Universal one-dimensional atomic gases near odd-wave resonance

Cui, Xiaoling

doi:10.1103/physreva.94.043636

Cited by 52 publications

(47 citation statements)

References 59 publications

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“…In the presence of SO coupling, only s-and p-wave scatterings are involved in the subspace K = 0 and J = 0, and the wave function at short distance takes the form of Eq. (25). Using the asymptotic behavior of the wave function, we easily evaluatê…”

Section: Discussionmentioning

confidence: 99%

“…All these relations are characterized by the only universal quantity named contact, and therefore known as the contact theory. During past few years, the concept of contact theory was further generalized to higher-partial-wave interactions [13][14][15][16][17][18][19][20] as well as to low dimensions [21][22][23][24][25][26][27][28][29], and more contacts appear when additional two-body parameters are involved.…”

Section: Introductionmentioning

confidence: 99%

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Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

2020

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We present a comprehensive derivation of a set of universal relations for spin-orbit-coupled Fermi gases in three or two dimension, which follow from the short-range behavior of the two-body physics. Besides the adiabatic energy relations, the large-momentum distribution, the grand canonical potential and pressure relation derived in our previous work for three-dimensional systems [Phys. Rev. Lett. 120, 060408 (2018)], we further derive high-frequency tail of the radio-frequency spectroscopy and the short-range behavior of the pair correlation function. In addition, we also extend the derivation to two-dimensional systems with Rashba type of spin-orbit coupling. To simply demonstrate how the spin-orbit-coupling effect modifies the two-body short-range behavior, we solve the twobody problem in the sub-Hilbert space of zero center-of-mass momentum and zero total angular momentum, and perturbatively take the spin-orbit-coupling effect into account at short distance, since the strength of the spin-orbit coupling should be much smaller than the corresponding scale of the finite range of interatomic interactions. The universal asymptotic forms of the two-body wave function at short distance are then derived, which do not depend on the short-range details of interatomic potentials. We find that new scattering parameters need to be introduced because of spin-orbit coupling, besides the traditional s-and p-wave scattering length (volume) and effective ranges. This is a general and unique feature for spin-orbit-coupled systems. We show how these twobody parameters characterize the universal relations in the presence of spin-orbit coupling. This work probably shed light for understanding the profound properties of the many-body quantum systems in the presence of the spin-orbit coupling. *

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

2020

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“…This interesting mapping was pointed out also directly in a very pedagogical paper [345], where the exact analytical solution (counterpart of the Busch et. al solution) for the two-particle problem with p-wave interactions in a harmonic trap was obtained (see also [348] for the solution obtained with different method). Based on this solution, in [349] the first analysis of inter-particle quantum correlations in the interacting two-body ground state was studied and compared with those induced by s-wave interactions.…”

Section: A Beyond S-wave Interactionsmentioning

confidence: 99%

One-dimensional mixtures of several ultracold atoms: a review

Sowiński¹,

2019

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Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

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“…Experimentally, a major obstacle for exploring p-wave effect in cold atoms is the severe atom loss, as observed in a 3D Fermi gas [26][27][28][29]. Recent studies have suggested that the p-wave system could be more stable against three-body loss if confined in the quasi-1D geometry [30,31]. In our system, an additional optical lattice is applied along the 1D tube and the space is further discretized.…”

Section: Introductionmentioning

confidence: 99%

Majorana edge state in a number-conserving Fermi gas with tunable p-wave interaction

Yin

Cui

2019

New J. Phys.

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The remarkable properties and potential applications of Majorana fermions have led to considerable efforts in recent years to realize topological matters that host these excitations. For a number conserving system, there have been a few proposals, using either coupled chain models or a multi-component system with spin-orbit coupling (SOC), to create number fluctuation of fermion pairs in achieving Majorana fermions. In this work, we show that Majorana edge states can occur in a spinless Fermi gas in 1D lattices with tunable p-wave interaction. This is facilitated by the conversion between a pair of (open-channel) fermions and a (close channel) boson, thereby allowing the number fluctuation of fermion pairs in a single chain. This scheme requires neither SOC nor a multi-chain setup and can be implemented easily. Using the density-matrixrenormalization-group method, we have identified the Majorana phase in a wide range of parameter regimes as well as its associated phase transitions. The topological nature of the Majorana phase manifests itself in a strong edge-edge correlation in an open chain that is robust against disorder, as well as in a non-trivial winding number in the bulk generated by using twisted boundary condition. It is also shown that the Majorana phase in this system can be stable against atom losses due to few-body collisions on the same site, and can be easily identified from the fermion momentum distribution. These results pave the way for probing the intriguing Majorana physics in a simple and stable cold atoms system. † ]. It is a mode of excitation rather than a particle in the usual sense. In 2001, Kitaev showed that spinless fermions in a 1D chain coupled to a pairing field will have Majorana fermions at the ends [4]. Efforts to simulate this model in solid state matter have led to the proposal of using 1D semiconducting wires with spin-orbit coupling (SOC) in contact with a superconductor [5,6]. Similar proposals have also been made in the cold atom studies by engineering SOC on an attractive Fermi gas [7][8][9][10][11][12].Since Majorana fermions also emerge in the number conserving systems such as the Pfaffian quantum Hall state [13,14] and Kitaev's honeycomb spin model [15], there have been questions of whether proximity superconductivity (or lack of number conservation) is necessary for realizing Majaronas in 1D chains. While a single Majorana excitation cannot exist in a number conserving system, the correlation of two Majoranas at different locations (i i j 1 2 l l á ñ) is well defined. This provides a natural generalization of the presence of Majorana edge modes in a number conserving system, which is defined as a non-zero correlation of the Majoranas at the OPEN ACCESS RECEIVED

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Universal one-dimensional atomic gases near odd-wave resonance

Cited by 52 publications

References 59 publications

Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

One-dimensional mixtures of several ultracold atoms: a review

Majorana edge state in a number-conserving Fermi gas with tunable p-wave interaction

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