Confinement induced molecules in a 1D Fermi gas

Formation of Ultracold Molecules by Merging Optical Tweezers

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation.

Solution of the BEC to BCS Quench in One Dimension

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.

New trends in quantum integrability: recent experiments with ultracold atoms

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.

In Situ Thermometry of Fermionic Cold-Atom Quantum Wires

We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature T/T_{F} at nearly constant entropy per particle S/Nk_{B}. The ability to probe individual atomic wires in situ paves the way to quantitatively study equilibrium and transport properties of strongly interacting 1D Fermi gases.

Topological pumping of a 1D dipolar gas into strongly correlated prethermal states

Long-lived excited states of interacting quantum systems that retain quantum correlations and evade thermalization are of great fundamental interest. We create nonthermal states in a bosonic one-dimensional (1D) quantum gas of dysprosium by stabilizing a super-Tonks-Girardeau gas against collapse and thermalization with repulsive long-range dipolar interactions. Stiffness and energy-per-particle measurements show that the system is dynamically stable regardless of contact interaction strength. This enables us to cycle contact interactions from weakly to strongly repulsive, then strongly attractive, and finally weakly attractive. We show that this cycle is an energy-space topological pump (caused by a quantum holonomy). Iterating this cycle offers an unexplored topological pumping method to create a hierarchy of increasingly excited prethermal states.

One-dimensional mixtures of several ultracold atoms: a review

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 higher-spin 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.

Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices

We propose a feasible way of engineering Majorana-type quasiparticles in ultracold fermionic gases on a one-dimensional (1D) optical lattice. For this purpose, imbalanced ultracold atoms interacting by the spin-orbit coupling should be hybridized with a three-dimensional Bose-Einstein condensate molecular cloud. We show that the Majorana-type excitations can be created or annihilated upon constraining the profile of a trapping potential and/or an internal scattering barier. This process is modeled within the Bogoliubov-de Gennes approach. Our study is relevant also to nanoscopic 1D superconductors, where both potentials can be imposed by electrostatic means.

High-Sensitivity rf Spectroscopy of a Strongly Interacting Fermi Gas

rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.

Hybrid Sound Modes in One-Dimensional Quantum Liquids

We study sound in a single-channel one-dimensional quantum liquid. In contrast to classical fluids, instead of a single sound mode we find two modes of density oscillations. The speeds at which these two sound modes propagate are nearly equal, with the difference that scales linearly with the small temperature of the system. The two sound modes emerge as hybrids of the first and second sounds, and combine oscillations of both density and entropy of the liquid.

Single-Atom Transistor as a Precise Magnetic Field Sensor

Feshbach resonances, which allow for tuning the interactions of ultracold atoms with an external magnetic field, have been widely used to control the properties of quantum gases. We propose a scheme for using scattering resonances as a probe for external fields, showing that by carefully tuning the parameters it is possible to reach a 10^{-5}  G (or nT) level of precision with a single pair of atoms. We show that, for our collisional setup, it is possible to saturate the quantum precision bound with a simple measurement protocol.

Second Sound in Systems of One-Dimensional Fermions

We study sound in Galilean invariant systems of one-dimensional fermions. At low temperatures, we find a broad range of frequencies in which in addition to the waves of density there is a second sound corresponding to the ballistic propagation of heat in the system. The damping of the second sound mode is weak, provided the frequency is large compared to a relaxation rate that is exponentially small at low temperatures. At lower frequencies, the second sound mode is damped, and the propagation of heat is diffusive.

Molecular electronic structure in one-dimensional Coulomb systems

Following two recent papers [Phys. Chem. Chem. Phys., 2015, 17, 3196; Mol. Phys., 2015, 113, 1843], we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally surprising, variety of stable 1D compounds (from diatomics to tetra-atomics) as well as a small collection of stable polymeric structures. We define the exclusion potential, a 1D analogue of the electrostatic potential, and show that it can be used to rationalise the nature of bonding within molecules. This allows us to construct a small set of simple rules which can predict whether a putative 1D molecule should be stable.

