Resonant five-body recombination in an ultracold gas of bosonic atoms

We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative a that are tied to an Efimov trimer.

Interaction-free measurements by quantum Zeno stabilization of ultracold atoms

Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object-realized by a laser beam-prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments.

Ultracold Bose-Fermi mixtures with pairing: quantum phase transition, mechanical stability, and trap confinement

Ultracold dilute gases occupy an important role in modern physics and they are employed to verify fundamental quantum theories in most branches of theoretical physics. The scope of this thesis work is the study of Bose-Fermi (BF) mixtures at zero temperature with a tunable pairing between bosons and fermions. The mixtures are treated with diagrammatic quantum many-body methods based on the so-called T-matrix formalism. Starting from the Fermi-polaron limit, I will explore various values of relative concentrations up to mixtures with a majority of bosons, a case barely considered in previous works. An unexpected quantum phase transition is found to occur in a certain range of BF coupling for mixture with a slight majority of bosons. The mechanical stability of mixtures has been analysed, when the boson-fermion interaction is changed from weak to strong values, in the light of experimental results recently obtained for a double-degenerate Bose-Fermi mixture of 23 Na - 40 K. A possible improvement in the description of the boson-boson repulsion based on Popov's theory is proposed. Finally, the effects of a harmonic trapping potential are described, with a comparison with the experimental data for the condensate fraction recently obtained for a trapped 23 Na - 40 K mixture.

Effective range from tetramer-dissociation data for cesium atoms

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by 3.9±0.8R vdW, where RvdW is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs2 system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position. © 2013 American Physical Society.

Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

Optical control of interactions in ultracold gases opens new fields of research by creating ``designer" interactions with high spatial and temporal resolution. However, previous optical methods using single optical fields generally suffer from atom loss due to spontaneous scattering. This thesis reports new optical methods, employing two optical fields to control interactions in ultracold gases, while suppressing spontaneous scattering by quantum interference. In this dissertation, I will discuss the experimental demonstration of two optical field methods to control narrow and broad magnetic Feshbach resonances in an ultracold gas of $^6$Li atoms. The narrow Feshbach resonance is shifted by $30$ times its width and atom loss suppressed by destructive quantum interference. Near the broad Feshbach resonance, the spontaneous lifetime of the atoms is increased from $0.5$ ms for single field methods to $400$ ms using our two optical field method. Furthermore, I report on a new theoretical model, the continuum-dressed state model, that calculates the optically induced scattering phase shift for both the broad and narrow Feshbach resonances by treating them in a unified manner. The continuum-dressed state model fits the experimental data both in shape and magnitude using only one free parameter. Using the continuum-dressed state model, I illustrate the advantages of our two optical field method over single-field optical methods.

Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of $\Rb{87}$ vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in $\Rb{87}$ with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use $\Rb{87}$ to sympathetically cool $\Yb{171}$ to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation.

Anomalous specific-heat jump in a two-component ultracold Fermi gas

The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.

Pairing in a two-component ultracold Fermi gas: Phases with broken-space symmetries

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li atoms trapped in two different hyperfine states.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Strongly correlated states of ultracold rotating dipolar Fermi gases

We study strongly correlated ground and excited states of rotating quasi-2D Fermi gases constituted of a small number of dipole-dipole interacting particles with dipole moments polarized perpendicular to the plane of motion. As the number of atoms grows, the system enters an intermediate regime, where ground states are subject to a competition between distinct bulk-edge configurations. This effect obscures their description in terms of composite fermions and leads to the appearance of novel quasihole ground states. In the presence of dipolar interactions, the principal Laughlin state at filling upsilon=1/3 exhibits a substantial energy gap for neutral (total angular momentum conserving) excitations and is well-described as an incompressible Fermi liquid. Instead, at lower fillings, the ground state structure favors crystalline order.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

Chaos in collapsing Bose-condensed gas

We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schrödinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos. ©2000 The American Physical Society.

Effects of rotation in the laser-pulse photoassociation in a thermal gas of atoms

Photoassociation is a possible route for the formation of chemical bonds. In this process, the binding of colliding atoms can be induced by means of a laser field. Photoassociation has been studied in the ultracold regime and also with temperatures well above millikelvins in the thermal energy domain, which is a situation commonly encountered in the laboratory. A photoassociation mechanism can be envisioned based on the use of infrared pulses to drive a transition from free colliding atoms on the electronic ground state to form a molecule directly on that state. This work takes a step in this direction, investigating the laser-pulse-driven formation of heteronuclear diatomic molecules in a thermal gas of atoms including rotational effects. Based on the assumption of full system controllability, the maximum possible photoassociation yield is deduced. The photoassociation probability is calculated as a function of the laser parameters for different temperatures. Additionally, the photoassociation yield induced by subpicosecond pulses of a priori fixed shape is compared to the maximum possible yield.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

Quantum Monte Carlo study of effective masses in a polarized unitary Fermi gas

Ultracold gases provide an ideal platform for quantum simulations of many-body systems. Here we are interested in a particular system which has been the focus of most experimental and theoretical works on ultracold fermionic gases: the unitary Fermi gas. In this work we study with Quantum Monte Carlo simulations a two-component gas of fermionic atoms at zero temperature in the unitary regime. Specifically, we are interested in studying how the effective masses for the quasi-particles of the two components of the Fermi liquid evolve as the polarization is progressively reduced from full to lower values. A recent theoretical work, based on alternative diagrammatic methods, has indeed suggested that such effective masses should diverge at a critical polarization. To independently verify such predictions, we perform Variational Monte Carlo (VMC) calculations of the energy based on Jastrow-Slater wavefunctions after adding or subtracting a particle with a given momentum to a full Fermi sphere. In this way, we determine the quasi-particle dispersions, from which we extract the effective masses for different polarizations. The resulting effective masses turn out to be quite close to the non-interacting values, even though some evidence of an increase for the effective mass of the minority component appears close to the predicted value for the critical polarization. Preliminary results obtained for the majority component with the Fixed-node Diffusion Monte Carlo (DMC) method seem to indicate that DMC could lead to an increase of the effective masses in comparison with the VMC results. Finally, we point out further improvements of the trial wave-function and boundary conditions that would be necessary in future simulations to draw definite conclusions on the effective masses of the polarized unitary Fermi gas.