Ultracold Fermi gases provide versatile and flexible settings for molecular interactions and reaction dynamics in quantum regimes. Recently, Lianghui Huang and colleagues created weakly bound Feshbach molecules from the two spin components of 40K atomic Fermi gas. They then investigated the radio-frequency (RF) spectra of the weakly bound molecules and from that obtained the magnetic-field-dependent binding energy. The RF dissociation spectroscopy of the weakly bound molecules could be used to study ultracold molecule–molecule and molecule–atom collisions in the presence or absence of spin–orbit coupling. [Chin Phys B, 2014; 23(1): 013402] Researchers Guanjun Wang and colleagues have constructed a new apparatus based on a collinear tandem time-of-flight mass spectrometer to measure infrared photodissociation spectroscopy of size-selected ions in the gas phase. A simple new assembly, integrated with a mass gate and deceleration and reacceleration ion optics, was designed to fulfill mass selection, infrared photodissociation and fragment and parent ion mass analysis. Such an experimental setup provides a powerful tool to measure the infrared spectra of size-selected ions in the gas phase with high sensitivity. [Sci China Chem, 2013; 56(10): 1–6] Schematic diagram of the experimental apparatus consisting of a laser vaporization supersonic ion source and a collinear tandem time-of-flight mass spectrometer for infrared photodissociation spectroscopy. Published in Sci China-Chem, 2013; 56(10): 1–6. Gravitational potential energy sources and sinks, associated with different oceanic model parameterizations, can be used as criteria in evaluating the performance of a model. The upper bound of energy associated with lateral diffusion or advection is estimated at 100 GW. Any parameterizations associated with energy larger than the bound energy are unphysical. Further, any energy sources resulting from cabbeling associated with lateral advection in the Eulerian coordinate are artificial. In particular, huge sources or sinks in the widely used sigma-coordinated models imply the unphysical nature of such parameterization. [Acta Oceanol Sin, 2014; 33(3): 1–18] Graphene, composed of a single sheet of carbon atoms, has the potential for use in numerous exciting applications. Realizing its potential, however, requires sophisticated large-scale fabrication techniques that do not leave any residue on the graphene surface. By incorporating a protective metal layer into the standard photolithographic process, Johnson et al. have fabricated large-scale arrays of chemical vapor sensors. Specifically, the arrays are based on graphene field-effect transistors that are functionalized with DNA. These chemically functionalized graphene transistors act as a highly sensitive ‘electronic nose’, capable of detecting organic compounds at very low levels (parts per billion). [Nano Res, 2014; 7(1): 95–103]
Ultracold Fermi gases provide versatile and flexible settings for molecular interactions and reaction dynamics in quantum regimes. Recently, Lianghui Huang and colleagues created weakly bound Feshbach molecules from the two spin components of 40K atomic Fermi gas. They then investigated the radio-frequency (RF) spectra of the weakly bound molecules and from that obtained the magnetic-field-dependent binding energy. The RF dissociation spectroscopy of the weakly bound molecules could be used to study ultracold molecule–molecule and molecule–atom collisions in the presence or absence of spin–orbit coupling. [Chin Phys B, 2014; 23(1): 013402] Researchers Guanjun Wang and colleagues have constructed a new apparatus based on a collinear tandem time-of-flight mass spectrometer to measure infrared photodissociation spectroscopy of size-selected ions in the gas phase. A simple new assembly, integrated with a mass gate and deceleration and reacceleration ion optics, was designed to fulfill mass selection, infrared photodissociation and fragment and parent ion mass analysis. Such an experimental setup provides a powerful tool to measure the infrared spectra of size-selected ions in the gas phase with high sensitivity. [Sci China Chem, 2013; 56(10): 1–6] Schematic diagram of the experimental apparatus consisting of a laser vaporization supersonic ion source and a collinear tandem time-of-flight mass spectrometer for infrared photodissociation spectroscopy. Published in Sci China-Chem, 2013; 56(10): 1–6. Gravitational potential energy sources and sinks, associated with different oceanic model parameterizations, can be used as criteria in evaluating the performance of a model. The upper bound of energy associated with lateral diffusion or advection is estimated at 100 GW. Any parameterizations associated with energy larger than the bound energy are unphysical. Further, any energy sources resulting from cabbeling associated with lateral advection in the Eulerian coordinate are artificial. In particular, huge sources or sinks in the widely used sigma-coordinated models imply the unphysical nature of such parameterization. [Acta Oceanol Sin, 2014; 33(3): 1–18] Graphene, composed of a single sheet of carbon atoms, has the potential for use in numerous exciting applications. Realizing its potential, however, requires sophisticated large-scale fabrication techniques that do not leave any residue on the graphene surface. By incorporating a protective metal layer into the standard photolithographic process, Johnson et al. have fabricated large-scale arrays of chemical vapor sensors. Specifically, the arrays are based on graphene field-effect transistors that are functionalized with DNA. These chemically functionalized graphene transistors act as a highly sensitive ‘electronic nose’, capable of detecting organic compounds at very low levels (parts per billion). [Nano Res, 2014; 7(1): 95–103]
We create weakly bound Feshbach molecules in ultracold Fermi gas 4~K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency （RF） technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.
