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 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.
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.