A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.
The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which is responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibirum of a magnet…
The spin diffusion and damped oscillations are studied in the collision of two spin polarized clouds of cold atoms with resonant interactions. The strong density dependence of the diffusion coefficient leads to inhomogeneous spin diffusion that changes from central to surface spin flow as the temperature increases. The inhomogeneity and the smaller finite trap size significantly reduce the spin diffusion rate at low temperatures. The resulting spin diffusion rates, spin drag and initial damped oscillations are compatible with measurements at low to high temperatures for resonant attractive int…
The position and momentum space information entropies of weakly interacting trapped atomic Bose-Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems contain $N$ atoms confined in a $D(\le 3)$-dimensional harmonic trap has a universal form as $ S_t^{(D)} = N(a D - b \ln N) $, where $a \simeq 2.332$ and $b = 2$ for interacting bosonic systems and $a \simeq 1.982$ and $b = 1$ for ideal fermionic systems. These results obey the entropic uncert…
Ground-state properties of a few spin-$1/2$ ultra-cold fermions confined in a one-dimensional trap are studied by the exact diagonalization method. In contrast to previous studies, it is not assumed that the projection of a spin of individual particles is fixed. Therefore, the spin is treated as an additional degree of freedom and the global magnetization of the system is established spontaneously. Depending on the shape of the trap, inter-particle interactions, and an external magnetic field, the phase diagram of the system is determined. It is shown that, for particular confinements, some va…
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for …
We show that puzzling recent experimental results on spin diffusion in a strongly interacting atomic gas may be understood in terms of the predicted spin diffusion coefficient for a generic strongly interacting system. Three important features play a central role: a) Fick's law for diffusion must be modified to allow for the trapping potential, b) the diffusion coefficient is inhomogeneous, due to the density variations in the cloud and c) the diffusion approximation fails in the outer parts of the cloud, where the mean free path is long.
The entropy of the coexisting gas of ultra cold fermionic atoms and Bosonic molecular condensate confined in a magnetic trap has been calculated from equation of motion approaches. We have found that the entropy production depends not only to the Feshbach resonance and but also under certain limits to Rabi type oscillation and Bose Josephson junction type oscillation.
This dissertation presents theoretical investigations of universality and finite-range corrections in few- and many-boson systems. The main focus is on ultra-cold atomic gases seen both from the three-body, many-body, and mean-field perspective. Topics include corrections to Efimov physics, the N-body Efimov effect, two-body correlations in condensates and higher-order interactions in mean-field BECs.
We report on highly effective trapping of cold atoms by a new method for a stable single optical trap in the near-optical resonant regime. An optical trap with the near-optical resonance condition consists of not only the dipole but also the radiative forces, while a trap using a far-off resonance dominates only the dipole force. We estimate a near-optical resonant trap for ultracold rubidium atoms in the range between -0.373 and -2.23 THz from the resonance. The time dependence of the trapped atoms indicates some difference of the stable center-of-mass positions in the near-optical resonant t…
We report on trapping and cooling Li-6 atoms in a monolithic ring bowtie cavity. To make the cavity insensitive to magnetic fields used to tune atomic interactions, we constructed it entirely from fused silica and Zerodur. The components were assembled using hydroxide bonding, which we show can be compatible with ultra-high vacuum. Backscattering in high-finesse ring cavities readily causes trap intensity fluctuations and heating, but with phase-controlled bi-directional pumping the trap lifetime can be made long enough for quantum gas experiments in both the crossed-beam trap (unidirectional …
We present the experimental realization of a compressible blue detuned crossed dipole trap for cold atoms allowing for fast dynamical compression (~ 5 - 10 ms) of 5x10^7 Rubidium atoms up to densities of ~ 10^13 cm^-3. The dipole trap consists of two intersecting tubes of blue-detuned laser light. These tubes are formed using a single, rapidly rotating laser beam which, for sufficiently fast rotation frequencies, can be accurately described by a quasi-static potential. The atomic cloud is compressed by dynamically reducing the trap volume leading to densities close to the Ioffe-Reggel criterio…
This paper is a short introduction to cold atom physics and Bose-Einstein condensation. Light forces on atoms are presented, together with laser cooling, and a few atom traps: the magneto-optical trap, dipole traps and magnetic traps. A brief description of Bose-Einstein condensation is given together with some important links with condensed matter physics. The reader is referred to comprehensive reviews and to other lecture notes for further details on atom cooling, trapping and Bose-Einstein condensation.
A double-helix optical trapping potential for cold atoms can be straightforwardly created inside the evanescent field of an optical nanofiber. It suffices to send three circularly polarized light fields through the nanofiber; two counterpropagating and far red-detuned with respect to the atomic transition and the third far blue-detuned. Assuming realistic experimental parameters, the transverse confinement of the resulting potential allows one to reach the one-dimensional regime with cesium atoms for temperatures of several \muK. Moreover, by locally varying the nanofiber diameter, the radius …
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half-partition …
Within the context of Hartree-Fock-Bogoliubov theory, we study the behavior of superfluid Fermi systems when they pass from a small to a large container. Such systems can be now realized thanks to recent progress in experimental techniques. It will allow to better understand pairing properties at overflow and in general in rapidly varying external potentials.
We study a novel millimetre-scale magnetic trap for ultracold atoms, in which the current carrying conductors can be situated outside the vacuum region, a few mm away from the atoms. This design generates a magnetic field gradient in excess of \SI{1000}{G/cm} at a distance of \SI{2}{mm} from the conductors. We perform electromagnetic and thermo-mechanical characterisation using Finite Element Methods (FEM). The predicted behaviour has been verified by electrical and thermal measurements on a prototype, but has not been implemented on an apparatus with cold atoms. Operating this trap at the hig…
We study light-assisted collisions in an ensemble containing a small number (~3) of cold Rb87 atoms trapped in a microscopic dipole trap. Using our ability to operate with one atom exactly in the trap, we measure the one-body heating rate associated to a near-resonant laser excitation, and we use this measurement to extract the two-body loss rate associated to light-assisted collisions when a few atoms are present in the trap. Our measurements indicate that the two-body loss rate can reach surprisingly large values beta>10^{-8} cm^{3}.s^{-1} and varies rapidly with the trap depth and the param…
We investigate the problem of a single ion in a radio-frequency trap and immersed in an ultracold Bose gas either in a condensed or a non-condensed phase. We develop master equation formalism describing the sympathetic cooling and we determine the cooling rates of ions. We show that cold atomic reservoir modifies the stability diagram of the ion in the Paul trap creating the regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential.
Overlapping Feshbach resonances are commonly observed in experiments with ultracold atoms and can influence the molecule production process. We derive an effective approach to describe magnetoassociation in an external trap in the presence of multiple overlapping resonances. We study how the strength and shape of the trap affects the energy level structure and demonstrate the existence of a regime in which the conventional two-channel Landau-Zener description of the molecule production process breaks down.
We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Luttinger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.
We study the spectrum of density fluctuations in the ultra-cold gas of neutral atoms, confined in a magneto-optical trap. We determine the corresponding amplitude and spectra of laser light scattered by this medium. We derive an expression for the dynamical structure function, by using a test particle method. We propose to use the collective laser scattering as a diagnostic method for the microscopic properties of the ultra-cold matter. This will also allow us to check on the atomic correlations which are mediated by the collective mean field inside the gas.
We investigate the position oscillation of a particle that models the center of mass quantum state of a trapped Bose-Einstein condensate coupled to the zero-point fluctuations of the gravitational field. A semiclassical analysis is performed that allows to calculate the mean square amplitude of the oscillation. In analogy with the Lamb shift in quantum electrodynamics, this gives rise to an upshift of the energy of the trapped condensates. We show that for an elongated trap, the energy shift scales quadratically with the length as well as cubically with the total number of atoms.
We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-topical traps, multiple-scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the re-scattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces results on a new polari…
Non-adiabatic decay rates for a radio-frequency dressed magnetic trap are calculated using Fermi's Golden Rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semi-classical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of non-adiabatic spin flip transitions in the adiabatic limit. This indicates that care is needed whe…
We identify regular structures in the globally chaotic spectra of an interacting bosonic quantum gas in tilted periodic potentials. The associated eigenstates exhibit strong localization properties on the lattice, and are dynamically robust against external perturbations.
Cold-Atom Buoy: A Differential Magnetic Sensing Technique in Cold Quadrupole Traps
HUN-REN Wigner Research Centre for Physics（匈牙利研究网络温格物理研究中心）；Department of Physics of Complex Systems, ELTE Eötvös Loránd University（厄特沃什·罗兰大学复杂系统物理系）；Center for Quantum Science, Physikalisches Institut, Eberhard Karls Universität Tübingen（蒂宾根大学物理研究所量子科学中心）；Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学物理研究所理论物理系）
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occur…
