arXiv:1701.08255 · Physical Review A

Appropriate conditions to realize a p -wave superfluid state starting from a spin-orbit-coupled s -wave superfluid Fermi gas

T. Yamaguchi, Daisuke Inotani, Yoji Ohashi

Published May 9, 2017• 0 citations

Abstract

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.

DOI: 10.1103/physreva.95.053609

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Proposed method to realize the p -wave superfluid state using an s -wave superfluid Fermi gas with a synthetic spin-orbit interaction

T. Yamaguchi, Yoji Ohashi

arXiv:1504.03835Physical Review AJul 13, 20159 citations

A Novel Route to Reach a p-Wave Superfluid Fermi Gas

T. Yamaguchi, Daisuke Inotani, Yoji Ohashi

arXiv:1610.09086Journal of the Physical Society of JapanDec 5, 20167 citations

Triplet pair amplitude in a trapped s-wave superfluid Fermi gas with broken spin rotation symmetry. II. Three-dimensional continuum case

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arXiv:1610.01026Physical Review AOct 18, 20162 citations

Engineering frequency-dependent superfluidity in Bose-Fermi mixtures

Maksims Arzamasovs, Bo Liu

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パリティを破るスピン軌道相互作用と可変な引力相互作用を駆使してp波フェルミ原子気体超流動を実現させる方法の理論的研究(本文)

辰威山口

Jan 1, 20160 citations

Triplet pair amplitude in a trapped s -wave superfluid Fermi gas with broken spin rotation symmetry

Yuki Endo, Daisuke Inotani, Ryo Hanai +1 more

arXiv:1505.05640Physical Review AAug 10, 20153 citations

arXiv:1701.08255 · Physical Review A

Appropriate conditions to realize a p -wave superfluid state starting from a spin-orbit-coupled s -wave superfluid Fermi gas

T. Yamaguchi, Daisuke Inotani, Yoji Ohashi

Published May 9, 2017• 0 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.95.053609

Related papers

Proposed method to realize the p -wave superfluid state using an s -wave superfluid Fermi gas with a synthetic spin-orbit interaction

T. Yamaguchi, Yoji Ohashi

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 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.

arXiv:1504.03835Physical Review AJul 13, 20159 citations

A Novel Route to Reach a p-Wave Superfluid Fermi Gas

T. Yamaguchi, Daisuke Inotani, Yoji Ohashi

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 ( $Φ_{p}$ ) 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 ( $U_{p}$ ) by using a Feshbach resonance, we reach the $p$ -wave superfluid phase with the $p$ -wave order parameter being symbolically written as $Δ_{p}\sim U_{p}Φ_{p}$ . 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 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 ($Φ_{p}$) 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 ($U_{p}$) by using a Feshbach resonance, we reach the $p$-wave superfluid phase with the $p$-wave order parameter being symbolically written as $Δ_{p}\sim U_{p}Φ_{p}$. 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.

arXiv:1610.09086Journal of the Physical Society of JapanDec 5, 20167 citations

Triplet pair amplitude in a trapped s-wave superfluid Fermi gas with broken spin rotation symmetry. II. Three-dimensional continuum case

Daisuke Inotani, Ryo Hanai, Yoji Ohashi

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 $p\text{-wave}$ Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s\text{-wave}$ superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the $s\text{-wave}$ pairing interaction to an appropriate $p\text{-wave}$ one by using a Feshbach technique in this case, a nonvanishing $p\text{-wave}$ superfluid order parameter is immediately obtained, which is given by the product of the $p\text{-wave}$ interaction and the $p\text{-wave}$ pair amplitude that has already been induced in the spin-imbalanced $s\text{-wave}$ superfluid Fermi gas. Thus, by definition, the system is in the $p\text{-wave}$ superfluid state, at least just after this manipulation. Since the achievement of a $p\text{-wave}$ 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.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 $p\text{-wave}$ Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s\text{-wave}$ superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the $s\text{-wave}$ pairing interaction to an appropriate $p\text{-wave}$ one by using a Feshbach technique in this case, a nonvanishing $p\text{-wave}$ superfluid order parameter is immediately obtained, which is given by the product of the $p\text{-wave}$ interaction and the $p\text{-wave}$ pair amplitude that has already been induced in the spin-imbalanced $s\text{-wave}$ superfluid Fermi gas. Thus, by definition, the system is in the $p\text{-wave}$ superfluid state, at least just after this manipulation. Since the achievement of a $p\text{-wave}$ 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.

