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We analyze the ground state of a two-dimensional quantum system of a few strongly confined dipolar bosons. Dipoles arrange in different stable structures that depend on the tilting polarization angle and the anisotropy of the confining trap. To this end, we use the exact diffusion Monte Carlo method and the quantum results are compared with classical ones obtained by stochastic optimization using simulated annealing. We establish the stability domains for the different patterns and estimate the transition boundaries delimiting them. Our results show significant differences between the classical and quantum regimes which are mainly due to the quantum kinetic energy.

The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.

We report the equilibrium vortex phase diagram of a rotating two-band Fermi gas confined to a cylindrically symmetric parabolic trapping potential, using the recently developed finite-temperature effective field theory (Klimin et al 2016 Phys. Rev. A 94 023620). A non-monotonic resonant dependence of the free energy as a function of the temperature and the rotation frequency is revealed for a two-band superfluid. We particularly focus on novel features that appear as a result of interband interactions and can be experimentally resolved. The resonant dependence of the free energy is directly manifested in vortex phase diagrams, where areas of stability for both integer and fractional vortex states are found. The study embraces the BCS–BEC crossover regime and the entire temperature range below the critical temperature T _c . Significantly different behavior of vortex matter as a function of the interband coupling is revealed in the BCS and BEC regimes.

We study the dynamics of a one-dimensional system composed of a bosonic background and one impurity in single- and double-well trapping geometries. In the limit of strong interactions, this system can be modeled by a spin chain where the exchange coefficients are determined by the geometry of the trap. We observe non-trivial dynamics when the repulsion between the impurity and the background is dominant. In this regime, the system exhibits oscillations that resemble the dynamics of a Josephson junction. Furthermore, the double-well geometry allows for an enhancement in the tunneling as compared to the single-well case.

In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological ${p}_{x}+{{\rm{i}}{p}}_{y}$ superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature T _c through p -wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature T _c for the fermionic pair formation using the Bethe–Salpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p -wave superfluid is at reach with state-of-the-art experiments.

The non-linear coupled particle light dynamics of an ultracold gas in the field of two independent counter-propagating laser beams can lead to the dynamical formation of a self-ordered lattice structure as presented in (2016) Phys. Rev. X 6 021026. Here we present new numerical studies on experimentally observable signatures to monitor the growth and properties of such a crystal in real time. While, at least theoretically, optimal non-destructive observation of the growth dynamics and the hallmarks of the crystalline phase can be performed by analyzing scattered light, monitoring the evolution of the particle’s momentum distribution via time-of-flight probing is an experimentally more accessible choice. In this work we show that both approaches allow us to unambiguously distinguish the crystal from independent collective scattering as it occurs in matter wave super-radiance. As a clear crystallization signature, we identify spatial locking between the two emerging standing laser waves, together creating the crystal potential. For sufficiently large systems, the system allows reversible adiabatic ramping into the crystalline phase as an alternative to a quench across the phase transition and growth from fluctuations.

We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb–Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan’s contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.

We use a variational order method to explore the ground state phase diagrams of spin–orbit coupled Bose atoms in optical lattices. By properly parameterizing the order with an ansatz function for each possible phase and comparing their energies which are minimized with respect to the variational parameters, we can effectively identify the lowest energy states and depict the phase diagram. While the Mott-insulator-superfluid phase boundary is computed by the usual Gutzwiller method, the spin-ordered phase structures of the deep Mott regime as well as the superfluid regime are studied by the variational order method. For the isotropic spin–orbit coupling, the phase diagram in the deep Mott insulator regime is qualitatively similar to results derived by the classical Monte-Carlo simulations or other numerical methods. The spiral phases with different spatial periods are discussed in detail. We find three new spin-ordered phases in the deep Mott insulator regime with anisotropic spin–orbit coupling. We also identify the uniform superfluid, stripe and checkerboard supersolid phases with exotic spin orders in the superfluid regime.

We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.

We present the properties of the ground state and low-energy excitations of Bose–Hubbard chains with a geometry that varies from open to closed and with a tunable twisted link. In the vicinity of the symmetric π -flux case the system behaves as an interacting gas of discrete semifluxons for finite chains and interactions in the Josephson regime. The energy spectrum of the system is studied by direct diagonalization and by solving the corresponding Bogoliubov–de Gennes equations. The atom–atom interactions are found to enhance the presence of strongly correlated macroscopic superpositions of semifluxons.

