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.     

Vortices and superfluidity in a strongly interacting Fermi gas

Quantum degenerate Fermi gases provide a remarkable opportunity to study strongly interacting fermions. In contrast to other Fermi systems, such as superconductors, neutron stars or the quark-gluon plasma of the early Universe, these gases have low densities and their interactions can be precisely controlled over an enormous range. Previous experiments with Fermi gases have revealed condensation of fermion pairs. Although these and other studies were consistent with predictions assuming superfluidity, proof of superfluid behaviour has been elusive. Here we report observations of vortex lattices in a strongly interacting, rotating Fermi gas that provide definitive evidence for superfluidity. The interaction and therefore the pairing strength between two 6Li fermions near a Feshbach resonance can be controlled by an external magnetic field. This allows us to explore the crossover from a Bose-Einstein condensate of molecules to a Bardeen-Cooper-Schrieffer superfluid of loosely bound pairs. The crossover is associated with a new form of superfluidity that may provide insights into high-transition-temperature superconductors.     

Coherent zero-state and pi-state in an exciton-polariton condensate array

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.     

Creation of ultracold molecules from a Fermi gas of atoms

Following the realization of Bose-Einstein condensates in atomic gases, an experimental challenge is the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation or a magnetic field Feshbach resonance. The availability of atomic Fermi gases offers the prospect of coupling fermionic atoms to bosonic molecules, thus altering the quantum statistics of the system. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of ultracold 40K2 molecules. Starting with a quantum degenerate Fermi gas of atoms at a temperature of less than 150 nK, we scan the system over a Feshbach resonance to create adiabatically more than 250,000 trapped molecules; these can be converted back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning the magnetic field away from the Feshbach resonance, and can be varied over a wide range. We directly detect these weakly bound molecules through their radio-frequency photodissociation spectra; these probe the molecular wavefunction, and yield binding energies that are consistent with theory.     

Attractive and repulsive Fermi polarons in two dimensions

The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well known case is an impurity coupled to a bosonic bath (such as lattice vibrations); the impurity and its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-transition-temperature superconductors, as well as in colossal magnetoresistance in manganites. For impurities in a fermionic bath, studies have considered heavy or immobile impurities which exhibit Anderson's orthogonality catastrophe and the Kondo effect. More recently, mobile impurities have moved into the focus of research, and they have been found to form new quasiparticles known as Fermi polarons. The Fermi polaron problem constitutes the extreme, but conceptually simple, limit of two important quantum many-body problems: the crossover between a molecular Bose-Einstein condensate and a superfluid with BCS (Bardeen-Cooper-Schrieffer) pairing with spin-imbalance for attractive interactions, and Stoner's itinerant ferromagnetism for repulsive interactions. It has been proposed that such quantum phases (and other elusive exotic states) might become realizable in Fermi gases confined to two dimensions. Their stability and observability are intimately related to the theoretically debated properties of the Fermi polaron in a two-dimensional Fermi gas. Here we create and investigate Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas, measuring their spectral function using momentum-resolved photoemission spectroscopy. For attractive interactions, we find evidence for a disputed pairing transition between polarons and tightly bound dimers, which provides insight into the elementary pairing mechanism of imbalanced, strongly coupled two-dimensional Fermi gases. Additionally, for repulsive interactions, we study novel quasiparticles--repulsive polarons--the lifetime of which determines the possibility of stabilizing repulsively interacting Fermi systems.     

Skyrmions in a ferromagnetic Bose-Einstein condensate.

Multi-component Bose-Einstein condensates provide opportunities to explore experimentally the wealth of physics associated with the spin degrees of freedom. The ground-state properties and line-like vortex excitations of these quantum systems have been studied theoretically. In principle, nontrivial spin textures consisting of point-like topological excitations, or skyrmions, could exist in a multi-component Bose-Einstein condensate, owing to the superfluid nature of the gas. Although skyrmion excitations are already known in the context of nuclear physics and the quantum-Hall effect, creating these excitations in an atomic condensate would offer an opportunity to study their physical behaviour in much greater detail, while also enabling an ab initio comparison between theory and experiment. Here we investigate theoretically the stability of skyrmions in a fictitious spin-1/2 condensate of 87Rb atoms. We find that skyrmions can exist in such a gas only as a metastable state, but with a lifetime comparable to (or even longer than) the typical lifetime of the condensate itself.     

Quantum dynamics of a single vortex

Vortices occur naturally in a wide range of gases and fluids, from macroscopic to microscopic scales. In Bose-Einstein condensates of dilute atomic gases, superfluid helium and superconductors, the existence of vortices is a consequence of the quantum nature of the system. Quantized vortices of supercurrent are generated by magnetic flux penetrating the material, and play a key role in determining the material properties and the performance of superconductor-based devices. At high temperatures the dynamics of such vortices are essentially classical, while at low temperatures previous experiments have suggested collective quantum dynamics. However, the question of whether vortex tunnelling occurs at low temperatures has been addressed only for large collections of vortices. Here we study the quantum dynamics of an individual vortex in a superconducting Josephson junction. By measuring the statistics of the vortex escape from a controllable pinning potential, we demonstrate the existence of quantized levels of the vortex energy within the trapping potential well and quantum tunnelling of the vortex through the pinning barrier.     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

