Unitary quantum three-body problem in a harmonic trap

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short-range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.     

Criterion for bosonic superfluidity in an optical lattice

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution n(k) can be misleading, for even a normal Bose gas can have a similarly sharp n(k). We show that superfluidity in a homogeneous system can be detected from the so-called visibility (v) of n(k)--that v must be 1 within O(N(-2/3)), where N is the number of bosons. We also show that the T=0 visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.     

Clock shift in a strongly interacting two-dimensional Fermi gas

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an S-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like 1/(ω2ln2ω). Its coefficient is proportional to ln2'(a'(2D)/a(2D)), where a(2D) and a'(2D) are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to ln(a'(2D)/a(2D)). If |ln(a'(2D)/a(2D))| > 1, the clock shift arises as a cancellation between much larger contributions proportional to ln2(a'(2D)/a(2D)) from bound-bound and bound-free rf transitions.     

Measurements of Tan's contact in an atomic Bose-Einstein condensate

A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with zero-range interactions. We report on measurements of the contact, using rf spectroscopy, for an (85)Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short time scales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In investigating this issue, we have located an Efimov resonance for (85)Rb atoms with loss measurements and thus determined the three-body interaction parameter. In our contact spectroscopy, in a region of observable beyond-mean-field effects, we find no measurable contribution from three-body physics.     

Exact relations for a strongly interacting fermi gas from the operator product expansion

The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.     

Temperature dependence of the universal contact parameter in a unitary Fermi gas

The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(k(F)a), where k(F) is the Fermi wave vector and a is the s-wave scattering length, and the temperature T/T(F), where T(F) is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.     

Properties of Universal Bosonic Tetramers

The system of four identical bosons is studied using momentum–space equations for the four-particle transition operators. Positions, widths and existence limits of universal unstable tetramers are determined with high accuracy. Their effect on the atom–trimer and dimer–dimer scattering observables is discussed. We show that a universal shallow tetramer intersects the atom–trimer threshold twice leading to resonant effects in ultracold atom–trimer collisions.     

Single-Particle Momentum Distributions for Bosonic Trimer States in Two and Three Dimensions

For a system formed by three bosons interacting by a pairwise zero-range potential we show how the functional form of the asymptotic momentum distribution changes drastically when passing from bi (2D) to tridimensional (3D) regime, mainly affected by the absence/presence of the Efimov effect in 2D/3D. The spectator functions and the momentum distribution are calculated analytically for both regimes.     

M1 transition strength in the SU(3) limit of the generalized IBM-2

We generalize the SU(3) limit of the standard IBM-2 formalism of sd bosons to sdg…λ bosons, where λ denotes a boson of arbitrarily large, even angular momentum λ, and investigate the effect on the B(M1, 0₁⁺ → 1⁺) transition strength. In the SU(3) limit, all the M1 transition strength resides in a single 1⁺ state and is proportional to λ.     

Dynamical consequences of spontaneous breakdown of symmetries

The spontaneous breakdown of a continuous symmetry group generated by conserved currents is considered. In the framework of general quantum field theory the possible dynamical consequences of spontaneous breakdown are analysed: a general relation is derived between n− and (n+1) — point functions involving Goldstone bosons in the limit of zero momentum. The technique is illustrated by a few examples for the SU(2) × SU(2) chiral group and the results generalized relations known from the perturbative treatment of the σ-model.     

Three dimensional anisotropic κ spectra of turbulence at subproton scales in the solar wind

We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales. We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs. We show that the cascade is carried by highly oblique kinetic Alfvén waves with ω(plas) ≤ 0.1ω(ci) down to k(⊥) ρ(i)～2. Each k spectrum in the direction perpendicular to B0 shows two scaling ranges separated by a breakpoint (in the interval [0.4,1]k(⊥)ρ(i): a Kolmogorov scaling k(⊥)?1?? followed by a steeper scaling ～k(⊥)????. We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate.     

磁阱中超冷玻色气体临界行为的观测

超冷玻色气体为研究量子临界现象提供了一个非常干净的实验系统. 弱相互作用下的三维玻色气体的临界行为与⁴He发生超流相变时的临界行为类似, 都属于三维XY型普适类. 从正常流体到超流的量子相变过程中, 系统会经历一个从无序相到长程有序相的转变; 而在相变点附近, 系统参量会表现出一些奇点的特征. 本文从实验上观测到了静磁阱中超冷⁸⁷Rb玻色气体在凝聚体相变温度T_c附近的临界行为. 原子气体从静磁阱中释放, 经过30 ms的自由飞行后, 通过吸收成像得到原子气体的动量分布; 然后从中扣除热原子气体的动量分布, 提取出空间上处于临界区域内的原子气体动量分布, 并对不同温度下的动量分布半高宽进行统计. 统计结果显示: 在非常接近相变温度T_c时, 动量分布的半高宽突然减小, 表现出十分明显的奇点行为.     