We establish an experimental method for a detailed investigation of inelastic collisional properties between ytterbium (Yb) in the metastable ${}^{3}{{\rm{P}}}_{2}$ state and ground state lithium (Li). By combining an optical lattice and a direct excitation to the ${}^{3}{{\rm{P}}}_{2}$ state we achieve high selectivity on the collisional partners. Using this method we determine inelastic loss coefficients in collisions between ^174 Yb( ${}^{3}{{\rm{P}}}_{2}$ ) with magnetic sublevels of m _J = 0 and −2 and ground state ^6 Li to be $(4.4\pm 0.3)\times {10}^{-11}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$ and $(4.7\pm 0.8)\times {10}^{-11}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$ , respectively. Absence of spin changing processes in Yb( ${}^{3}{{\rm{P}}}_{2}$ )–Li inelastic collisions at low magnetic fields is confirmed by inelastic loss measurements on the m _J = 0 state. We also demonstrate that our method allows us to look into loss processes in few-body systems separately.

Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such schemes are typically associated with space-dependent effective masses (tunneling amplitudes) and non-uniform flux patterns. In this work we investigate this phenomenon theoretically, by computing the effective Hamiltonians and quasienergy spectra associated with several kinds of lattice-shaking protocols. A detailed comparison with a method based on moving lattices, which are added on top of a main static optical lattice, is provided. This study allows the identification of novel shaking schemes, which simultaneously provide uniform effective mass and magnetic flux, with direct implications for cold-atom experiments and photonics.

We investigate the applicability of laser assisted tunneling in a strongly interacting one-dimensional (1D) Bose gas (the Tonks–Girardeau gas) in optical lattices. We find that the stroboscopic dynamics of the Tonks–Girardeau gas in a continuous Wannier–Stark-ladder potential, supplemented with laser assisted tunneling, effectively realizes the ground state of 1D hard-core bosons in a discrete lattice with nontrivial hopping phases. We compare observables that are affected by the interactions, such as the momentum distribution, natural orbitals and their occupancies, in the time-dependent continuous system, to those of the ground state of the discrete system. Stroboscopically, we find an excellent agreement, indicating that laser assisted tunneling is a viable technique for realizing novel ground states and phases with hard-core 1D Bose gases.

We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general p -ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the mixtures exhibit non-additive interactions. In this situation the out-of-equilibrium evolution is characterized by the formation of metastable domains that reach partial equilibration long before the attainment of stationarity. In experimental settings with mesoscopic sizes, this collective behavior may in fact take the appearance of dynamic symmetry breaking.

The Fermi-Hubbard model is one of the key models of condensed matter physics, which holds a potential for explaining the mystery of high-temperature superconductivity. Recent progress in ultracold atoms in optical lattices has paved the way to studying the model’s phase diagram using the tools of quantum simulation, which emerged as a promising alternative to the numerical calculations plagued by the infamous sign problem. However, the temperatures achieved using elaborate laser cooling protocols so far have been too high to show the appearance of antiferromagnetic (AF) and superconducting quantum phases directly. In this work, we demonstrate that using the machinery of dissipative quantum state engineering, one can observe the emergence of the AF order in the Fermi-Hubbard model with fermions in optical lattices. The core of the approach is to add incoherent laser scattering in such a way that the AF state emerges as the dark state of the driven-dissipative dynamics. The proposed controlled dissipation channels described in this work are straightforward to add to already existing experimental setups.

We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at $2{\rm{\Delta }}$ . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with ^6 Li or ^40 K atoms using Bragg spectroscopy.

In spintronics the active control and manipulation of spin currents is studied in solid-state systems. Opposed to charge currents, spin currents are strongly damped due to collisions between different spin carriers in addition to relaxation due to impurities and lattice vibrations. The phenomenon of relaxation of spin currents is called spin drag. Here we study spin drag in ultra-cold bosonic atoms deep in the hydrodynamic regime and show that spin drag is the dominant damping mechanism for spin currents in this system. By increasing the phase space density we find that spin drag is enhanced in the quantum regime by more than a factor of two due to Bose stimulation, which is in agreement with recent theoretical predictions and, surprisingly, already occurs considerably above the phase transition.

