Critical Stability of Quantum Few-Body Systems

Efimov Physics originated from a reflection on nuclear physics and in particular from the observation that the light nuclei spectrum presents shallow states, the deuteron and the triton. Afterwards, the possibility to change and tune the inter-particle interaction made atomic physics the privileged playground of Efimov physics allowing fantastic achievements both from the experimental and theoretical sides. In the last few years there is a renewed effort bring Efimov physics back to the origins, back to nuclear physics, and in this talk I'll try to understand where we are now in this challenge.

Ground state properties of weakly bound few-body systems consisting of helium and spin-polarized hydrogen isotopes, and alkali atoms have been explored. Stability of different cluster species has been tested with a special emphasis on a universality of quantum halo states - weakly bound systems with a radius extending well into the classically forbidden region. The study of realistic systems is supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled very precise calculation of both size and binding energy of few-body systems. Using dimensionless measures of the binding energy and cluster size, studied atomic clusters are compared to other known halos in different fields of physics. Different characteristic scaling lengths, which make size-energy ratio to be universal, are tested. As the scaled binding energy decreases, samba and tango type trimers separate from Borromean type~[1]. Research is extended to tetramers and pentamers. Furthermore, the structural properties of different trimers are compared with the most recent experimental results~[2,3] obtained by Coulomb explosion imaging of diffracted clusters. [1] Stipanovi\'{c} P. et al., Phys. Rev. Lett. \textbf{113}, 253401 (2014). [2] Voigtsberger J. et al., Nature Communications \textbf{5}, 5765 (2014). [3] Kunitski M. et al., Science \textbf{348}, 551 (2015).

This talk considers selected aspects of spin-orbit coupled few-atom systems. Spin-orbit coupling, which leads to a locking of the spin and the spatial degrees of freedom, can be realized in cold atom systems in a variety of ways. This contribution discusses the modifications of the few-body dynamics due to the spin-orbit coupling. Scattering and bound state properties will be considered.

Wave-particle duality in quantum mechanics allows for a halo bound state whose spatial extension far exceeds a range of the interaction potential. What is even more striking is that such quantum halos can be arbitrarily large on special occasions. The two examples known so far are the Efimov effect and the super Efimov effect, which predict that spatial extensions of higher excited states grow exponentially and double-exponentially, respectively [1,2]. Here we establish yet a new class of arbitrarily large quantum halos formed by spinless bosons with short-range interactions in two dimensions [3]. When the two-body interaction is absent but the three-body interaction is resonant, four bosons exhibit an infinite tower of bound states whose spatial extensions scale as $R_n\sim e^{(\pi n)^2/27}$ for large $n$. The emergent scaling law is universal and termed a semi-super Efimov effect, which together with the Efimov and super Efimov effects constitutes a trio of few-body universality classes allowing for arbitrarily large quantum halos. [1] V. Efimov, "Energy levels arising from resonant two-body forces in a three-body system," Phys. Lett. B 33, 563-564 (1970). [2] Y. Nishida, S. Moroz, and D. T. Son, "Super Efimov effect of resonantly interacting fermions in two dimensions," Phys. Rev. Lett. 110, 235301 (2013). [3] Y. Nishida, "Semi-super Efimov effect of two-dimensional bosons at a three-body resonance," to be published in Phys. Rev. Lett. (2017).

The system of few identical fermions interacting resonantly with a distinguishable atom exhibits a rich and interesting physics, including universal states and the celebrated Efimov effect. The (2+1) system, composed of two heavy fermions and lighter atom, supports a universal trimer state if the ratio of the particle masses exceeds critical value. For even larger mass ratio the system becomes Efimovian, introducing a three-body scale and showing geometric series of bound states. Interestingly, this trend continues in the (3+1) system as well as in the (4+1) system, having their own universal states and pure (N+1)-body Efimov effects. Adding another particle, however, this series seems to stop. This should be a sign of a shell structure and screening effects, which may shed light on the crossover from the few-body systems to the many-body polaron case.

