Cold Fermionic Atoms Research Articles

Perspective on new implementations of atomtronic circuits

In this article, we provide perspectives for atomtronics circuits on quantum technology platforms beyond simple bosonic or fermionic cold atom matter-wave currents. Specifically, we consider (i) matter-wave schemes with multi-component quantum fluids; (ii) networks of Rydberg atoms that provide a radically new concept of atomtronics circuits in which the flow, rather than in terms of matter, occurs through excitations; (iii) hybrid matterwave circuits—a combination of ultracold atomtronic circuits with other quantum platforms that can lead to circuits beyond the standard solutions and provide new schemes for integrated matter-wave networks. We also sketch how driving these systems can open new pathways for atomtronics.

Engineering Higgs dynamics by spectral singularities

We generalize the dynamical phase diagram of a Bardeen-Cooper-Schrieffer condensate, considering attractive to repulsive, i.e., critical quenches (CQ) and a non-constant density of states (DOS). We show that different synchronized Higgs dynamical phases can be stabilized, associated with singularities in the density of states (DOS) and different quench protocols. In particular, the CQ can stabilize an overlooked high-frequency Higgs dynamical phase related to the upper edge of the fermionic band. For a compensated Dirac system we find a Dirac-Higgs mode associated with the cusp singularity at the Fermi level, and we show that synchronized phases become more pervasive across the phase diagram. The relevance of these remarkable phenomena and their realization in ensembles of fermionic cold atoms confined in optical lattices is also discussed.

Fermionic superfluidity: from cold atoms to neutron stars

From flow without dissipation of energy to the formation of vortices when placed within a rotating container, the superfluid state of matter has proven to be a very interesting physical phenomenon. Here we present the key mechanisms behind superfluidity in fermionic systems and apply our understanding to one of the most exotic systems in the universe: the superfluid interior of a neutron star. The extreme conditions of neutron stars prevent us from directly probing the internal superfluid properties, however, we can experimentally realize conditions resembling the interior through the use of cold atoms prepared in a laboratory and simulated on a computer. Key insights can be gained by simulating the neutron star superfluid using another system with analogous properties: a cold atomic Fermi gas. Computational physicists are leveraging the power of supercomputers to simulate interacting atomic systems with unprecedented accuracy. In this paper we provide a pedagogical introduction to the physics, guiding the reader through the major conceptual steps to understand the relation between cold atoms, superfluids, and neutron stars. We stress the surprising similarity between these systems, which stems from universality, a fundamental notion in many-body physics. These topics are available in advanced textbooks, but introductory materials are harder to come by; this paper is intended to fill the gap for curious undergraduate and graduate students. We will show how cold atoms can help us make significant strides towards understanding the exotic physics found deep within the universe.

Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder

We report the numerical discovery of a pair-density-wave (PDW) superconductor from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t-J$ model, and are further coupled to a spin $1/2$ Heisenberg model through the Kondo coupling $J_K$. When the density of electrons $x$ is one, the Mott insulator is in a Haldane phase or in a rung singlet phase depending on whether $J_K$ is negative or positive. Upon doping, a pair-density-wave with $\mathbf Q=\pi$ can emerge for both signs of $J_K$. In the $J_K \rightarrow -\infty$ limit, the model reduces to the recently proposed type II t-J model and we observes a continuous transition between the PDW superconductor and an unconventional Luttinger liquid phase with doping. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1 chains formed by Ni$^{2+}$ in a solid state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity.

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Algebraic theory of quantum synchronization and limit cycles under dissipation

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

On the Accuracy of Random Phase Approximation for Dynamical Structure Factors in Cold Atomic Gases

Many-body physics poses one of the greatest challenges to science in the 21st century. Still more daunting is the problem of accurately calculating the properties of quantum many-body systems in the strongly correlated regime. Cold atomic gases provide an excellent test ground, for both experimentalists and theorists, to study the exotic and sometimes counterintuitive behavior of quantum many-body problems. Of particular interest is the appearance of collective excitations in these systems, such as the famous Goldstone mode and the elusive Higgs mode. It is particularly important to assess the robustness of theoretical and computational techniques to study such excitations. We build on the unprecedented opportunity provided by the fact that, in some cases, exact numerical predictions can be obtained through quantum Monte Carlo. We use these predictions to assess the accuracy of the Random Phase Approximation, which is widely considered to be a method of choice for the study of the collective excitations in a cold atomic Fermi gas modeled with a Fermi–Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamic properties, particularly for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential. We determined that using a renormalized potential is likely too simplistic a method for improving the accuracy of generalized Random Phase Approximation and that a more sophisticated approach is needed.

Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions

The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices.

Layer-by-layer assembly of multilayer optical lattices: A theoretical proposal

We propose methods for synthesizing multilayer optical lattices of cold atoms in a layer-by-layer manner, to unlock the potential of optical lattices in simulating the fascinating physics of multilayer systems. Central to the approach is to compress the beam profile of a red-detuned Gaussian laser beam from disklike to a thin line by a telescope with two cylindrical lenses. A highly tunable multilayer optical lattice is obtained by passing the compressed Gaussian beam through an optical device consisting of beam splitters, mirrors, and glass plates. We illustrate the proposal with the displaced dice lattice, which is a trilayer lattice that maps to the dice lattice when projected to the same layer. Both the dice model and its interesting variants may be realized. For a model of fermionic cold atoms, featuring an isolated flat band between two dispersive bands, we find valley-contrasting interband transitions involving the flat band.