Anomalous Conductances in an Ultracold Quantum Wire

We analyze the recently measured anomalous transport properties of an ultracold gas through a ballistic constriction [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)]. The quantized conductance observed at weak interactions increases severalfold as the gas is made strongly interacting, which cannot be explained by the Landauer theory of single-channel transport. We show that this phenomenon is due to the multichannel Andreev reflections at the edges of the constriction, where the interaction and confinement result in a superconducting state. Andreev processes convert atoms of otherwise reflecting channels into the condensate propagating through the constriction, leading to a significant excess conductance. Furthermore, we find the spin conductance being suppressed by superconductivity; the agreement with experiment provides an additional support for our model.

1D to 3D Crossover of a Spin-Imbalanced Fermi Gas

We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a two-component spin-imbalanced Fermi gas of ^{6}Li atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate t with respect to the pair binding energy ε_{B}, we observe a collapse of the data to a universal crossover point at a scaled tunneling value of t[over ˜]_{c}=0.025(7).

Mapping out spin and particle conductances in a quantum point contact

We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at [Formula: see text] for weak interactions to plateau-like features at nonuniversal values as high as [Formula: see text] for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.

Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Unconventional pairings of spin-orbit coupled attractive degenerate Fermi gas in a one-dimensional optical lattice

Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to a new phase called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. For the strong SOC strength, the intraband BCS pairing always dominates in the whole parameter regime, including the half filling. We figure out the whole phase diagrams as functions of filling factor, SOC strength, and Zeeman field. Our results are qualitatively different from recent mean-field predictions. Finally, we address that our predictions could be observed in a weaker trapped potential.

Chemistry in one dimension

Orbital basis functions in a one-dimensional triatomic molecule ABC.

Critical behaviours of contact near phase transitions

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviours, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition, and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviours in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.

Contact parameterises two-body correlations at short distances in dilute systems like ultracold atomic gases. Using a fundamental thermodynamic relation, Chen et al. study the contact near a continuous classical or quantum phase transition and find that it displays a number of critical behaviours.

Photon-assisted confinement-induced resonances for ultracold atoms

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The modulation opens additional photon-assisted resonant scattering channels. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Floquet-Schrödinger equation which is universal at low energies. The effective one-dimensional scattering length can be controlled by the external driving.

The confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling

The confinement induced resonance provides an indispensable tool for the realization of the low-dimensional strongly interacting quantum system. Here, we investigate the confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling. We find that the quasi-bound levels induced by the spin-orbit coupling and Raman coupling result in the Feshbach-type resonances. For sufficiently large Raman coupling, the bound states in one dimension exist only for sufficiently strong attractive interaction. Furthermore, the bound states in quasi-one dimension exist only for sufficient large ratio of the length scale of confinement to three dimensional s-wave scattering length. The Raman coupling substantially changes the confinement-induced resonance position. We give a proposal to realize confinement induced resonance through increasing Raman coupling strength in experiments.

Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r3, much slower than the van der Waals interaction ∼1/r6, where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

One-dimensional fermions with neither Luttinger-liquid nor Fermi-liquid behavior

It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such a liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both a Tomonaga-Luttinger liquid and a Fermi liquid. Similar to a Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates a finite discontinuity at the Fermi energy, which is a hallmark feature of a Fermi liquid. A possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

The ground state properties of the Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interactions are investigated by means of the exact diagonalization method. We show that the appearance of N-crests in the density profile of a trapped N-fermion system is a natural result of 'fermionization' between antiparallel-spin fermions in the strongly repulsive limit and cannot be taken as the only signature of the Wigner crystal phase, as the static structure factor does not show any signature of crystallization. In contrast, both the density distribution and the static structure factor of the Hubbard model with strong long-range interactions display clear signatures of the Wigner crystal phase. Our results indicate the important role of long-range interaction in the formation of the Wigner crystal phase.