In this work we investigate three-body systems when the dimension changes in a continuous way from three (3D) to two (2D) dimensions. This amounts to confining the particles into a narrower and narrower layer, such that, eventually, when the layer has zero width, the particles are forced to move in 2D. In practice, this can be done by putting the particles under the effect of an external trap potential confining the particles in the space. In particular, this can be done by means of a harmonic oscillator potential in the z-coordinate. For two-body systems the numerical implementation of the external field is simple, and it does not present particular problems. However, for three-body systems, although conceptually the procedure is exactly the same, the numerical difficulties increase when the frequency of the harmonic oscillator increases. In fact, for very large frequencies, i.e., when approaching 2D, the method is quite inefficient. For this reason, in this work we propose to implement the confinement of the particles, not by means of an external potential, but by introducing the dimension d as a parameter in the Schrödinger (or Faddeev) equations to be solved. The dimension is then allowed to take non-integer values within the range 2 ≤ d ≤ 3. The purpose of this work is twofold. First, we want to see the connection between the two confinement methods mentioned above. It is necessary to see the equivalence between a given value of the confining harmonic oscillator frequency and the dimension d describing the same physical situation. Once this is done, we shall use the second method, which is numerically much simpler, to investigate the Efimov states in mass imbalanced systems, focusing in particular on how those states disappear when increasing the confinement of the particles.

Some phenomena in three-body systems can be drastically affected by the dimension where the system is inserted. The Efimov effect is a remarkable example: it exists only in three spatial dimensions. However, if we consider non-integer dimensions, the Efimov effect is allowed for dimensions (d) in the interval 2.3 < d < 3.8, where this result holds for three identical bosons. In this presentation I will show a very simple method to extend this interval for a general AAB system. I will also show a framework for studying the three-body problem as one continuously changes the dimensionality of the system. Some interesting results for two dimensions will be detailed.

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S-waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system.

Recently, the heavy pentaquark system has been observed as a resonant state. It is requested theoretically to describe this state. For this purpose, we should treat continuum states and resonant states explicitly. Here, I will report how to calculate resonant state and continuum state to explain the heavy pentaquark system.

We explain how the emergent phenomenon of dynamical chiral symmetry breaking ensures that Poincaré covariant analyses of the three valence-quark scattering problem in continuum quantum field theory yield a picture of the nucleon as a Borromean bound-state, in which binding arises primarily through the sum of two separate contributions. One involves aspects of the non-Abelian character of QCD that are expressed in the strong running coupling and generate tight, dynamical color-antitriplet quark-quark correlations in the scalar-isoscalar and pseudovector-isotriplet channels. This attraction is magnified by quark exchange associated with diquark breakup and reformation, which is required in order to ensure that each valence-quark participates in all diquark correlations to the complete extent allowed by its quantum numbers. Combining these effects, we arrive at a properly antisymmetrised Faddeev wave function for the nucleon and calculate, e.g., the flavor-separated versions of the Dirac and Pauli form factors and conclude that available data and planned experiments are capable of validating the proposed picture.

In this talk I will revise recent studies on multiquark spectroscopy regarding four, five and six quark systems making emphasis on the role played by confinement. I will address the role played by entangled thresholds and the failure of heavy quark mass expansions in some particular systems. The talked is based on some recent works in collaboration with J. Vijande and J.-M. Richard.