Observation of a resonant four-body interaction in cold cesium Rydberg atoms

Cold Rydberg atoms subject to long-range dipole-dipole interactions represent a particularly interesting system for exploring few-body interactions and probing the transition from 2-body physics to the many-body regime. In this work we report the direct observation of a resonant 4-body Rydberg interaction. We exploit the occurrence of an accidental quasicoincidence of a 2-body and a 4-body resonant Stark-tuned F?rster process in cesium to observe a resonant energy transfer requiring the simultaneous interaction of at least four neighboring atoms. These results are relevant for the implementation of quantum gates with Rydberg atoms and for further studies of many-body physics.     

Application of the unitarity conditions to calculating interaction amplitudes for Ramond states in superstring theory

The unitarity conditions for superstring amplitudes of boson interaction are used to calculate the Green's function for Ramond states—that is, for 10-spinor states and Ramond bosons. It is shown that, from the unitarity conditions, it follows, among other things, that local quantities specifying the sought amplitudes satisfy some integral relations. The amplitude for the transition of two massless Neveu-Schwarz bosons into a system of two massless Ramond states is obtained in an arbitrary order in the number of loops. For this amplitude, the aforementioned integral relations are verified in the tree approximation.     

Momentum distribution and contact of the unitary Fermi gas

We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/?(F) as well as in the ground state. At large momenta k/k(F), we find that n(k) falls off as C/k?, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/?(F) and present a comparison with theory. At low T/?(F), we find that C increases with temperature, and we tentatively identify a maximum around T/?(F) ? 0.4. Our calculations are performed on lattices of spatial extent up to N(x) = 14 with a particle number per unit volume of ? 0.03-0.07.     

Nonequilibrium dynamics of Tonks-Girardeau gases on optical lattices

We summarize in the present work exact results obtained for Tonks-Girardeau gases on one-dimensional optical lattices both for the ground state and nonequilibrium dynamics. On the theoretical side, impenetrable bosons offer the opportunity to study strongly interacting systems in one-dimensional lattices exactly, by means of the Jordan-Wigner transformation, and hence contribute to the topic of strong correlations at the center of interest in both condensed matter physics and quantum gases. This motivation is further enhanced by recent experimental realizations of such systems with ultracold atoms. After having shown their universal properties in equilibrium, we concentrate on their nonequilibrium dynamics. It will be shown that, starting from a pure Fock state, quasi-long-range correlations develop dynamically and lead to the formation of quasicondensates with a momentum determined by the underlying lattice. We expect this effect to be relevant for atom lasers with full control of the wavelength. Then, we will show that the free evolution of an initially confined Tonks-Girardeau gas leads to a momentum distribution that approaches at long times that of the equivalent fermionic system, giving rise to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium. Remarkably, although the momentum distribution function of the Tonks-Girardeau gas becomes equal to the one of the fermions, no loss in coherence is observed in the system, as reflected by a large occupation of eigenstates of the one-particle density matrix.     

Ca+CH_3I→CaI+CH_3反应的矢量相关研究(英文)

本文采用准经典轨线方法,在LEPS势基础上计算了Ca+CH3I→CaI+CH3在不同碰撞能下的矢量相关计算了质心系中四个广义极化微分反应截面(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt),(2π/σ)(dσ22+/dωt),(2π/σ)(dσ21-/dωt),k-j′两矢量相关的P(θr)分布、k-k′-j′三矢量相关的极角分布P(φr)以及用θr和φr表示的产物转动角动量的空间分布P(θr,φr).     

Universal order statistics of random walks

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of n steps with step lengths of finite variance σ(2). We show that the statistics of the gap d(k,n) = M(k,n)-M(k+1,n) between the kth and the (k+1)th maximum of the time series becomes stationary, i.e., independent of n as n → ∞ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large k, ~d(k,∞)-/σ 1/sqrt[2πk], independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Pr(d(k,∞) = δ) ~/= (sqrt[k]/σ)P(δsqrt[k]/σ), in the regime δ~ (d(k,∞)). The scaling function P(x) is universal and has an unexpected power law tail, P(x) ~ x(-4) for large x. For δ> (d(k,∞)) the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.     

Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.