arXiv:1610.01026Physical Review AOct 18, 20162 citations

Engineering frequency-dependent superfluidity in Bose-Fermi mixtures

Maksims Arzamasovs, Bo Liu

Unconventional superconductivity and superfluidity are among the most exciting and fascinating quantum phenomena in condensed-matter physics. Usually such states are characterized by nontrivial spin or spatial symmetry of the pairing order parameter, such as ``spin triplet'' or `` $p$ wave.'' However, besides spin and spatial dependence the order parameter may have unconventional frequency dependence which is also permitted by Fermi-Dirac statistics. Odd-frequency fermionic pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be achieved through our proposed approach. Second, by taking advantage of recent rapid developments in producing spin-orbit-coupled dispersions in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency-dependent superfluid. The key idea is introducing the frequency-dependent attraction between fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superfluids with cold atoms.Unconventional superconductivity and superfluidity are among the most exciting and fascinating quantum phenomena in condensed-matter physics. Usually such states are characterized by nontrivial spin or spatial symmetry of the pairing order parameter, such as ``spin triplet'' or ``$p$ wave.'' However, besides spin and spatial dependence the order parameter may have unconventional frequency dependence which is also permitted by Fermi-Dirac statistics. Odd-frequency fermionic pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be achieved through our proposed approach. Second, by taking advantage of recent rapid developments in producing spin-orbit-coupled dispersions in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency-dependent superfluid. The key idea is introducing the frequency-dependent attraction between fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superfluids with cold atoms.

arXiv:1707.08331Physical Review AApr 6, 20183 citations

パリティを破るスピン軌道相互作用と可変な引力相互作用を駆使してp波フェルミ原子気体超流動を実現させる方法の理論的研究(本文)

辰威山口

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.

Jan 1, 20160 citations

Triplet pair amplitude in a trapped s -wave superfluid Fermi gas with broken spin rotation symmetry

Yuki Endo, Daisuke Inotani, Ryo Hanai +1 more

We investigate the possibility that the broken spatial inversion symmetry caused by a trap potential induces a spin-triplet Cooper pair amplitude in an $s$ -wave superfluid Fermi gas. Based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is actually induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$ -wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a $p$ -wave superfluid Fermi gas by suddenly changing the $s$ -wave pairing interaction to a $p$ -wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into a spin-singlet (and even-parity) state and a spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such an admixture has recently attracted much attention in the field of noncentrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, from the viewpoint of cold Fermi gas physics.We investigate the possibility that the broken spatial inversion symmetry caused by a trap potential induces a spin-triplet Cooper pair amplitude in an $s$-wave superfluid Fermi gas. Based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is actually induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a $p$-wave superfluid Fermi gas by suddenly changing the $s$-wave pairing interaction to a $p$-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into a spin-singlet (and even-parity) state and a spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such an admixture has recently attracted much attention in the field of noncentrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, from the viewpoint of cold Fermi gas physics.

arXiv:1505.05640Physical Review AAug 10, 20153 citations

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.

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 (

Φ_{p}

) 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 (

U_{p}

) by using a Feshbach resonance, we reach the

p

-wave superfluid phase with the

p

-wave order parameter being symbolically written as

Δ_{p}\sim U_{p}Φ_{p}

. 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.

T=0

, we point out that an odd-parity

p\text{-wave}

Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity)

s\text{-wave}

superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the

s\text{-wave}

pairing interaction to an appropriate

p\text{-wave}

one by using a Feshbach technique in this case, a nonvanishing

p\text{-wave}

superfluid order parameter is immediately obtained, which is given by the product of the

p\text{-wave}

interaction and the

p\text{-wave}

pair amplitude that has already been induced in the spin-imbalanced

s\text{-wave}

superfluid Fermi gas. Thus, by definition, the system is in the

p\text{-wave}

superfluid state, at least just after this manipulation. Since the achievement of a

p\text{-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.

p

wave.'' However, besides spin and spatial dependence the order parameter may have unconventional frequency dependence which is also permitted by Fermi-Dirac statistics. Odd-frequency fermionic pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be achieved through our proposed approach. Second, by taking advantage of recent rapid developments in producing spin-orbit-coupled dispersions in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency-dependent superfluid. The key idea is introducing the frequency-dependent attraction between fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superfluids with cold atoms.

We investigate the possibility that the broken spatial inversion symmetry caused by a trap potential induces a spin-triplet Cooper pair amplitude in an

s

-wave superfluid Fermi gas. Based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is actually induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped

s

-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a

p

-wave superfluid Fermi gas by suddenly changing the

s

-wave pairing interaction to a

p

-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into a spin-singlet (and even-parity) state and a spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such an admixture has recently attracted much attention in the field of noncentrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, from the viewpoint of cold Fermi gas physics.