A lot of evidences for the Efimov states were found in the cold atomic system. However, there are few discussions about the Efimov physics in hadron systems. The most important requirements of Efimov physics is (1) the scattering length of the sub-system should be $\pm \infty$ ({\it first criterion}); (2) The result is that the three-body binding energies condense on the three-body threshold where the energy level structure is given by $E_{n}/E_{n+1}=$constant with respect to the principal quantum number $n$ ({\it second criterion}); (3) It is known that such an energy level structure can be obtained by the $1/r^2$ potential ({\it third criterion}). For the three criteria, we would like to check the hadron systems. (1) The {\it first criterion} is that the hadron scattering length $a_{NN} ({\rm or}~ a_{N\pi})\rightarrow \pm\infty$ is not satisfied in the hadron system. (2) The {\it second criterion} is that there are some instances that energy levels come near the threshold region. However, it is very hard to confirm whether they are Efimov levels or not. (3) The {\it third criterion} is that the nuclear potential is usually a short-range where the longest-range is one pion exchange Yukawa potential. Therefore, it seems that such a potential does not support Efimov physics in the hadron system. However, we can reevaluate the Efimov physics from another vantage point.\\ ~~ First of all we would like to pay attention to the thresholds in the three-body reactions. The three-body break-up thresholds (3BT) appear in the reactions: $d+p\rightarrow n+n+p$ and $N+N'\rightarrow N+N+\pi$, etc.. However, we have another threshold from the { three-body bound state to the quasi two-body system} which is the {\it quasi two-body threshold} (Q2T) such as $^3$He$\rightarrow d+p$ and $D\rightarrow N+N'$. The Born term of the Faddeev or the Alt-Grassberger-Sandhas (AGS) equation has a singularity at the 3BT ($E=0$,~$q=0$), and also the propagator $\tau(E-q^2/2\mu)$ diverges at 3BT ($E=0,~q=0$). The coincidence of both singularities causes a serious problem. This situation is very similar to the Coulomb scattering by the Lippmann-Schwinger equation where the Rutherford singularity coincides with the Green's function singularity. However, we have many energy levels in the Hydrogen atom by the potential $-e^2/r$. For the three-body singularity at the 3BT, Efimov discovered a new potential $-V_0/r^2$ which causes a lot of energy levels in the negative energy region. Recently, we found that the quasi-two-body Born term causes a singularity at the Q2T. From this singularity, we derived a general {\it particle transfer} (GPT) { potential} $-V'_0a^{2\gamma+2}/[r(r/2+a)^{2\gamma+2}]$ in the negative energy region. It is easily seen that the GPT potential includes a potential $-V_0'/r^2$ (for $\gamma=-1/2$ and $a\ll r$), and also Van der Waals potentials (for $\gamma=3/2,~2$ and $a\ll r$), which also includes the Yukawa-type potentials for $r\ll a$. Contrary to the {\it first Efimov criterion}, the Q2T does not require $a_{NN}~(a_{N\pi})\rightarrow \pm \infty$. The parameter $\gamma$ depends on the particle masses which transfer. It is because $\gamma=-1$ corresponds to the mass-less particle. In this stage, the question that the Efimov-like energy levels {\it could appear or not} is one side, but an interesting question of another side is about the long range interactions which we discover. Besides the Yukawa-type short range potential, these long range interactions could give rise to unusual phenomena in the hadron systems. In the case that such a long range potential does not produce additional bound states, still our attractive long range part of GPT potential could interfere with the Coulomb potential and the centrifugal potential, and affect the final-state interactions in the break-up reaction.\\ ~~ Finally, this kind of {\it additional long range potential} could universally occur, not only in three-body systems, but also in many-body systems. Then the most popular benefit of the potential will be seen in the neutron-rich nucleus such as a halo, or unstable nuclei, or the nuclear fusion problems.\\

We have found a candidate tetra-neutron resonant state via a missing-mass spectroscopy in the double-charge exchange (DCX) reaction $^4$He($^8$He,$^8$Be) at 190 $A$ MeV by using the SHARAQ spectrometer at the RIBF facility in RIKEN. Production mechanism with kinematical consideration for the reaction is introduced and analysis for the obtained missing mass spectrum is presented. Nuclear forces relevant for formation of multi-neutron resonance are discussed for consistent understanding of few-body systems. Other experimental approaches for the tetra-neutron system are also shown including a new measurement of the DCX reaction.

In this talk I will present the recent developments regarding the emergence of short range correlations in nuclear physics both experimentally and theoretically.

The key ingredient of standard few-body reaction formalisms to describe the collison of a projectile with A nucleons with a target (taken here for simplicity as a proton) is the reduction of the overwhelming many-body problem, into an effective effective 3-body system composed by an (A-1) core plus a nucleon and the target proton. Within a mean field description of the projectile the nucleon can be taken as occupying a inner or a valence shell. The standard Faddeev/AGS(Alt-Grassberger-Sandhas) \cite{Alt67,Cr09} is a non-relativistic exact formalism that treats in equal footing all particles and simultaneously all open channels, elastic, inelastic knockout/breakup and transfer simultaneously. It is an useful tool to extract structure information from experimental data. The formalism can be viewed as a multiple scattering expansion in terms of the transition amplitude of each interacting pair. The bridging between the exact standard Faddeev/AGS framework with other reaction formalisms will be discussed.In addition, the need of merging ab initio many body structure information into the reaction framework will also be addressed. %%------------------------------------ \bibitem{Alt67} E.O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. {\bf B2} 167 (1967). \bibitem{Cr09} R. Crespo, A. Deltuva, M. Rodriguez-Gallardo, E. Cravo and A.C. Fonseca, Phys. Rev. C {\bf 79}, 014609 (2009). %%------------------------------------

