Bose-Einstein condensation of exciton polaritons

Phase transitions to quantum condensed phases--such as Bose-Einstein condensation (BEC), superfluidity, and superconductivity--have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 10(9) times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase.     

Bose-Einstein condensation of atomic gases

The early experiments on Bose-Einstein condensation in dilute atomic gases accomplished three long-standing goals. First, cooling of neutral atoms into their motional ground state, thus subjecting them to ultimate control, limited only by Heisenberg's uncertainty relation. Second, creation of a coherent sample of atoms, in which all occupy the same quantum state, and the realization of atom lasers - devices that output coherent matter waves. And third, creation of a gaseous quantum fluid, with properties that are different from the quantum liquids helium-3 and helium-4. The field of Bose-Einstein condensation of atomic gases has continued to progress rapidly, driven by the combination of new experimental techniques and theoretical advances. The family of quantum-degenerate gases has grown, and now includes metastable and fermionic atoms. Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.     

Bose-Einstein condensation on a microelectronic chip

Although Bose-Einstein condensates of ultracold atoms have been experimentally realizable for several years, their formation and manipulation still impose considerable technical challenges. An all-optical technique that enables faster production of Bose-Einstein condensates was recently reported. Here we demonstrate that the formation of a condensate can be greatly simplified using a microscopic magnetic trap on a chip. We achieve Bose-Einstein condensation inside the single vapour cell of a magneto-optical trap in as little as 700 ms-more than a factor of ten faster than typical experiments, and a factor of three faster than the all-optical technique. A coherent matter wave is emitted normal to the chip surface when the trapped atoms are released into free fall; alternatively, we couple the condensate into an 'atomic conveyor belt', which is used to transport the condensed cloud non-destructively over a macroscopic distance parallel to the chip surface. The possibility of manipulating laser-like coherent matter waves with such an integrated atom-optical system holds promise for applications in interferometry, holography, microscopy, atom lithography and quantum information processing.     

Towards Bose-Einstein condensation of excitons in potential traps

An exciton is an electron-hole bound pair in a semiconductor. In the low-density limit, it is a composite Bose quasi-particle, akin to the hydrogen atom. Just as in dilute atomic gases, reducing the temperature or increasing the exciton density increases the occupation numbers of the low-energy states leading to quantum degeneracy and eventually to Bose-Einstein condensation (BEC). Because the exciton mass is small--even smaller than the free electron mass--exciton BEC should occur at temperatures of about 1 K, many orders of magnitude higher than for atoms. However, it is in practice difficult to reach BEC conditions, as the temperature of excitons can considerably exceed that of the semiconductor lattice. The search for exciton BEC has concentrated on long-lived excitons: the exciton lifetime against electron-hole recombination therefore should exceed the characteristic timescale for the cooling of initially hot photo-generated excitons. Until now, all experiments on atom condensation were performed on atomic gases confined in the potential traps. Inspired by these experiments, and using specially designed semiconductor nanostructures, we have collected quasi-two-dimensional excitons in an in-plane potential trap. Our photoluminescence measurements show that the quasi-two-dimensional excitons indeed condense at the bottom of the traps, giving rise to a statistically degenerate Bose gas.     

Bose-Einstein condensation of excitons in bilayer electron systems

An exciton is the particle-like entity that forms when an electron is bound to a positively charged 'hole'. An ordered electronic state in which excitons condense into a single quantum state was proposed as a theoretical possibility many years ago. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron-electron bilayers as in electron-hole bilayers. In current quantum Hall excitonic condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer counterflow conductivity.     

光学微腔中WSe2激子与光子耦合效应的研究

研究了300 K下,自制的法布里-珀罗(Fabry-P6rot,F-P)半导体微腔中,光场与WSe2单分子薄膜激子之间的强弱耦合作用.利用集成角分辨功能的显微荧光/白光反射光谱系统研究了样品的光学性质,并在强耦合区间内看到了激子极化激元的形成,对应的拉比分裂能量为46.7 meV.理论拟合结果跟实验现象吻合,为激子极化...     

谐振势阱中有限粒子玻色-爱因斯坦凝聚的数值计算

从统计力学原理出发,用数值方法研究了三维等方谐振势阱中有限粒子数玻色子系统的化学势及其导数随温度的变化．结果表明,粒子数有限的系统没有一级相变,但在有限温度发生玻色-爱因斯坦凝聚;利用化学势二阶导数的极小值定义的玻色-爱因斯坦凝聚临界温度很好地符合实验结果．     

Effective mass approach for a Bose-Einstein condensate in an optical lattice

We study the stationary and propagating solutions for a Bose-Einstein condensate （BEC） in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrodinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.     

2001年度诺贝尔物理学奖与玻色-爱因斯坦凝聚

简要介绍了2001年度诺贝尔物理学奖及其获得者--埃里克·科内尔,卡尔·维曼与沃尔夫冈·克特勒的有关研究工作;评述了玻色-爱因斯坦凝聚的实现及其应用.     