We have measured the damped motion of a trapped Bose–Einstein condensate, oscillating with respect to a thermal cloud. The cigar-shaped trapping potential provides enough transverse confinement that the dynamics of the system are intermediate between three-dimensional and one-dimensional. We find that the scaling of the damping rate with temperature is consistent with Landau theory, but that the damping rate for axial oscillations at a given temperature is consistently smaller than expected for a three-dimensional gas. We attribute this to the suppressed density of states for low-energy transverse excitations (essential excitations for axial Landau damping), which results from the quantization of the radial motion.

The time-dependent non-equilibrium dynamics of a Bose–Einstein condensate (BEC) typically generates incoherent excitations out of the condensate due to the finite frequencies present in the time evolution. We present a detailed derivation of a general non-equilibrium Greenʼs function technique that describes the coupled time evolution of an interacting BEC and its single-particle excitations in a trap, based on an expansion in terms of the exact eigenstates of the trap potential. We analyze the dynamics of a Bose system in a small double-well potential with initially all particles in the condensate. When the trap frequency is larger than the Josephson frequency, $\Delta \gt {{\omega }_{{\rm J}}}$ , the dynamics changes at a characteristic time, ${{\tau }_{{\rm c}}}$ , abruptly from the slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times $t\lt {{\tau }_{{\rm c}}}$ , the Josephson oscillations are undamped, in agreement with the experiments. We analyze the physical origin of the finite scale ${{\tau }_{{\rm c}}}$ as well as its dependence on the trap parameter Δ .

We consider a correlated Bose gas tightly confined into a ring shaped lattice, in the presence of an artificial gauge potential inducing a persistent current through it. A weak link painted on the ring acts as a source of coherent back-scattering for the propagating gas, interfering with the forward scattered current. This system defines an atomic counterpart of the rf-SQUID: the atomtronics quantum interference device. The goal of the present study is to corroborate the emergence of an effective two-level system in such a setup and to assess its quality, in terms of its inner resolution and its separation from the rest of the many-body spectrum, across the different physical regimes. In order to achieve this aim, we examine the dependence of the qubit energy gap on the bosonic density, the interaction strength, and the barrier depth, and we show how the superposition between current states appears in the momentum distribution (time-of-flight) images. A mesoscopic ring lattice with intermediate-to-strong interactions and weak barrier depth is found to be a favorable candidate for setting up, manipulating and probing a qubit in the next generation of atomic experiments.

We develop theory for a flattened dipolar Bose–Einstein condensate produced by harmonic confinement along one direction. The role of both short-ranged contact interactions and long-ranged dipole–dipole interactions is considered, and the dipoles are allowed to be polarized along an arbitrary direction. We discuss the symmetry properties of the condensate and the part of the excitation spectrum determining stability, and introduce two effective interaction parameters that allow us to provide a general description of the condensate properties, rotons, and stability. We diagonalize the full theory to obtain benchmark results for the condensate and quasiparticle excitations, and characterize the exact mean field stability of the system. We provide a unified formulation for a number of approximate schemes to describe the condensate and quasiparticles, including the standard quasi-two-dimensional approximation, two kinds of variational ansatz, and a Thomas–Fermi approximation. Some of these schemes have been widely used in the literature despite not being substantiated against the exact theory. We provide this validation and establish the regimes where the various theories perform well.

We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential. The Hamiltonian of the non-interacting system reduces to the well known ‘Aubry–André model’, which shows the localization transition at a critical strength of the potential. In the presence of repulsive interaction we observe multi-site localization and obtain a phase diagram of the dilute Bose gas by computing the superfluid fraction and the inverse participation ratio. We construct a low-dimensional classical Hamiltonian map and show that the onset of localization is manifested by the chaotic phase space dynamics. The level spacing statistics also identify the transition to localized states resembling a Poisson distribution that are ubiquitous for both non-interacting and interacting systems. We also study the quantum fluctuations within the Bogoliubov approximation and compute the quasiparticle energy spectrum. Enhanced quantum fluctuation and multi-site localization phenomenon of non-condensate density are observed above the critical coupling of the potential. We briefly discuss the effect of the trapping potential on the localization of matter wave.