Anderson localization of pairs in bichromatic optical lattices

We investigate the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasiperiodic optical lattice. We derive the quantum phase diagram for Anderson localization of both attractively and repulsively bound pairs. We calculate the pair binding energy and show analytically that its behavior as a function of the interaction strength depends crucially on the nature-extended, multifractal, localized-of the single-particle atomic states. Experimental implications of our results are discussed.

Triplet pair correlations in s-wave superfluids as a signature of the Fulde-Ferrell-Larkin-Ovchinnikov state

We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.

Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas

We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.

Lattice-induced resonances in one-dimensional bosonic systems

We study the resonant effects produced when a Feshbach dimer crosses a scattering continuum band of atoms in an optical lattice. We numerically obtain the exact spectrum of two particles in a one-dimensional lattice and develop an effective atom-dimer Hamiltonian that accurately captures resonant effects. The lattice-induced resonances lead to the formation of bound states simultaneously above and below the scattering continuum and significantly modify the curvature of the dimer dispersion relation. The nature of the atom-dimer coupling depends strongly on the parity of the dimer state leading to a novel coupling in the case of negative parity dimers.

Crossover from adiabatic to sudden interaction quench in a Luttinger liquid

Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LLs), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regime, and a LL regime with a time-dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.

Parametric excitation of a 1D gas in integrable and nonintegrable cases

We study the response of a highly excited 1D gas with pointlike interactions to a periodic modulation of the coupling constant. We calculate the corresponding dynamic structure factors and show that their low-frequency behavior differs dramatically for integrable and nonintegrable models. Nonintegrable systems are sensitive to excitations with frequencies as low as the mean level spacing, whereas much higher frequencies are required to excite an integrable system. This effect can be used as a probe of integrability for mesoscopic 1D systems and can be observed experimentally by measuring the heating rate of a parametrically excited gas.

Radio-frequency spectroscopy of a strongly interacting two-dimensional Fermi gas

We realize and study a strongly interacting two-component atomic Fermi gas confined to two dimensions in an optical lattice. Using radio-frequency spectroscopy we measure the interaction energy of the strongly interacting gas. We observe the confinement-induced Feshbach resonance on the attractive side of the 3D Feshbach resonance and find the existence of confinement-induced molecules in very good agreement with theoretical predictions.

Super-Tonks-Girardeau gas of spin-1/2 interacting fermions

Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that a stable excited state with no pairing between attractive fermionic atoms can be realized by a sudden switch of interaction from the strongly repulsive regime to strongly attractive regime. Such a state is an exact fermionic analog of the experimentally observed super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)] and should be possible to be observed by the experiment. The frequency of the lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated as a function of the interaction strength, which could be used as a detectable signature for the experimental observation.

π phases in balanced fermionic superfluids on spin-dependent optical lattices

We study a balanced two-component system of ultracold fermions in one dimension with attractive interactions and subject to a spin-dependent optical lattice potential of opposite sign for the two components. We find states with different types of modulated pairing order parameters which are conceptually similar to π phases discussed for superconductor-ferromagnet heterostructures. Increasing the lattice depth induces sharp transitions between states of different parity. While the origin of the order parameter oscillations is similar to the Fulde-Ferrel-Larkin-Ovchinnikov phase for paired states with spin imbalance, the current system is intrinsically stable to phase separation. We discuss experimental requirements for creating and probing these novel phases.

Tunable Luttinger liquid physics in biased bilayer graphene

Electronically gated bilayer graphene behaves as a tunable gap semiconductor under a uniform interlayer bias V(g). Imposing a spatially varying bias, which changes polarity from -V(g) to +V(g), leads to one dimensional (1D) chiral modes localized along the domain wall of the bias. Because of the broad transverse spread of their low-energy wave functions, we find that the dominant interaction between these 1D electrons is the forward scattering part of the Coulomb repulsion. Incorporating these interactions and the gate voltage dependence of the dispersion and wave functions, we find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid with three distinct mode velocities and a bias dependent Luttinger parameter, and discuss its experimental signatures.

Resonance scattering in optical lattices and molecules: interband versus intraband effects

We study the low-energy two-body scattering in optical lattices with higher-band effects included in an effective potential, using a renormalization group approach. The approach captures the most dominating higher-band effects as well as all multiple scattering processes in the lowest band. For an arbitrary negative free space scattering length (a(s)), a resonance of low-energy scattering occurs as the lattice potential depths reach a critical value v(c); these resonances, with continuously tunable positions v(c) and widths W, can be mainly driven either by intraband or both intra- and interband effects depending on the magnitude of a(s). We have also studied the scattering amplitudes and the formation of molecules when interband effects are dominating, and discussed an intimate relation between molecules for negative a(s) and repulsively bound states pioneered by Winkler et al. [Nature (London) 441, 853 (2006)].

Scattering in mixed dimensions with ultracold gases

We experimentally investigate the mix-dimensional scattering occurring when the collisional partners live in different dimensions. We employ a binary mixture of ultracold atoms and exploit a species-selective 1D optical lattice to confine only one atomic species in 2D. By applying an external magnetic field in proximity of a Feshbach resonance, we adjust the free-space scattering length to observe a series of resonances in mixed dimensions. By monitoring 3-body inelastic losses, we measure the magnetic field values corresponding to the mix-dimensional scattering resonances and find a good agreement with the theoretical predictions based on simple energy considerations.

Luttinger liquid of trimers in Fermi gases with unequal masses

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states--"trimers"--exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities n(up) = n(down)/2 an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid correlations. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.

Multiparticle composites in density-imbalanced quantum fluids

We consider two-component one-dimensional quantum gases with a density imbalance. While generically such fluids are two-component Luttinger liquids, we show that if the ratio of the densities is a rational number, p/q, and mass asymmetry between components is sufficiently strong, one of the two eigenmodes acquires a gap. The gapped phase corresponds to (algebraic) ordering of (p+q)-particle composites. In particular, for attractive mixtures, this implies that the superconducting correlations are destroyed. We illustrate our predictions by numerical simulations of the fermionic Hubbard model with hopping asymmetry.

Universal dephasing of many-body Rabi oscillations of atoms in one-dimensional traps

We study a quantum quench in a system of two coupled one-dimensional tubes of interacting atoms. After the quench the system is out of equilibrium and oscillates between the tubes with a frequency determined by microscopic parameters. Despite the high energy at which the system is prepared we find an emergent long time scale responsible for the dephasing of the oscillations and a transition at which this time scale diverges. We show that the universal properties of the dephasing and the transition arise from an infrared orthogonality catastrophe. Furthermore, we show how this universal behavior is realized in a realistic model of fermions with attractive interactions.

Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

Exact solution for infinitely strongly interacting Fermi gases in tight waveguides

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for an arbitrary confining potential. The eigenfunctions are constructed by the combination of Girardeau's hard-core contacting boundary condition and group theoretical method, which guarantees the obtained states to be simultaneously the eigenstates of S and S_{z} and satisfy antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.

Recent ARPES experiments on quasi-1D bulk materials and artificial structures

The spectroscopy of quasi-one-dimensional (1D) systems has been a subject of strong interest since the first experimental observations of unusual line shapes in the early 1990s. Angle-resolved photoemission (ARPES) measurements performed with increasing accuracy have greatly broadened our knowledge of the properties of bulk 1D materials and, more recently, of artificial 1D structures. They have yielded a direct view of 1D bands, of open Fermi surfaces, and of characteristic instabilities. They have also provided unique microscopic evidence for the non-conventional, non-Fermi-liquid, behavior predicted by theory, and for strong and singular interactions. Here we briefly review some of the remarkable experimental results obtained in the last decade.

Time-dependent current-density-functional theory of spin-charge separation and spin drag in one-dimensional ultracold Fermi gases

Motivated by the large interest in the nonequilibrium dynamics of low-dimensional quantum many-body systems, we present a fully microscopic theoretical and numerical study of the charge and spin dynamics in a one-dimensional ultracold Fermi gas following a quench. Our approach, which is based on time-dependent current-density-functional theory, is applicable well beyond the linear-response regime and produces both spin-charge separation and spin-drag-induced broadening of the spin packets.