Three- and four-body scattering is described solving Faddeev-Yakubovsky or equivallent Alt-Grassberger-Sandhas integral equations for transition operators in momentum-space with realistic nuclear interaction models. The studied cases include neutron-${}^{19}$C scattering and (d,p) and (d,n) reactions for deuteron or heavier nuclei targets. Extension to four-boson system is discussed as well.

Three-body Efimov physics is relevant for the understanding of both dynamics and stability of ultracold gases. Efimov predicted the existence of an infinite sequence of three-body bound states, of which many properties scale universally, at diverging scattering length for a zero-range interaction potential. Experiments with ultracold atoms in which the scattering length is tuned through Feshbach resonances have also shown that the three-body parameter is universally linked to the finite-range of the two-body interaction potential. For small scattering lengths non-universal features appear in the Efimov spectrum, which are also linked to the finite-range nature of the interactions. We consider the full non-separable off-shell two-body T-matrix which is present in the three-body Faddeev equations and analyze the corresponding separable expansions. This momentum space treatment allows us, for instance, to show that strong d-wave interactions lower the energy of the second Efimov state making it possible to prevent this Efimov state from merging with the atom-dimer threshold. We also show that calculations of the three-body parameter corresponding to the potential resonances of deep square well potentials require many terms in the expansion the off-shell two-body T-matrix.

For systems with resonant two-body interactions, Efimov predicted an infinite series of three-body bound states with geometric scaling symmetry. These Efimov states, first observed in cold caesium atoms, have been recently reported in a variety of other atomic systems. The intriguing prospect of a universal absolute Efimov resonance position across Feshbach resonances remains an open question. Theories predict a strong dependence on the resonance strength for closed-channel-dominated Feshbach resonances, whereas experimental results have so far been consistent with the universal prediction. We directly compare the Efimov spectra in a 6Li–133Cs mixture near two Feshbach resonances which are very different in their resonance strengths, but otherwise almost identical. Our result shows a clear dependence of the absolute Efimov resonance position on Feshbach resonance strength and a clear departure from the universal prediction for the narrow Feshbach resonance.

Since the theoretical prediction of confinement-induced resonances in one- or two-dimensional systems, they have attracted much interest due to their universality. In fact, later it turned out that there are two types of universal confinement-induced resonances: elastic ones as predicted originally as well as inelastic ones that are due to the coupling of center-of-mass and relative motion. While the elastic resonances are a useful tool for changing the interaction strength between particles, the inelastic ones can also be used for creating molecules by a transfer of the binding energy into center-of-mass motion.In fact, the universality of the inelastic resonances persists also for particles interacting by the long-ranged Coulomb interactions, e.g., in quantum-dot systems. There, they might be used as on-demand single-photon sources. In ultracold gases with dipolar interaction, tuning the dipole strength allows for a manipulation of the resonance position, yielding a high degree of quantum control. After a survey of the confinement-induced resonances some more recent results will be given, especially in the context of time-dependent variations of the trap potential.

The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg topology, with corresponding spectra that differ fundamentally from the homonuclear case. A semi-analytical treatment of the three-body recombination predicts an unusual spectra with intertwined resonance peaks and minima, and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the pattern of maxima and minima are shown to depend strongly on the degree of diabaticity, which strongly affects the universality of the heteronuclear Efimov states.

At energies lower than the deuteron breakup, the doublet nd scattering is known to have a virtual state and a zero in the amplitude just below the elastic threshold. We formulate a halo/cluster EFT incorporating both physics and their behavior as the deuteron binding energy decreases. We confirm previous studies, that associates the nature of the virtual state to an excited Efimov state.

