We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature “fermionization” through the measurement of the rates of two-body inelastic processes, such as photoassociation.

We report the observation of a Bose-Einstein condensation of ytterbium atoms by evaporative cooling in a novel crossed optical trap. Unlike the previously observed condensates, a ytterbium condensate is a two-electron system in a singlet state and has distinct features such as the extremely narrow intercombination transitions which are ideal for future optical frequency standard and the insensitivity to external magnetic field which is important for precision coherent atom optics, and the existence of the novel metastable triplet states generated by optical excitation from the singlet state.

It is proved that the Lieb-Liniger cusp condition implementing the delta function interaction in one-dimensional Bose gases is dynamically conserved under phase imprinting by pulses of arbitrary spatial form, and the subsequent many-body dynamics in the thermodynamic limit is expressed approximately in terms of solutions of the time-dependent single-particle Schrödinger equation for a set of time-dependent orbitals evolving from an initial Lieb-Liniger-Fermi sea. As an illustrative application, a generation of gray solitons in a Lieb-Liniger gas on a ring by a phase-imprinting pulse is studied.

We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.

We study the persistence probability $P(t)$ that, starting from a random initial condition, the magnetization of a $d^{\prime }$-dimensional manifold of a $d$-dimensional spin system at its critical point does not change sign up to time $t$. For $d^{\prime }>0$ we find three distinct late-time decay forms for $P(t)$: exponential, stretched exponential, and power law, depending on a single parameter $\zeta =(D-2+\eta )/z$, where $D=d-d^{\prime }$ and $\eta ,z$ are standard critical exponents. In particular, we predict that for a line magnetization in the critical $d=2$ Ising model, $P(t)$ decays as a power law while, for $d=3$, $P(t)$ decays as a power of $t$ for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov–de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.

We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction $\nu$, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for $\nu =2/3,3/4,4/3,5/4$ in addition to the Laughlin state $\nu =1/2$ as well as the Pfaffian state for $\nu =1$. We give gap estimates by finite-size scaling of both charged and neutral excitations.

We analyze the field theoretic functions of the dynamical model $C$ in two-loop order. Our results correct long-standing errors in these functions published by several authors. We discuss, in particular, the fixed points for the ratio $w^{*}$ of the two time scales involved, as well as their stability. The regions of the “phase diagram,” whose axes are the spatial dimension $d$ and number of order parameter components $n$, correspond to these fixed points; previous authors have found, in addition, an anomalous region in which the scaling properties were unclear. We show that such an anomalous region does not exist. There are only two regions: one with a finite fixed-point $w^{*}$ where the dynamical exponent $z=2+\alpha /\nu$, and another where $w^{*}=0$ and $z$ is equal to the model $A$ value. We show how the one-loop result is recovered from the two-loop result in the limit $ϵ=4-d$ going to zero.

We show how to simulate a system in thermal equilibrium when the energy cannot be evaluated exactly: the error distribution needs to be symmetric, but it does not need to be known. We also solve the Ceperley-Dewing version of this problem, where the error distribution is taken to be fully known. These underlying ideas give an effective optimization strategy for problems where the evaluation of each design can be sampled only statistically, including an application to protein folding.

We investigate the strongly interacting regime in an optically trapped ${}^6\mathrm{L}\mathrm{i}$ Fermi mixture near a Feshbach resonance. The resonance is found at $800(40)\mathrm{G}$ in good agreement with theory. Anisotropic expansion of the gas is interpreted by collisional hydrodynamics. We observe an unexpected and large shift (80 G) between the resonance peak and both the maximum of atom loss and the change of sign of the interaction energy.

We report on a new test of Lorentz invariance performed by comparing the resonance frequencies of two orthogonal cryogenic optical resonators subject to Earth’s rotation over $\sim 1\mathrm{y}\mathrm{r}$. For a possible anisotropy of the speed of light $c$, we obtain ${\Delta }_{\theta }c/c_0=(2.6\pm 1.7)\times {10}^{-15}$. Within the Robertson-Mansouri-Sexl (RMS) test theory, this implies an isotropy violation parameter $\beta -\delta -\frac{1}{2}=(-2.2\pm 1.5)\times {10}^{-9}$, about 3 times lower than the best previous result. Within the general extension of the standard model of particle physics, we extract limits on seven parameters at accuracies down to ${10}^{-15}$, improving the best previous result by about 2 orders of magnitude.

We measure the axial momentum distribution of Bose-Einstein condensates with an aspect ratio of 152 using Bragg spectroscopy. We observe the Lorentzian momentum distribution characteristic of one-dimensional phase fluctuations. The temperature dependence of the width of this distribution provides a quantitative test of quasicondensate theory. In addition, we observe a condensate length consistent with the suppression of density fluctuations, even when phase fluctuations are large.

We measure the intensity correlation function of two interfering spatially displaced copies of phase fluctuating Bose-Einstein condensates. It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated condensates. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.

We investigate the macroscopic diffusion of carriers in the multiple-trapping (MT) regime, in relation with electron transport in nanoscaled heterogeneous systems, and we describe the differences, as well as the similarities, between MT and the continuous-time random walk (CTRW). Diffusion of free carriers in MT can be expressed as a generalized continuity equation based on fractional time derivatives, while the CTRW model for diffusive transport generalizes the constitutive equation for the carrier flux.

We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum nonlocality has to be redefined in the presence of superselection rules: there exist separable states that cannot be prepared locally and exhibit some form of nonlocality. Moreover, the notion of local distinguishability in the presence of classical communication has to be altered. This can be used to perform quantum information tasks that are otherwise impossible. In particular, this leads to the introduction of perfect quantum data hiding protocols, for which quantum communication (eventually in the form of a separable but nonlocal state) is needed to unlock the secret.

An outstanding open problem in nanoscience is how to control the motion of tiny particles. Ratchetlike devices, inspired by biological motors, have been proposed as a way to achieve this goal. However, the net directed transport is almost suppressed if the diffusing particles are weakly coupled to the underlying spatially asymmetric substrate. Here we show how adding particles of an auxiliary species, that interact with both the primary particles of interest and the substrate, provides a controlled enhancement of the flow for both species. These can move either together or in opposite directions, depending upon the strength of the interaction, and whether it is attractive or repulsive.

We study the preparation and manipulation of states involving a small number of interacting particles. By controlling the splitting and fusing of potential wells, we show how to interconvert Mott-insulator-like and trapped BEC-like states. We also discuss the generation of “Schrödinger cat” states by splitting a microtrap and taking into practical consideration the asymmetry between the resulting wells. These schemes can be used to perform multiparticle interferometry with neutral atoms, where interference effects can be observed only when all the participating particles are measured.

We numerically show that a topologically nontrivial 3D Skyrmion can be energetically stable in a trapped two-component atomic Bose-Einstein condensate, for the parameters of ${}^{87}\mathrm{R}\mathrm{b}$ condensate experiments. The separate conservation of the two atomic species can stabilize the Skyrmion against shrinking to zero size, while drift of the Skyrmion due to the trap-induced density gradient can be prevented by rotation or by a laser potential.

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] and in cavity QED [B. Varcoe et al., Nature (London) 403, 743 (2000)]. The values of the Wigner functions of the underlying states at the origin of phase space are $W_{|0⟩}(0)=+1.75$ for the vibrational ground state and $W_{|1⟩}(0)=-1.4$ for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.