Spontaneous coherence in a cold exciton gas

If bosonic particles are cooled down below the temperature of quantum degeneracy, they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis of a number of fundamental phenomena in physics, including superconductivity, superfluidity and Bose-Einstein condensation. Spontaneous coherence is the key characteristic of condensation in momentum space. Excitons--bound pairs of electrons and holes--form a model system to explore the quantum physics of cold bosons in solids. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy owing to their long lifetimes. Here we report measurements of spontaneous coherence in a gas of indirect excitons. We found that spontaneous coherence of excitons emerges in the region of the macroscopically ordered exciton state and in the region of vortices of linear polarization. The coherence length in these regions is much larger than in a classical gas, indicating a coherent state with a much narrower than classical exciton distribution in momentum space, characteristic of a condensate. A pattern of extended spontaneous coherence is correlated with a pattern of spontaneous polarization, revealing the properties of a multicomponent coherent state. We also observed phase singularities in the coherent exciton gas. All these phenomena emerge when the exciton gas is cooled below a few kelvin.     

Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms.

For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.     

玻色—爱因斯坦凝聚在一维周期量子阱中的有效质量研究

当玻色爱因斯坦凝聚体处于一维周期量子阱中的时候,我们可以得到定态GP方程的一组精确解,利用这组精确解我们对玻色爱因斯坦凝聚体在一维周期量子阱中的有效质量进行了研究,经过研究发现原子间的非线性相互作用使得有效质量增大。     

玻色-爱因斯坦凝聚体与双模光场相互作用中光场的量子特性

目的 研究玻色-爱因斯坦凝聚体与双模光场相互作用中光场的量子特性.方法 在波戈留波夫近似下,求解系统的动力学方程.结果 双模光场与波色-爱因斯坦凝聚体相互作用过程中,光场的两正交分量交替呈现周期性压缩现象,光子是聚束的.结论 模间相关恒为非经典相关.     

Universal spin transport in a strongly interacting Fermi gas

Transport of fermions, particles with half-integer spin, is central to many fields of physics. Electron transport runs modern technology, defining states of matter such as superconductors and insulators, and electron spin is being explored as a new carrier of information. Neutrino transport energizes supernova explosions following the collapse of a dying star, and hydrodynamic transport of the quark-gluon plasma governed the expansion of the early Universe. However, our understanding of non-equilibrium dynamics in such strongly interacting fermionic matter is still limited. Ultracold gases of fermionic atoms realize a pristine model for such systems and can be studied in real time with the precision of atomic physics. Even above the superfluid transition, such gases flow as an almost perfect fluid with very low viscosity when interactions are tuned to a scattering resonance. In this hydrodynamic regime, collective density excitations are weakly damped. Here we experimentally investigate spin excitations in a Fermi gas of (6)Li atoms, finding that, in contrast, they are maximally damped. A spin current is induced by spatially separating two spin components and observing their evolution in an external trapping potential. We demonstrate that interactions can be strong enough to reverse spin currents, with components of opposite spin reflecting off each other. Near equilibrium, we obtain the spin drag coefficient, the spin diffusivity and the spin susceptibility as a function of temperature on resonance and show that they obey universal laws at high temperatures. In the degenerate regime, the spin diffusivity approaches a value set by [planck]/m, the quantum limit of diffusion, where [planck]/m is Planck's constant divided by 2π and m the atomic mass. For repulsive interactions, our measurements seem to exclude a metastable ferromagnetic state.     

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen-Cooper-Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose-Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose-Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS-BEC continuum.     

Direct observation of Anderson localization of matter waves in a controlled disorder

In 1958, Anderson predicted the localization of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose-Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We operate in a regime of pure Anderson localization, that is, with weak disorder-such that localization results from many quantum reflections of low amplitude-and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction-a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.     

基于量子力学的相互作用绘景构造非线性哈密顿系统的数值计算方法

文章在量子力学的相互作用绘景中给出了非线性哈密顿系统离散格式的构造方法.首先将原非线性哈密顿问题变换至相互作用绘景,导出一个含时的常微分方程系统,离散该常微分方程并变换回原系统的态矢即可得到原问题的离散格式.基于不同的常微分方程数值方法,可得到原系统不同的离散格式.该方法还可以有效地求解多组分的Bose-Einstein凝聚态物理问题.     

Magnetic trapping of rare-earth atoms at millikelvin temperatures

The ability to create quantum degenerate gases has led to the realization of Bose-Einstein condensation of molecules, atom-atom entanglement and the accurate measurement of the Casimir force in atom-surface interactions. With a few exceptions, the achievement of quantum degeneracy relies on evaporative cooling of magnetically trapped atoms to ultracold temperatures. Magnetic traps confine atoms whose electronic magnetic moments are aligned anti-parallel to the magnetic field. This alignment must be preserved during the collisional thermalization of the atomic cloud. Quantum degeneracy has been reached in spherically symmetric, S-state atoms (atoms with zero internal orbital angular momentum). However, collisional relaxation of the atomic magnetic moments of non-S-state atoms (non-spherical atoms with non-zero internal orbital angular momentum) is thought to proceed rapidly. Here we demonstrate magnetic trapping of non-S-state rare-earth atoms, observing a suppression of the interaction anisotropy in collisions. The atoms behave effectively like S-state atoms because their unpaired electrons are shielded by two outer filled electronic shells that are spherically symmetric. Our results are promising for the creation of quantum degenerate gases with non-S-state atoms, and may facilitate the search for time variation of fundamental constants and the development of a quantum computer with highly magnetic atoms.     

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.