Spin-orbit-coupled Bose-Einstein condensates

Spin-orbit (SO) coupling--the interaction between a quantum particle's spin and its momentum--is ubiquitous in physical systems. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Quantum many-body systems of ultracold atoms can be precisely controlled experimentally, and would therefore seem to provide an ideal platform on which to study SO coupling. Although an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the centre-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Such coupling has not been realized previously for ultracold atomic gases, or indeed any bosonic system. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase-separated state (above a critical laser intensity). We develop a many-body theory that provides quantitative agreement with the observed location of the transition. The engineered SO coupling--equally applicable for bosons and fermions--sets the stage for the realization of topological insulators in fermionic neutral atom systems.     

玻色-爱因斯坦凝聚体的光学色散关系

最近的研究表明,玻色-爱因斯坦凝聚体(Bose-Einstein Condensate, BEC)可作为量子电介质材料对光场产生反作用,实现光场-物质波的协同操控.然而BEC的色散性质还没有被研究.为此,解析得到了BEC对大失谐光的一阶色散和二阶色散的计算公式.数值计算表明, BEC的折射率以及二阶色散系数与红、蓝失谐的性质有关:在红失谐时,折射率大于1,且二阶色散是正常色散;在蓝失谐时,折射率小于1,二阶色散为反常色散.二阶色散系数会随着失谐量的改变而剧烈变化,当失谐量在GHz数量级时,表现为强色散介质.一阶色散和红、蓝失谐的性质关系不大,随着失谐量的增加,一阶色散减小,相应的群速度增加.因此,对于超短脉冲光, BEC是一种新型的色散介质.     

Bose-Einstein condensates: microscopic magnetic-field imaging

Today's magnetic-field sensors are not capable of making measurements with both high spatial resolution and good field sensitivity. For example, magnetic force microscopy allows the investigation of magnetic structures with a spatial resolution in the nanometre range, but with low sensitivity, whereas SQUIDs and atomic magnetometers enable extremely sensitive magnetic-field measurements to be made, but at low resolution. Here we use one-dimensional Bose-Einstein condensates in a microscopic field-imaging technique that combines high spatial resolution (within 3 micrometres) with high field sensitivity (300 picotesla).     

玻色-爱因斯坦凝聚体中的三角涡旋格子

 讨论了玻色-爱因斯坦凝聚体中的三角涡旋格子,从磁光阱里玻色-爱因斯坦凝聚体波函数满足的Gross-Pitaevskii方程求出三角格子的解,并简要解释了相关实验观察结果.     

理想的玻色爱因斯坦凝聚体杂质间的相互作用

运用热场动力学理论研究了一维情况下有限温度的玻色爱因斯坦凝聚体杂质问的相互作用,计算了系统的能量和杂质间的相互作用力,给出相互作用力与温度和杂质间距离的关系.研究结果有助于进一步了解玻色爱因斯坦凝聚体中杂质所带来的物理效应,并为Casimir效应和玻色一爱因斯坦凝聚的实验研究提供参考.     

Squeezing and entanglement in a Bose-Einstein condensate

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means. This results in the standard quantum limit, which is reached in today's best available sensors of various quantities such as time and position. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states) at the two input ports. Bose-Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.     

Dynamics of collapsing and exploding Bose-Einstein condensates.

When atoms in a gas are cooled to extremely low temperatures, they will-under the appropriate conditions-condense into a single quantum-mechanical state known as a Bose-Einstein condensate. In such systems, quantum-mechanical behaviour is evident on a macroscopic scale. Here we explore the dynamics of how a Bose-Einstein condensate collapses and subsequently explodes when the balance of forces governing its size and shape is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the interatomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally applied magnetic field yields detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wavefunction and oscillating remnant condensates that survive the collapse. All these processes have curious dependences on time, on the strength of the interaction and on the number of condensate atoms. Although the system would seem to be simple and well characterized, our measurements reveal many phenomena that challenge theoretical models.     

周期边界下玻色爱因斯坦凝聚体杂质间相互作用

应用黎曼才塔函数(Riemann zeta function)研究了一维情况下周期边界下的玻色爱因斯坦凝聚体杂质间的相互作用力.通过计算杂质间的相互作用力,给出了力与杂质间距离的关系.结果表明,杂质间的距离越大,力越小.研究结果有助于进一步了解玻色爱因斯坦凝聚体中杂质所带来的物理效应.     

