Theoretical study of an idea to realize a p-wave superfluid Fermi gas using a parity-violating spin-orbit coupling and tunable pairing interactionsIn this thesis, I theoretically propose an idea to realize a p-wave superfluid state in an ultracold Fermi gas, which may avoid the difficulties that the current experiments aiming to achieve this unconventional pairing state are facing.While the current experimental approaches always start from a p-wave interacting Fermi gas, my idea first prepares a pwave Cooper pair amplitude in a spin-orbit coupled s-wave superfluid Fermi gas, without using any p-wave interaction.Although this system is still in the s-wave superfluid state at this stage, one then suddenly replaces the s-wave pairing interaction with an appropriate p-wave one, by using a Feshbash resonance technique.The p-wave superfluid state is then realized, where the p-wave superfluid order parameter is given by the product of the introduced p-wave interaction and the p-wave pair amplitude that has already been prepared in the s-wave superfluid state.In this thesis, after I overview cold Fermi gas physics, as well as the difficulties that the current experiments are facing, I first examine the p-wave Cooper-pair amplitude induced in a spin-orbit coupled s-wave superfluid Fermi gas.Within the framework of the BCS (Bardeen-Cooper-Schrieffer)-Leggett theory at zero temperature, I clarify what type of p-wave pair amplitude is induced in the presence of a spin-orbit interaction.I also evaluate the magnitude of the induced p-wave pair amplitude, from the weak-coupling BCS regime to the strong-coupling BEC (Bose-Einstein condensation) regime.Using the strong-coupling theory developed by Nozières and Schmitt-Rink, I also calculate the superfluid phase transition temperature and effects of a spin-orbit interaction in the whole BCS-BEC crossover region, to confirm that the region with large p-wave pair amplitude is accessible within the current experimental technology.The latter part of this thesis deals with the time evolution of the p-wave superfluid order parameter, after the s-wave interaction is replaced by an appropriate p-wave one.Employing the time-dependent Bogoliubov de-Gennes theory, I show that, under a certain condition, the induced p-wave superfluid order parameter remains finite, even long after the p-wave interaction is turned on.I also clarify the condition for the realization of large magnitude of the p-wave superfluid order parameter.図 1.1: 6 Li で観測されたフェルミ原子気体超流動における Cooper 対分子の重心運動量 分布 [4].図手前側の強度分布は, フェルミ原子気体をトラップから解放して 6 ms 後の原 子気体に共鳴光を照射し, 測定した吸収像の柱密度の 3 mm 四方プロット.これから計 算された分子の空間的密度分布が図奥側にある.このような原子気体の測定法を飛行時 間法といい, ここで得られた空間的密度分布はそのまま分子の速度分布 (運動量分布) に 対応する.図中左側から右側へ向け, 系の温度が T /T F = 0.2, 0.1, 0.05 と低くなっている (T F はフェルミ縮退温度). 図中奥は, 各温度における重心運動量分布を表している. (赤 線：観測値, 青線：同じ温度での古典統計の運動量分布.) 系を冷却するにつれ, Cooper 対分子が, 重心運動量ゼロの状態 (図中の分布のピーク位置) に Bose-Einstein 凝縮するた め, 古典統計 (Boltzmann 分布) に従わない鋭いピークの運動量分布が見られている. こ の図では, 中央および右側が超流動状態である.
Theoretical study of an idea to realize a p-wave superfluid Fermi gas using a parity-violating spin-orbit coupling and tunable pairing interactionsIn this thesis, I theoretically propose an idea to realize a p-wave superfluid state in an ultracold Fermi gas, which may avoid the difficulties that the current experiments aiming to achieve this unconventional pairing state are facing.While the current experimental approaches always start from a p-wave interacting Fermi gas, my idea first prepares a pwave Cooper pair amplitude in a spin-orbit coupled s-wave superfluid Fermi gas, without using any p-wave interaction.Although this system is still in the s-wave superfluid state at this stage, one then suddenly replaces the s-wave pairing interaction with an appropriate p-wave one, by using a Feshbash resonance technique.The p-wave superfluid state is then realized, where the p-wave superfluid order parameter is given by the product of the introduced p-wave interaction and the p-wave pair amplitude that has already been prepared in the s-wave superfluid state.In this thesis, after I overview cold Fermi gas physics, as well as the difficulties that the current experiments are facing, I first examine the p-wave Cooper-pair amplitude induced in a spin-orbit coupled s-wave superfluid Fermi gas.Within the framework of the BCS (Bardeen-Cooper-Schrieffer)-Leggett theory at zero temperature, I clarify what type of p-wave pair amplitude is induced in the presence of a spin-orbit interaction.I also evaluate the magnitude of the induced p-wave pair amplitude, from the weak-coupling BCS regime to the strong-coupling BEC (Bose-Einstein condensation) regime.Using the strong-coupling theory developed by Nozières and Schmitt-Rink, I also calculate the superfluid phase transition temperature and effects of a spin-orbit interaction in the whole BCS-BEC crossover region, to confirm that the region with large p-wave pair amplitude is accessible within the current experimental technology.The latter part of this thesis deals with the time evolution of the p-wave superfluid order parameter, after the s-wave interaction is replaced by an appropriate p-wave one.Employing the time-dependent Bogoliubov de-Gennes theory, I show that, under a certain condition, the induced p-wave superfluid order parameter remains finite, even long after the p-wave interaction is turned on.I also clarify the condition for the realization of large magnitude of the p-wave superfluid order parameter.図 1.1: 6 Li で観測されたフェルミ原子気体超流動における Cooper 対分子の重心運動量 分布 [4].図手前側の強度分布は, フェルミ原子気体をトラップから解放して 6 ms 後の原 子気体に共鳴光を照射し, 測定した吸収像の柱密度の 3 mm 四方プロット.これから計 算された分子の空間的密度分布が図奥側にある.このような原子気体の測定法を飛行時 間法といい, ここで得られた空間的密度分布はそのまま分子の速度分布 (運動量分布) に 対応する.図中左側から右側へ向け, 系の温度が T /T F = 0.2, 0.1, 0.05 と低くなっている (T F はフェルミ縮退温度). 図中奥は, 各温度における重心運動量分布を表している. (赤 線：観測値, 青線：同じ温度での古典統計の運動量分布.) 系を冷却するにつれ, Cooper 対分子が, 重心運動量ゼロの状態 (図中の分布のピーク位置) に Bose-Einstein 凝縮するた め, 古典統計 (Boltzmann 分布) に従わない鋭いピークの運動量分布が見られている. こ の図では, 中央および右側が超流動状態である.