We create weakly bound Feshbach molecules in ultracold Fermi gas 40 K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency (RF) technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.
Rapid progress in atomic, molecular, and optical (AMO) physics techniques enabled the creation of ultracold samples of molecular species and opened opportunities to explore chemistry in the ultralow temperature regime. In particular, both the external and internal quantum degrees of freedom of the reactant atoms and molecules are controlled, allowing studies that explored the role of the long-range potential in ultracold reactions. The kinetics of these reactions have typically been determined using the loss of reactants as proxies. To extend such studies into the short-range, we developed an experimental apparatus that combines the production of quantum-state-selected ultracold KRb molecules with ion mass and kinetic energy spectrometry, and directly observed KRb + KRb reaction intermediates and products [M.-G. Hu and Y. Liu, et al., Science, 2019, 366, 1111]. Here, we present the apparatus in detail. For future studies that aim for detecting the quantum states of the reaction products, we demonstrate a photodissociation based scheme to calibrate the ion kinetic energy spectrometer at low energies.
Ultracold 39K gases provide an ideal platform to study quantum few- and many-body systems, due to the high degree of control present in these systems. In particular, Feshbach resonances facilitate a magnetically tunable interaction strength between the atoms in the gas, and allow the formation of two- and three-body bound states, called Feshbach molecules and Efimov trimers respectively. Radio-frequency dissociation spectroscopy of weakly bound Feshbach molecules is one of the most precise ways to characterize the properties of a Feshbach resonance. We apply a numerical method to our Feshbach molecule binding energy data to compute the shift in the molecule’s binding energy due to the presence of a confining potential. These simulations are first used to replicate the confinement shift found for 6Li Feshbach molecules by another group, and then to correct our measurement results for the binding energy of 39K Feshbach molecules. The correction of these measurements is necessary for our determination of the Feshbach resonance location with unprecedented accuracy.
The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.
Ultracold atomic gases provide an ideal system with which to study fundamental many-body physics.Exhibiting universal interactions in clean and controllable environments, long-used simple models as well as more exotic models can now be realized.The interplay between theory and experiment is therefore very active, and, in this thesis, I will detail several works, both exact analytic results and numerical calculations, which have impacts on current experiments.I begin with an introduction to the field including a brief discussion of experiments, the microscopic model of two species of interacting fermions, the BCS-BEC crossover and an overview of the various phases of atomic Fermi gases.I then describe the various results of my theoretical investigations, which are divided into five chapters.First, I describe radio frequency (RF) spectroscopy experiments and how they probe the single-particle spectral function.This leads to my results on an exact feature of the spectral lineshape, a universal large-momentum structure which exists for all states of interacting Fermi systems and has been verified in recent angle-resolved RF experiments.Second, I focus on gases which have a normal Fermi liquid ground state and show that their lineshape exhibits a characteristic jump discontinuity.I illustrate this Fermi surface singularity and the previously mentioned universal large momentum tail with explicit calculations.Third, I turn to the low energy structure of the single-particle spectral function in the superfluid state.I argue that sharp low energy quasiparticle excitations exist across the BCS-BEC crossover using a general argument that includes the interaction of fermions with the low-energy collective mode.This is illustrated with an explicit calculation within an approximation scheme.Fourth, I address the trap-induced inhomogeneity and use a Bogoliubov-deGennes analysis to test if a simple local density approximation (LDA) can provide an adequate description of a spin imbalanced Fermi system.Finally, I discuss dynamics of atomic gases motivated by a recent experiment in which two spin-polarized clouds are allowed to collide with each other.Despite the underlying attractive interactions, the clouds are seen to bounce off of each other.Using a hydrodynamic description, I argue that the short and intermediate time dynamics reflects a metastable state in which the effective interaction is repulsive.It is my hope that the work presented in this thesis can be used to gain key insights which inspire future endeavors.6.2 Time dependence of the center-of-mass positions zσ of the two spin clouds at unitarity for an initial separation z↑ (t = 0) = R z , z↓ (t = 0) = -R z using the upper branch energy functional and damping γ = 1.Red (upper) and blue (lower) curves denote the different spin species. . . . . . . . . . . . . . . .71 6.3 The upper branch energy functional obtained from lowest order constraint variational method.(a), energy as a function of the polarization P for various values of k F a s as indicated in the figure.(b), energy as a function of the interaction parameter k F a s for various values of polarization P as indicated in the figure.(c), phase diagram of the interacting two-component Fermi gases.The two vertical red dashed lines indicates the separation between three phases.For 1/(k F a s ) > 1.124, the system is in the Fermi liquid (FL) phase.For 1.124 > 1/(k F a s ) > 0.91, the system is in the partially polarized phase (PP) and for 1/(k F a s ) < 0.91, the system is fully polarized. . . . . .74 6.4 (Color online) Time dependence of the center-of-mass positions zσ of the two spin clouds for k F (0)a s = 2. . . . . . . . . . . . . . . . . . . . . . . . . . .75 6.5 (Color online) Time dependence of the center-of-mass positions zσ of the two spin clouds for k F (0)a s = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . .