Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.
Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.
The Fulde-Ferrell Larkin-Ovchinnikov (FFLO) type superconductor is an exotic form of matter known as a supersolid because it simultaneously supports superfluid and magnetic order. In both condensed matter and ultracold atomic gases, this phase has yet to be conclusively observed despite long interest in both theory and experiment. In one-dimension (1D), unlike expectations for higher dimensions, the FFLO phase is found in a large region of the phase diagram [1]. The effect of quantum and thermal fluctuations, however, are expected to be reduced in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover [2], which we have identified and characterized [3]. We confine a spin-imbalanced Fermi gas of lithium 6 to an array of 1D tubes using a 2D optical lattice. We bring the system into the dimensional crossover by increasing the inter-tube tunneling rate and using a Feshbach resonance to tune interactions. The periodicity of these domain walls, which depends on the magnitude of the polarization, is a definitive signature of the FFLO phase. In this work, we develop new experimental and analytical methods to extract periodic signals that, if they indeed are domain walls, lay the foundation for full confirmation of the FFLO phase. [1] Y. A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, “Spin-imbalance in a one-dimensional Fermi gas,” Nature 467, 567 (2010). [2] M. M. Parish, S. K. Baur, E. J. Mueller, and D. A. Huse, “Quasi-One- Dimensional Polarized Fermi Superfluids,” Phys. Rev. Lett. 99, 250403 (2007). [3] M. C. Revelle, J. A. Fry, B. A. Olsen, and R. G. Hulet, “1D to 3D Crossover of a Spin-Imbalanced Fermi Gas,” Physical Review Letters 117 (2016).
Ultracold gases are of great interest in modern physics. The main reason is that in the systems of ultracold gases the parameters can be easily tuned, thus they can be used as a testing ground for various quantum many-body theories. Interesting macroscopic quantum effects have been observed in the ultracold gas systems, for instance Bose-Einstein condensation. In this thesis, theoretical knowledge of ultracold gases is extended. A summary of the methods used in this thesis is given, including a detailed description of the density response theory and the time-evolving block decimation (TEBD) algorithm. Collective excitations of an ultracold gas in a three-dimensional (3D) spherically symmetric trap are studied in detail in publications II and III. As a result, several collective modes are discovered such as a low energy Higgs-type mode, a second sound-like mode, and a strong mode resembling the Leggett mode. Using the TEBD algorithm, physics of a polaron in a one-dimensional (1D) lattice, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in 1D are studied in publications IV and I, respectively. In publication I a method to detect the FFLO phase is suggested, namely by the observation of the change in the double occupancy after a lattice depth modulation. Publication IV compares a variational ansatz and the TEBD simulations and finds an excellent agreement, indicating that the variational ansatz can be used to describe the system for a certain range of interactions.
We investigate the finite-temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a nonpolarized Bardeen-Cooper-Schrieffer superfluid (P<Pc) or a fully polarized normal gas (P>Pc), depending on the smallness of the spin polarization P, relative to a critical value Pc. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite-temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the ongoing experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.
Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.
Department of Physics and Zhejiang Institute of Modern Physics,Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang 310027, China andSynergetic Innovation Center of Quantum Information and Quantum Physics, Hefei, Anhui 230026, China(Dated: May 6, 2014)Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent op-portunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of greatinterest in condensed matter physics. However, the FFLO states have been elusive and not been observed ex-perimentally in Fermi gases in three dimensions (3D), due to their small phase space volume and extremely lowtemperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainlyin a
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.