We propose a theoretical idea to reach the p-wave superfluid phase in an ultracold Fermi gas. The key of our idea is that the pairing symmetry of a Fermi superfluid is fully dominated by the symmetry of the superfluid order parameter, which is essentially given by the product of a pair amplitude and a pairing interaction. Noting this, in our proposal, we first prepare a p-wave pair amplitude not by using a p-wave interaction, but by using the phenomenon that a p-wave pair amplitude is induced in an s-wave superfluid Fermi gas with antisymmetric spin-orbit interaction. In this case, although the system is still in the s-wave superfluid state with the s-wave superfluid order parameter, when one suddenly replaces the s-wave interaction by an appropriate p-wave one (which is possible in cold Fermi gases by using a Feshbach resonance technique), the product of the p-wave interaction and the p-wave pair amplitude that has already been prepared in the spin-orbit-coupled s-wave superfluid state immediately gives a finite p-wave superfluid order parameter. Thus, at least just after this manipulation, the system is in the p-wave superfluid state, being characterized by the artificially produced p-wave superfluid parameter. In this paper, to assess our idea, we evaluate the p-wave pair amplitude in a spin-orbit-coupled s-wave superfluid Fermi gas at T=0. We determine the region where a large p-wave pair amplitude is obtained in the phase diagram with respect to the strengths of the s-wave pairing interaction and the spin-orbit coupling. We also discuss the accessibility of this optimal region on the viewpoint of the superfluid phase transition temperature. Since the achievement of a p-wave superfluid Fermi gas is one of the most crucial issues in cold-atom physics, our proposal would be useful for this exciting challenge.
We theoretically investigate a spin-orbit-coupled s-wave superfluid Fermi gas, to examine the time evolution of the system, after an s-wave pairing interaction is replaced by a p-wave one at t=0. In our recent paper [T. Yamaguchi, D. Inotani, and Y. Ohashi, J. Phys. Soc. Jpn. 86, 013001 (2017)], we proposed that this manipulation may realize a p-wave superfluid Fermi gas because the p-wave pair amplitude that is induced in the s-wave superfluid state by a parity-broken antisymmetric spin-orbit interaction gives a nonvanishing p-wave superfluid order parameter, immediately after the p-wave interaction is turned on. In this paper, using a time-dependent Bogoliubov-de Gennes theory, we assess this idea under various conditions with respect to the s-wave and p-wave interaction strengths, as well as the spin-orbit coupling strength. From these, we clarify that the momentum distribution of Fermi atoms in the initial s-wave state (t<0) is a key to produce a large p-wave superfluid order parameter. Since the realization of a p-wave superfluid state is one of the most exciting and difficult challenges in cold Fermi gas physics, our results may provide a possible way to accomplish this.
Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.
We theoretically propose an idea to realize a p-wave superfluid Fermi gas. To overcome the experimental difficulty that a p-wave pairing interaction to form p-wave Cooper pairs damages the system before the condensation growth, we first prepare a p-wave pair amplitude (Φp) in a spin-orbit coupled s-wave superfluid Fermi gas, without any p-wave interaction. Then, by suddenly changing the s-wave interaction with a p-wave one (Up) by using a Feshbach resonance, we reach the p-wave superfluid phase with the p-wave order parameter being symbolically written as Δp∼UpΦp. In this letter, we assess this scenario within the framework of a time-dependent Bogoliubov-de Gennes theory. Our results would contribute to the study toward the realization of unconventional pairing states in an ultracold Fermi gas.
We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)] for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at T=0, we point out that an odd-parity p-wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) s-wave superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the s-wave pairing interaction to an appropriate p-wave one by using a Feshbach technique in this case, a nonvanishing p-wave superfluid order parameter is immediately obtained, which is given by the product of the p-wave interaction and the p-wave pair amplitude that has already been induced in the spin-imbalanced s-wave superfluid Fermi gas. Thus, by definition, the system is in the p-wave superfluid state, at least just after this manipulation. Since the achievement of a p-wave superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.
Ultracold Fermi gas is an exciting field benefiting from atomic physics, optical physics and condensed matter physics. It covers many aspects of quantum mechanics. Here I introduce some of my work during my graduate study. We proposed an optical spectroscopic method based on electromagnetically-induced transparency (EIT) as a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. Both quasiparticle picture and pseudogap picture are constructed to facilitate the physical explanation of the pairing signature in the EIT spectra. Motivated by the prospect of realizing a Fermi gas of 40 K atoms with a synthetic non-Abelian gauge field, we investigated theoretically BEC-HCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We studied the properties of Rashba pairs using a standard pair fluctuation theory. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We discussed in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment. The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we studied the effect of a single classical impurity in trapped ultracold Fermi superfluids. Although a non-magnetic impurity does not change macroscopic properties of s-wave Fermi superfluids, depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we proposed a modified radio frequency spectroscopic method to measure the focal density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.