微腔对玻色子-费米子混合体系隧穿动力学的影响

从光学微腔与双阱中玻色子—费米子混合凝聚体耦合体系的薛定谔方程出发,推导出了粒子数算符以及光子数算符随时间演化的表达式,构造出系统有效的经典哈密顿量,利用数值方法和图示法研究了系统的动力学行为.通过相图发现玻色子和费米子的相互作用以及费米子之间的相互作用能够影响相对粒子数差随时间的变化;光学微腔能使系统稳定点增多,运动模式增加,混沌加剧.     

Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping

Bose-Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle density exceeds a critical value. To achieve Bose-Einstein condensation, one can either decrease the temperature or increase the density of bosons. It has been predicted that a quasi-equilibrium system of bosons could undergo Bose-Einstein condensation even at relatively high temperatures, if the flow rate of energy pumped into the system exceeds a critical value. Here we report the observation of Bose-Einstein condensation in a gas of magnons at room temperature. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equilibrium, they can be described by Bose-Einstein statistics with zero chemical potential and a temperature-dependent density. In the experiments presented here, we show that by using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential. With increasing pumping intensity, the chemical potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.     

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.     

Temperature-dependent optical resonance in a thin-walled tubular oxide microcavity

This work proposes a temperature-response capability of optical resonance in tubular optical oxide microcavities. The thin wall thickness with a subwavelength scale enables these microcavities to interact with the environment effectively. By optimization of the geometries and materials, the tubular microcavities can be tuned into temperature-inert in vacuum, and the experiments support this design. The experiments prove the idea of utilizing them as temperature-inert microcavities. Contrary wavelength shifts from previous studies were observed, which can be explained with the theoretical model. Furthermore, the theoretical results of the present work suggest that novel rolled-up microtubes could act as an exceptional optical microcavity for the application in temperature response.     

Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl3

Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.     

二维双色型光晶格中玻色-爱因斯坦凝聚的局域化

利用含时变分法研究了二维双色型光晶格中玻色爱因斯坦凝聚中稳定局域态的性质.根据含时变分法利用高斯型试探波函数和Euler-Lagrange方程给出了高斯型局域态的波包宽度随时间变化的二阶微分方程,确定稳定了局域态的波包宽度.利用数值计算方法直接求解了Gross-Pitaevskii方程,给出了稳定局域态的空间分布.结果表明,在原子之间存在非线性排斥和吸引作用,或者非线性相互作用为零时,在二维玻色-爱因斯坦凝聚中均可以形成稳定的局域态.     

Trapping an atom with single photons

The creation of a photon-atom bound state was first envisaged for the case of an atom in a long-lived excited state inside a high-quality microwave cavity. In practice, however, light forces in the microwave domain are insufficient to support an atom against gravity. Although optical photons can provide forces of the required magnitude, atomic decay rates and cavity losses are larger too, and so the atom-cavity system must be continually excited by an external laser. Such an approach also permits continuous observation of the atom's position, by monitoring the light transmitted through the cavity. The dual role of photons in this system distinguishes it from other single-atom experiments such as those using magneto-optical traps, ion traps or a far-off-resonance optical trap. Here we report high-finesse optical cavity experiments in which the change in transmission induced by a single slow atom approaching the cavity triggers an external feedback switch which traps the atom in a light field containing about one photon on average. The oscillatory motion of the trapped atom induces oscillations in the transmitted light intensity; we attribute periodic structure in intensity-correlation-function data to 'long-distance' flights of the atom between different anti-nodes of the standing-wave in the cavity. The system should facilitate investigations of the dynamics of single quantum objects and may find future applications in quantum information processing.     

反抛物势与双光晶格势中的三维玻色-爱因斯坦凝聚涡旋孤子

提出了一种处理囚禁于反抛物势和双光晶格复合势中玻色-爱因斯坦凝聚涡旋孤子动力学的能量密度泛函和直接数值仿真相结合的方法.利用静态Gross-Pitaevskii方程和柱对称玻色-爱因斯坦凝聚涡旋孤子试探波函数,给出了玻色-爱因斯坦凝聚静态涡旋孤子能量密度泛函的解析式,再运用数值模拟含时Gross-Pi-taevskii方程的方法,得到了稳定演化的涡旋孤子;并且通过调控双光晶格势,实现了玻色-爱因斯坦凝聚涡旋孤子从某一晶格势槽为初始位置到任意位置的操控,为玻色-爱因斯坦凝聚的实验和应用研究提供了一定的理论依据.值得指出的是,双涡旋孤子的稳定演化与操控是最重要的发现.     

一维,二维和三维对称双色型光晶格中玻色-爱因斯坦凝聚的局域化

利用含时变分法研究了一维,二维和三维对称情形下双色型光晶格中玻色-爱因斯坦凝聚中局域化态的稳定性.首先采用高斯型试探波函数得出了三种维度下稳定性分析所需要的有效势能表达式.其次根据有效势能是否具有局域最小值来判断体系是否具有稳定状态,结果表明,双色型光晶格强度,两体,三体和高阶相互作用在稳定性中所起的作用是不同的,两体和高阶相互作用对体系的稳定性有决定性作用,而三体和晶格强度只对稳定性起调节作用,在有些情况下这种调节作用是必须的.最后给出了参数相空间中的稳定区域.