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases.

Controllable finite-momenta dynamical quasicondensation in the periodically driven one-dimensional Fermi-Hubbard model

In the strongly interacting limit of the Hubbard model localized double-occupancies form effective hard-core bosonic excitations, called a doublons, which are long-lived due to energy conservation. Using time-dependent density-matrix renormalisation group we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analysing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an eta-quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon-hopping and doublon-repulsion are strongly renormalised by the drive, breaking the eta-SU(2) symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrate that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering non-equilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.

Quantized Conductance through a Spin-Selective Atomic Point Contact.

We implement a microscopic spin filter for cold fermionic atoms in a quantum point contact (QPC) and create fully spin-polarized currents while retaining conductance quantization. Key to our scheme is a near-resonant optical tweezer inducing a large effective Zeeman shift inside the QPC while its local character limits dissipation. We observe a renormalization of this shift due to interactions of only a few atoms in the QPC. Our work represents the analog of an actual spintronic device and paves the way to studying the interplay between spin splitting and interactions far from equilibrium.

Dynamical Thermalization of Interacting Fermionic Atoms in a Sinai Oscillator Trap

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the interactions, with a strength above a certain quantum chaos border given by the Åberg criterion, lead to the Fermi–Dirac distribution and relaxation of many-body initial states to the thermalized state in the absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt–Boltzmann dispute.

How to Directly Measure Floquet Topological Invariants in Optical Lattices.

The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the gaps. We propose a feasible scheme for measuring these winding numbers in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a by-product, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.

Statistics-tuned phases of pseudofermions in one dimension

We show that a quadratic system of pseudofermions, with tunable fractionalised statistics, can host a rich phase diagram on a one dimensional chain with nearest and next nearest neighbor hopping. Using a combination of numerical and analytical techniques, we show that that by varying the statistical angle and the ratio of the hopping, the system stabilizes two Tomonaga-Luttinger liquids (TLL) with central charges c = 1 and 2 respectively along with the inversion symmetry broken bond ordered (BO) insulating phase. Interestingly, the two quantum phase transitions in the system - (1) between the two TLLs, and, (2) the c = 1 TLL and BO phase can be engendered by solely tuning the statistics of the pseudofermions. Our analysis shows that both these transition are continuous and novel with the former lacking a local order-parameter based description and the latter of Berezinskii-Kosterlitz-Thouless type. These phases and phase transitions can be of direct experimental relevance in context of recent studies of fermionic cold atoms.

Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length

Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic $^{6}$Li and bosonic $^{7}$Li atoms, which approximately have the same masses, is discussed.

The pseudogap regime in the unitary Fermi gas

We discuss the pseudogap regime in the cold atomic unitary Fermi gas, with a particular emphasis on the auxiliary-field quantum Monte Carlo (AFMC) approach. We discuss possible signatures of the pseudogap, review experimental results, and survey analytic and quantum Monte Carlo techniques before focusing on AFMC calculations in the canonical ensemble. For the latter method, we discuss results for the heat capacity, energy-staggering pairing gap, spin susceptibility, and compare to experiment and other theoretical methods.

Coboson many-body formalism for atom–dimer scattering length

We use the composite boson (coboson) many-body formalism to tackle scattering lengths for cold fermionic atoms. We show that bound dimers can be taken as elementary entities provided that fermion exchanges between them are treated exactly, as can be done through the coboson formalism. This alternative tool extended to cold atom physics not only makes transparent many-body processes through Shiva diagrams specific to cobosons, but also simplifies calculations. Indeed, the integral equation we derive for the atom–dimer scattering length and solve by restricting the dimer relative motion to the ground state, gives values in remarkable agreement with the exact scattering length values for all fermion mass ratios. This remarkable agreement also holds true for the dimer–dimer scattering length, except for equal fermion masses where our restricted procedure gives a value slightly larger than the accepted one (0.64ad instead of 0.60ad). All this proves that the scattering of a cold-atom dimer with an atom or another dimer is essentially controlled by the dimer relative-motion ground state, a physical result not obvious at first.

Symmetry protected topological phases in two-orbital SU(4) fermionic atoms

We study one-dimensional systems of two-orbital SU(4) fermionic cold atoms. In particular, we focus on an SU(4) spin model [named SU(4) $e$-$g$ spin model] that is realized in a low-energy state in the Mott insulator phase at the filling $n_g=3, n_e=1$ ($n_g, n_e$: numbers of atoms in ground and excited states, respectively). Our numerical study with the infinite-size density matrix renormalization group shows that the ground state of SU(4) $e$-$g$ spin model is a nontrivial symmetry protected topological (SPT) phase protected by $Z_4 \times Z_4$ symmetry. Specifically, we find that the ground state belongs to an SPT phase with the topological index $2\in\mathbb{Z}_4$ and show sixfold degenerate edge states. This is topologically distinct from SPT phases with the index $1\in\mathbb{Z}_4$ that are realized in the SU(4) bilinear model and the SU(4) Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We explore the phase diagram of SU(4) spin models including $e$-$g$ spin model, bilinear-biquadratic model, and AKLT model, and identify that antisymmetrization effect in neighboring spins (that we quantify with Casimir operators) is the driving force of the phase transitions. Furthermore, we demonstrate by using the matrix product state how the $\mathbb{Z}_4$ SPT state with six edge states appears in the SU(4) $e$-$g$ spin model.

From chains to plane with a fermionic cold atom quantum simulator

From chains to plane with a fermionic cold atom quantum simulator