir

The decoherence speed limit (DSL) of a single impurity atom immersed in a Bose‐Einstein‐condensed (BEC) reservoir when the impurity atom is in a double‐well potential is studied. It is demonstrated how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. It is shown that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double‐well potential imposed on the impurity. The physical mechanisms of controlling the DSL at root of the spectral density of the BEC reservoir are uncovered.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC).导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响.以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合.     

Levinson-like theorem for scattering from a Bose-Einstein condensate

A relation between the number of bound elementary excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalizes Levinson's theorem. Specific features of the Bogoliubov model such as complex energy and continuum bound states are discussed and a numerical example is given.     

Tunable second-order sideband effects in hybrid optomechanical cavity assisted with a Bose—Einstein condensate

We theoretically investigated a second-order optomechanical-induced transparency (OMIT) process of a hybrid optomechanical system (COMS), which a Bose—Einstein condensate (BEC) in the presence of atom—atom interaction trapped inside a cavity with a moving end mirror. The advantage of this hybrid COMS over a bare COMS is that the frequency of the second mode is controlled by the s-wave scattering interaction. Based on the traditional linearization approximation, we derive analytical solutions for the output transmission intensity of the probe field and the dimensionless amplitude of the second-order sideband (SS). The numerical results show that the transmission intensity of the probe field and the dimensionless amplitude of the SS can be controlled by the s-wave scattering frequency. Furthermore, the control field intensities, the effective detuning, the effective coupling strength of the cavity field with the Bogoliubov mode are used to control the transmission intensity of the probe field and the dimensionless amplitude of the SS.