We discuss the effect of the three-nucleon force (3NF) in d-d, p-3H and n-3He scattering at low energies. The used 3NF is derived from effective field theory at next-to-next-to-leading order. The four-nucleon scattering observables are calculated using the Kohn variational principle and the hyperspherical harmonics technique and the results are compared with available experimental data.

Early three-body approaches developed to study nuclear reactions such as the compound nucleus theory [1,2,3] were adopted in the 70s in the context of Molecular Physics to investigate the dynamics of atom-diatom reactive collisions [4,5]. In particular, a statistical quantum mechanical (QM) method which employs ab initio potential energy surfaces and fully QM techniques to calculate reaction probabilities has been largely used to characterize processes mediated by a complex-forming mechanism between reactants and products [6,7]. In my talk I will review some of the basic ingredients of the method and some of the most interesting applications in a number of reactions in which the formation of an intermediate species plays a significant role in the overall dynamics. Special emphasis is made in cold reactions at low collision energy [8,9,10] [1] L. Wolfenstein, Phys. Rev. 87, 366 (1951) [2] W. Hauser and H. Fesbach, Phys. Rev. 87, 366 (1952) [3] R. M. Eisberg and N. M. Hintz, Phys. Rev. 103, 645 (1956) [4] P. Pechukas et al., J. Chem. Phys. 42, 3281 (1964); R. A. White et al., J. Chem. Phys. 53, 379 (1971) [5] W. H. Miller J. Chem. Phys. 52, 543 (1970) [6] E. J. Rackham et al. J. Chem. Phys. 119, 12895 (2003) [7] T. Gonzalez-Lezana Int. Rev. Phys. Chem. 26, 29 (2007) [8] T. Gonzalez-Lezana and P. Honvault, Int. Rev. Phys. Chem. 33, 371 (2014) [9] C. Makrides et al. Phys. Rev. A 91, 012708 (2015) [10] P. Honvault et al. Phys. Rev. Lett. 107, 023201 (2011)

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s-wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalisation of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalisation. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multi-channel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

Impurities immersed in a Bose-Einstein condensate form Bose polarons. The polarons can interact with each other through an interaction that is mediated by the Bose-Einstein condensate. For a weak boson-impurity interaction, this mediated interaction is known to be a weak Yukawa attraction. For a resonant boson-impurity, it turns into a strong Efimov attraction involving a single boson as the mediator. In this study, I look into this interesting crossover which bridges few-body to many-body physics.

The successful application of $s$-wave ``contact" to unitary Fermi gases exemplifies the importance of few-body correlations in understanding strongly interacting many-body systems. Recent experimentally measured radio-frequency spectrum and momentum distribution of three-dimensional Fermi gases close to a $p$-wave Feshbach Resonance show universal tails different from the $s$-wave case [1]. We emphasise that the difference is due to the necessity of using both the scattering volume $v$ and the effective range $R$ to parameterise the two-body $p$-wave interatomic interaction, and show that by including two-body correlations at short range, the interaction effects of the system are captured by two contacts, $C_v$ and $C_R$, which are related to the variation of energy with $v$ and $R$ in two adiabatic theorems [2]. Based on the two contacts, we derive the universal properties of the system regarding momentum distribution, radio-frequency and photo-association spectroscopies, and pressure and virial relations. We also establish coupled rate equations to explain the time evolution of the p-wave contacts observed in the quench experiment [1]. Beyond two-body correlations at short range, $p$-wave resonances are predicted to give rise to universal super Efimov three-body bound states in two-dimensions [3]. We use the hyper-spherical formalism and show that these new universal states originate from an emergent effective potential, which is different from the one responsible for the familiar Efimov states [4]. In the many-body context, we introduce a new thermodynamic quantity, the three-body contact $C_\theta$, to quantify the three-body correlations due to the super Efimov Effect [5]. We determine how $C_\theta$ affects various physical observables; signature of the elusive super Efimov effect in the thermodynamic system can be pinned down by the detection of the three-body contact $C_\theta$ via these observables. [1] C. Luciuk, S. Trotzky, S. Smale, Zhenhua Yu, Shizhong Zhang, and J. H. Thywissen 2016 \emph{Nature Physics} \textbf{12} 599-605 [2] Zhenhua Yu, J.H. Thywissen, and Shizhong Zhang 2015 \emph{Phys. Rev. Lett.} \textbf{115} 135304 [3] Yusuke Nishida, Sergej Moroz, and Dam Thanh Son 2013 \emph{Phys. Rev. Lett.} \textbf{110} 235301 [4] Chao Gao, Jia Wang, and Zhenhua Yu 2015 \emph{Phys. Rev. A} \textbf{92} 020504(R) [5] Pengfei Zhang, Zhenhua Yu 2016 arXiv:1611.09454