Atom interferometers (AIs) are promising tools for precision measurement with applications ranging from geophysical exploration and tests of the equivalence principle of general relativity to the detection of gravitational waves. Their optimal sensitivity is ultimately limited by their detection noise. We review resonant and near-resonant methods to detect the atom number of the interferometer outputs, and we theoretically analyze the relative influence of various scheme dependent noise sources and the technical challenges affecting the detection. We show that for the typical conditions under which an AI operates, simultaneous fluorescence detection with a charge-coupled device sensor is the optimal imaging scheme. We extract the laser beam parameters such as detuning, intensity, and duration required for reaching the atom shot noise limit.

We theoretically develop and experimentally demonstrate a holographic method for imaging cold atoms at the diffraction and photon shot noise limits. Aided by a double point source reference field, a simple iterative algorithm robustly removes the twin image of an ^87 Rb cold atom sample during the image reconstruction. Shot-noise limited phase shift and absorption images are consistently retrieved at various probe detunings, and during the laser cooling process. We consistently resolve less than 2 mrad phase shift ( $0.4\%$ attenuation) of the probe light, outperforming shot-noise limited phase-contrast (absorption) imaging by a factor of 4 or more if the same camera is used without pixel saturation. We discuss the possible extension of this work for precise phase imaging of dense atomic gases, and for off-resonant probing of multiple atoms in optical lattices.

We study the quantum melting of quasi-one-dimensional lattice models in which the dominant energy scale is given by a repulsive dipolar interaction. By constructing an effective low-energy theory, we show that the melting of crystalline phases can occur into two distinct liquid phases having the same algebraic decay of density–density correlations but showing a different non-local correlation function expressing string order. We present possible experimental realizations using ultracold atoms and molecules, introducing an implementation based on resonantly driven Rydberg atoms that offers additional benefits compared to a weak admixture of the Rydberg state.

We propose an experimental scheme to effectively assemble chains of dipolar gases with a uniform length in a multi-layer system. The obtained dipolar chains can form a chain crystal with the system temperature easily controlled by the initial lattice potential and the external field strength during processing. When the density of chains increases, we further observe a second order quantum phase transition for the chain crystal to be dissociated toward layers of 2D crystal, where the quantum fluctuation dominates the classical energy and the compressibility diverges at the phase boundary. The experimental implication of such a dipolar chain crystal and its quantum phase transition is also discussed.

We predict the existence of novel collapse and revival oscillations that are a distinctive signature of the short-range off-diagonal coherence. Starting with an atomic Mott state in a one-dimensional optical lattice, suddenly raising the lattice depth freezes particle–hole pairs in place and induces phase oscillations. The peak of the quasi-momentum distribution, revealed through time-of-flight interference, oscillates between a maximum occupation at zero quasi-momentum (the Γ point) and the edge of the Brillouin zone. We show that the population enhancements at the edge of the Brillouin zone are due to short-range coherence due to particle–hole pairs, and we find similar effects for fermions and Bose–Fermi mixtures in a lattice. Our results open a new dynamic probe for strongly correlated many-body states with short-range phase coherence that is distinct from the matter–wave collapse and revivals previously observed in the long-range coherent superfluid regime.

We study the phase diagram of a two-dimensional assembly of bosons interacting via a soft-core repulsive pair potential of varying strength, and compare it to that of the equivalent system in which particles are regarded as distinguishable. We show that quantum-mechanical exchanges stabilize a ‘cluster crystal’ phase in a wider region of parameter space than predicted by calculations in which exchanges are neglected. This physical effect is diametrically opposite to that which takes place in hard-core Bose systems such as ^4 He, wherein exchanges strengthen the fluid phase. This is underlain in the cluster crystal phase of soft-core bosons by the free energy gain associated with the formation of local Bose–Einstein condensates.

The phenomenon of self-pumped slow light, where a single beam appears to be slowed by a solid-state media, is both subtle and controversial. Here, we reply to a comment on our recent work, which uses an observation of enhanced photon drag to distinguish between group delay and pulse reshaping.

We consider a Bose–Hubbard ladder subject to an artificial magnetic flux and discuss its different ground states, their physical properties, and the quantum phase transitions between them. A low-energy effective field theory is derived, in the two distinct regimes of a small and large magnetic flux, using a bosonization technique starting from the weak-coupling limit. Based on this effective field theory, the ground-state phase diagram at a filling of one particle per site is investigated for a small flux and for a flux equal to π per plaquette. For π -flux, this analysis reveals a tricritical point, which has been overlooked in previous studies. In addition, the Mott insulating state at a small magnetic flux is found to display Meissner currents.