旋量玻色-爱因斯坦凝聚体平均自旋在外场中的演化

利用平均场理论和单空间模近似,研究了总自旋F=1的旋量玻色-爱因斯坦凝聚体的平均自旋在外磁场的演化行为．理论研究结果表明平均自旋演化行为与对称相互作用无关;当处于不同量子态的粒子数不随时间变化时,体系自旋的行为由外磁场、反对称相互作用决定．     

Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip

An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this 'strong coupling regime' of cavity quantum electrodynamics has been the subject of many experimental advances. Efforts have been made to control the coupling rate by trapping the atom and cooling it towards the motional ground state; the latter has been achieved in one dimension so far. For systems of many atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einstein condensates (BECs). Although experiments combining BECs and optical cavities have been reported recently, coupling BECs to cavities that are in the strong-coupling regime for single atoms has remained an elusive goal. Here we report such an experiment, made possible by combining a fibre-based cavity with atom-chip technology. This enables single-atom cavity quantum electrodynamics experiments with a simplified set-up and realizes the situation of many atoms in a cavity, each of which is identically and strongly coupled to the cavity mode. Moreover, the BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field; we demonstrate that this gives rise to a controlled, tunable coupling rate. We study the heating rate caused by a cavity transmission measurement as a function of the coupling rate and find no measurable heating for strongly coupled BECs. The spectrum of the coupled atoms-cavity system, which we map out over a wide range of atom numbers and cavity-atom detunings, shows vacuum Rabi splittings exceeding 20 gigahertz, as well as an unpredicted additional splitting, which we attribute to the atomic hyperfine structure. We anticipate that the system will be suitable as a light-matter quantum interface for quantum information.     

阱的非简谐性对玻色-爱因斯坦凝聚集体激发的影响

研究了在一个二次方加四次方势阱V(x)=12(x2 λx4)中玻色-爱因斯坦凝聚体(BEC)的集体激发.运用变分法得到了准一维BEC的2个低能激发模,研究了阱的非简谐性对BEC集体激发的影响,发现当λ>0时,两低能模频谱发生蓝移;当λ<0时,两低能模频谱发生红移.讨论了不同振幅驱动激发下BEC质量中心和宽度的变化:由于囚禁势阱的非简谐性,BEC两低能激发模会发生耦合,使宽度变化产生谐拍.给出了频率驱动下宽度的响应结果.     

Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.     

两非等同纠缠原子与单模光场相互作用系统的纠缠特性

研究了在考虑腔场有能量损耗、原子有自发辐射时,两非等同纠缠原子与单模腔场相互作用过程中两原子之间的纠缠特性。结果表明;两纠缠原子的纠缠特性与两原子初态、腔场耗散系数k、原子的自发辐射率Γ及两原子与腔、场的耦合系数g1g2有一定的联系。     

拉曼耦合作用下玻色-爱因斯坦凝聚的磁化性质

研究双分量玻色气体在拉曼耦合作用下的磁化性质。对于宏观占据单一动量态的玻色?爱因斯坦凝聚, 磁化强度和磁化率分别与凝聚动量和有效质量存在普适的线性关系, 这些普适关系不依赖于拉曼耦合的强度、失谐大小及原子间的相互作用。推导出磁化率与有效质量的线性关系, 可以在经典物理图像下描述简谐势阱中凝聚体的偶极振荡, 自旋空间、动量空间及坐标空间的振幅之比可表达为有效质量和自旋磁化率的解析形式。这组振幅关系对于亚稳态附近的小幅振荡也同样适用。     

玻色—爱因斯坦凝聚状态下的轴子:一种新的冷暗物质模型

最近的研究表明冷轴子在宇宙背景辐射光子温度低于T～100 eV(f/1012GeV)1/2后可以达到热平衡状态,由此将形成冷轴子的玻色—爱因斯坦凝聚。文章同时对轴子凝聚和普通冷暗物质模型的区别进行了探讨。     

Experimental determination of entanglement with a single measurement

Nearly all protocols requiring shared quantum information--such as quantum teleportation or key distribution--rely on entanglement between distant parties. However, entanglement is difficult to characterize experimentally. All existing techniques for doing so, including entanglement witnesses or Bell inequalities, disclose the entanglement of some quantum states but fail for other states; therefore, they cannot provide satisfactory results in general. Such methods are fundamentally different from entanglement measures that, by definition, quantify the amount of entanglement in any state. However, these measures suffer from the severe disadvantage that they typically are not directly accessible in laboratory experiments. Here we report a linear optics experiment in which we directly observe a pure-state entanglement measure, namely concurrence. Our measurement set-up includes two copies of a quantum state: these 'twin' states are prepared in the polarization and momentum degrees of freedom of two photons, and concurrence is measured with a single, local measurement on just one of the photons.     

3体作用下2耦合Bose-Einstein 凝聚的混沌动力学行为

研究了双势阱束缚下具有含时原子散射长度的弱耦合BEC系统.考虑了2种情况:对应着无含时情况下,系统有一个稳定的静态解;对应没有含时情况下,系统有2个稳定的静态解和一个不稳定的静态解.在含时情况下,混沌会在系统中出现,讨论了其动力学行为.