Interactions between atoms often introduce large amounts of complexity into many-particle systems, but they can also lead to new and interesting physical regimes. In this presentation I will discuss several examples of interacting ultra cold atomic systems, where tuneable interactions allow to access new dynamical situations or create new control techniques. The first example will be taken from our efforts towards a full set of techniques to coherently control the external state of small samples of ultracold atoms and the second from the description of non-equilibrium situations in single- and multi-component systems. This will include a discussion of a thermodynamical machine build on Feshbach resonances.

The van der Waals three-body systems at ultralow energies are studied using Faddeev equations in configuration space. The spectra of LiHe2 systmes and the scattering length are calculated. The results obtained indicate on the Efimov character of the excited state in both systems.

Integrable systems can be found in different areas of Physics, such as statistical mechanics, quantum field theory,condensed matter, string theory and more recently in cold atoms. Here we provide an overview of the basic construction and the impact of Yang-Baxter integrable systems in condensed matter and ultracold atoms, focusing on some prominent examples, specially those cases connected to experiments [1]. Then recent results, such as quantum integrable multi-well tunneling models [2],[3] and a geometric ansatz for a few particles system will be presented. Finally we discuss the effects of breaking the integrability in some models. [1] Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms, M. T. Batchelor, A. Foerster, J. Phys. A: Math. Theor. 49 (2016) 173001; [2] Quantum integrable multi-well tunneling models, L H Ymai, A P Tonel, A Foerster, J Links, arXiv:1606.00816; [3] Integrable model of bosons in a four-well ring with anisotropic tunneling, A. P. Tonel, L. H. Ymai, A. Foerster, J. Links, J. Phys. A: Math. Theor. 48 (2015) 494001;

This talk presents examples of physics at the weak-interaction limit and the hard-core limit of two-particle and few-particle interactions. Level splitting and state evolution under the adiabatic and diabatic evolution of control parameters can be understood in terms of topological shifts and/or symmetry breaking in few-body configuration space. This approach provides methods for classifying spectral structures in trapped, ultracold atomic few-body systems, supplies methods for state control that are robust under fluctuations of physical parameters, and suggests procedures for identifying new solvable models that assist analytic and numerical methods. These techniques are especially effective low dimensions because symmetry and topology provide more constraining structures.

In this talk, I will show that the property of a 3D p-wave interacting Fermi gas can be significantly changed if confined in (quasi-)1D geometry. Counterintuitively, it is found that the application of transverse confinements can greatly stretch the shallow p-wave molecules near the induced 1D resonance, and this strongly indicates a much stable p-wave interacting gas in 1D near resonance, contrary to the 3D case[1]. I will then discuss the interaction renormalization for 1D p-wave scattering[2], and use it to derive the universal relations and address the Bloch-wave scattering and effective model in optical lattices[3]. Finally, based on the effective lattice model, I will introduce our most recent results in establishing the long-sought Majorana fermions in 1D p-wave cold atoms system[4]. References: [1] L. Zhou, X. Cui, arxiv:1707.03512. [2] X. Cui, PRA 94, 043636 (2016); H. Dong, X. Cui, PRA 94, 063650 (2016). [3] X. Cui, PRA 95, 041601(R)(2017). [4] X. Yin, T.-L. Ho, X. Cui, in preparation.

We discuss the ground state properties of a one-dimensional bosonic system doped with other particles (the so-called Bose polaron problem). We introduce a formalism that allows us to study this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. We use available numerically exact results, and develop a numerical method based on the in-medium similarity renormalization group to test the formalism. We argue that the introduced approach provides a simple tool for studies of strongly interacting impurity problems in one dimension. Furthermore, it can be used to investigate correlations between impurity particles in a Bose gas.