Fulde–Ferrell–Larkin–Ovchinnikov states in equally populated Fermi gases in a two-dimensional moving optical lattice

We study the possibility of stabilizing a Fulde–Ferrell–Larkin–Ovchinnikov(FFLO) state in an equally populated two-component Fermi gas trapped in a moving two-dimensional optical lattice. For a system with nearly half filling, we find that a finite pairing momentum perpendicular to the moving direction can be spontaneously induced for a proper choice of lattice velocity. As a result, the total pairing momentum is tilted towards the nesting vector to take advantage of the significant enhancement of the density of states.     

格子气的声振荡衰减

采用格子气数值方法模拟了共振腔中气体声振荡衰减过程．计算结果表明：格子气中声振荡衰减的规律和经典理论结果一致；衰减系数随频率增加而减小，并且随密度增加而减小．该结果可以用来说明一些大学统计物理教科书中的一个经典例子存在不完善之处．本中采用了一种新的扭转9-bit格子气模型和并行计算方法，这些结果对今后研究格子气中的热声问题有参考价值．     

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.     

Superfluid to Mott‐insulator transition in an anisotropic two‐dimensional optical lattice

We study the superfluid to Mott‐insulator transition of bosons in an optical anisotropic lattice by employing the Bose‐Hubbard model living on a two‐dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott‐insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one‐dimensional.     

Probing many-body interactions in an optical lattice clock

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p$p$-wave and s$s$-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA ⁸⁷${}^{87}$Sr and NIST ¹⁷¹${}^{171}$Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems.     

Fast frictionless expansion of an optical lattice

We investigate fast frictionless expansion of an optical lattice with dynamically variable spacing (accordion lattice). We design an expansion trajectory that yields a final state identical to the initial state up to an irrelevant phase factor. We discuss the effect of additional force and nonlinear interaction on the fast frictionless expansion.     

光晶格中超流费米气体的能隙孤子

研究了一维光晶格中超流费米气体的能隙孤子. 应用平均场理论和超流费米气体的流体动力学模型, 利用变分法得到了在整个跨越区超流费米气体在光晶格中存在带隙孤子的条件, 即原子间的非线性相互作用项与系统化学势以及晶格深度的相互关系. 通过对超流费米气体的基态能隙孤子空间分布的分析与对比, 揭示了在一维情况下超流费米气体能隙孤子的存在并发现超流费米气体能隙孤子在整个跨越区当系统从Bose-Einstein凝聚端跨越到BCS端时孤子存在的条件与孤子空间分布存在明显的差别.     

Superfluid to Mott-insulator transition in a one-dimensional optical lattice

Bose-Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ～ 13.7 E_r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

The t‐U‐V‐J model in cuprates: Strengths of the interactions

The t‐U‐V‐J model fits together three major parts of the superconductivity puzzle of the cuprite compounds: (i) it describes the opening of a d‐wave pairing gap, (ii) it is consistent with the fact that the basic pairing mechanism arises from the antiferromagnetic exchange correlations, and (iii) it takes into account the charge fluctuations associated with double occupancy of a site which play an essential role in doped systems. The strengths of the interactions U, V and J in YBa₂Cu₃O_6.7 and La_2‐xSr_xCuO₄ (_x = 0.16) samples are obtained by requiring quantitative consistency between the angle‐resolved photoemission spectroscopy (ARPES) measurements, the sharp collective mode at the antiferromagnetic wave vector Q _AF=(π,π), and the observed inelastic neutron scattering resonance (INSR) positions of the incommensurate peaks at wave vectors Q _δ = ((1 ± δ)π,π) and Q _δ = (π(1 ± δ)π).     

超流Fermi气体在非简谐势阱中的集体激发

研究了非谐振势中超流Fermi气体的集体激发. 基于一维超流流体动力学模型, 采用变分法获得了体系从分子Bose-Einstein凝聚端渡越到Cooper对凝聚端时系统的两个低能激发模, 即偶极模和呼吸模. 分析发现: 在整个跨越区偶极模和呼吸模都发生了频移现象, 且在BCS端频移更加显著. 进一步研究发现在不同驱动振幅激发下超流Fermi气体质量中心和宽度变化呈现出了复杂动力学特性, 由于非谐振势的贡献,超流Fermi气体两低能模发生耦合, 使宽度变化产生量子拍频现象, 且拍频频率随着驱动振幅的增加而增大. 这种非线性耦合对外部驱动的响应在幺正区尤其显著. 关键词： 超流Fermi气体 非谐振势 集体激发     

一维光晶格中超流Fermi气体基态性质的研究

研究了一维光晶格中超流Fermi气体基态解的性质.在平均场理论框架下,利用超流Fermi体系中原子间相互作用能与晶格势能相互平衡的条件,得到了一维光晶格中超流Fermi气体在整个BEC-BCS跨越区的一组基态解,给出了基态的原子数密度空间分布、总原子数和能量.进一步对系统从BEC端转变到BCS端时的基态解性质进行了深入分析和对比.结果表明,一维光晶格中超流Fermi气体基态分布具有一些特殊的性质,由于Fermi压力,相比而言超流Fermi气体在BCS端的基态原子数密度空间分布较为扩展,平均能量明显偏高.     

Vortex splitting in the interference effect for a quantized vortex released from an optical lattice

For a quantized vortex in a harmonic trap and an optical lattice, we study the interference effect after the combined potentials are switched off. Both numerical and analytical calculations show that there is a vortex splitting in the interference effect of this freely expanding quantum gas, i.e. every interference peak is also a quantized vortex. The experimental scheme to verify this interference effect is discussed.     

强相互作用费米气体在谐振子势中的干涉演化

通过数值求解超流序参量方程,研究了强相互作用费米气体从光晶格中释放后的干涉条纹在谐振子势中的演化．发现对于强相互作用的费米气体,膨胀时弹性碰撞使得干涉条纹模糊．为了消除原子间的弹性碰撞而获得近弹道膨胀,实验上采用了快速磁场扫描技术．数值模拟了强相互作用费米气体在膨胀前的快速磁场扫描过程,得到了清晰的干涉条纹,且发现干涉条纹在谐振子势中做长时间周期振荡．计算了在不同超流区域所形成的干涉条纹,与实验观测到的一致．     

Mechanical bistability in an optical lattice

A probed optical lattice is modelled as a driven anharmonic oscillator with noise. For specific values of the probe intensity and detuning, atoms are forced in bistable solutions. The friction and fluctuations that arise from laser cooling, determine the equilibrium between these two modes of vibration. The distribution determines the absorption spectrum and the transient emission spectrum that is emitted by the optical lattice after the probe has been switched off. Received 23 May 2000 and Received in final form 17 August 2000     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

Bright soliton dynamics in Fourier synthesized optical lattice

We consider the dynamics of bright solitons in one dimensional Bose Einstein condensate with spin orbit coupling and trapped by an optical lattice potential. We mainly focus on the effects of the spin orbit coupling, Rabi coupling and detuning parameter on the soliton dynamics. The solution of the coupled Gross Pitaevskii equation is performed with the help of the variational and numerical methods for various parameters. The population imbalance and the center of mass motion show different dynamic behaviors depending on the parameters. We also obtain traveling bright solitons related with a given finite initial momentum.     

Diffusive Thermal Conductivity of Superfluid Fermi Gas in p-Wave State at Low Temperatures

The diffusive thermal conductivity tensor of p-wave superfluid at low temperatures is calculated by using the Boltzmann equation approach. We use the Sykes and Brooker procedure and show that K xx is equal to K yy and these are related to T-1 , also K zz is proporated to T-3 .     

A strongly attractive Fermi gas in an optical lattice

We study strongly attractive fermions in an optical lattice superimposed by a trapping potential. We calculate the densities of fermions and condensed bound molecules at zero temperature. There is a competition between dissociated fermions and molecules leading to a reduction of the density of fermions at the trap center.     

Fermi gas on a lattice in the van Hove limit

We study a Fermi gas with general translation-invariant many-body interactions on a (v3)-dimensional lattice. A complete analysis is given of the perturbative terms up to second order and the program put forward by N. M. Hugenholtz for the derivative of the Boltzmann equation is verified to second order.