Cold Atoms In Optical Lattices Research Articles

Characteristic features of strong correlation: lessons from a 3-fermion one-dimensional harmonic trap

Abstract Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.

Few-body bound topological and flat-band states in a Creutz ladder

We investigate the properties of a few interacting bosons in a Creutz ladder, which has become a standard model for topological systems, and which can be realized in experiments with cold atoms in optical lattices. At the single-particle level, this system may exhibit a completely flat energy landscape with nontrivial topological properties. In this scenario, we identify topological two-body edge states resulting from the bonding of single-particle edge and flat-band states. We also explore the formation of two- and three-body bound states in the strongly interacting limit, and we show how these quasiparticles can be engineered to replicate the flat-band and topological features of the original single-particle model. Furthermore, we show that in this geometry perfect Aharonov-Bohm caging of two-body bound states may occur for arbitrary interaction strengths, and we provide numerical evidence that the main features of this effect are preserved in an interacting many-body scenario resulting in many-body Aharonov-Bohm caging. Published by the American Physical Society 2024

Injection spectroscopy of momentum state lattices

The energy spectrum of quantum systems contain a wealth of information about their underlying properties. Spectroscopic techniques, especially those with access to spatially resolved measurements, can be challenging to implement in real-space systems of cold atoms in optical lattices. Here we explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique and observe qualitative agreement between the measured and simulated energy spectra for small two- and three-site lattices as well as a uniform many-site lattice. Finally, through simulations, we show that this technique should allow for the exploration of the topological bands and the fractal energy spectrum of the Hofstadter model as realized in synthetic lattices.

Unruh effect and Takagi's statistics inversion in strained graphene

We present a theoretical study of how a spatially varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependence to the local tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski space-time. Within this setup, a sudden switch on of the spatially varying tunneling (or strain) yields a spontaneous production of electron-hole pairs, an analog version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photoemission and scanning tunneling microscopy experiments. We also calculate the average electronic conductivity and find that it grows linearly with frequency $\ensuremath{\omega}$. Finally, we find that the total system energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction.

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two nonzero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At nonzero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first order in three dimensions, but to change to second order in two dimensions (2D). As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

Observation of Light Thermalization to Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers.

Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative-temperature equilibrium states are also possible. Negative-temperature equilibriums have been observed with spin systems, cold atoms in optical lattices, and two-dimensional quantum superfluids. Here we report the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber-i.e., in a conservative Hamiltonian system. The bounded energy spectrum of the optical fiber enables negative-temperature equilibriums with high energy levels (high-order fiber modes) more populated than low energy levels (low-order modes). Our experiments show that negative-temperature speckle beams are featured, in average, by a nonmonotonic radial intensity profile. The experimental results are in quantitative agreement with the Rayleigh-Jeans theory without free parameters. Bringing negative temperatures to the field of optics opens the door to the investigation of fundamental issues of negative-temperature states in a flexible experimental environment.

Flat-band-induced superconductivity in synthetic bilayer optical lattices

Stacking two layers of graphene with a relative twist angle gives rise to moir\'e patterns, which can strongly modify electronic behavior and may lead to unconventional superconductivity. A synthetic version of twisted bilayers can be engineered with cold atoms in optical lattices. Here, the bilayer structure is mimicked through coupling between atomic sublevels, and the twist is achieved by a spatial modulation of this coupling. In the present paper, we investigate the superconducting behavior of fermionic atoms in such a synthetic twisted bilayer lattice. Attractive interactions between the atoms are treated on the mean-field level, and the superconducting behavior is analyzed via the self-consistently determined pairing gap. A strong enhancement of the pairing gap is found, when a quasi-flat band structure occurs at the Fermi surface, reflecting the prominent role played by the twist on the superconductivity. The tunability of interactions allows for the switching of superconducting correlations from intra (synthetic) layer to inter (synthetic) layer. This includes also the intermediate scenario, in which the competition between inter- and intra-layer coupling completely destroys the superconducting behavior, resulting in re-entrant superconductivity upon tuning of the interactions

Robust quantum boomerang effect in non-Hermitian systems

Anderson localization is a general phenomenon that applies to a variety of disordered physical systems. Recently, a novel manifestation of Anderson localization for wave packets launched with a finite average velocity was proposed, the Quantum boomerang effect (QBE). This phenomenon predicts that the disorder-averaged center of mass of a particle initially moves ballistically, then makes a U-turn, and finally slowly returns to its initial position. The QBE has been predicted to take place in several Hermitian models with Anderson localization and has been experimentally observed in the paradigmatic quantum kicked rotor model. In this work, we investigate the emergence of the QBE in non-Hermitian systems and clarify the importance of symmetries of the Hamiltonian and the initial state. We generalize the analytical arguments available in the literature and show that even in the case of complex spectrum a boomerang-like behavior can appear in a non-Hermitian system. We confirm our analytical results through a careful numerical investigation of the dynamics for several non-Hermitian models. We find that non-Hermiticity leads to the breakdown of the dynamical relation, though the QBE is preserved. This work opens up new avenues for future investigations in Anderson localized systems. The models studied here may be implemented using cold atoms in optical lattices.

Resonance and antiresonance characteristics in linearly delayed Maryland model

The Maryland model is a critical theoretical model in quantum chaos. This model describes the motion of a spin-1/2 particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field. In this work, we propose the linearly delayed quantum relativistic Maryland model (LDQRMM) as a novel generalization of the original Maryland model and systematically study its physical properties. We derive the resonance and antiresonance conditions for the angular momentum spread. The “characteristic sum” is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters. In addition, different topological patterns emerge in the LDQRMM. It predicts some additions to the Anderson localization in the corresponding tight-binding systems. Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.

Exploration of doped quantum magnets with ultracold atoms

In the last decade, quantum simulators, and in particular cold atoms in optical lattices, have emerged as a valuable tool to study strongly correlated quantum matter. These experiments are now reaching regimes that are numerically difficult or impossible to access. In particular they have started to fulfill a promise which has contributed significantly to defining and shaping the field of cold atom quantum simulations, namely the exploration of doped and frustrated quantum magnets and the search for the origins of high-temperature superconductivity in the fermionic Hubbard model. Despite many future challenges lying ahead, such as the need to further lower the experimentally accessible temperatures, remarkable studies have already been conducted. Among them, spin-charge separation in one-dimensional systems has been demonstrated, extended-range antiferromagnetism in two-dimensional systems has been observed, connections to modern day large-scale numerical simulations were made, and unprecedented comparisons with microscopic trial wavefunctions have been carried out at finite doping. In many regards, the field has acquired new realms, putting old ideas to a new test and producing new insights and inspiration for the next generation of physicists.In the first part of this paper, we review the results achieved in cold atom realizations of the Fermi–Hubbard model in recent years. We put special emphasis on the new probes available in quantum gas microscopes, such as higher-order correlation functions, full counting statistics, the ability to study far-from-equilibrium dynamics, machine learning and pattern recognition of instantaneous snapshots of the many-body wavefunction, and access to non-local correlators. Our review is written from a theoretical perspective, but aims to provide basic understanding of the experimental procedures. We cover one-dimensional systems, where the phenomenon of spin-charge separation is ubiquitous, and two-dimensional systems where we distinguish between situations with and without doping. Throughout, we focus on the strong coupling regime where the Hubbard interactions U dominate and connections to t−J models can be justified.In the second part of this paper, with the stage set and the current state of the field in mind, we propose a new direction for cold atoms to explore: namely mixed-dimensional bilayer systems, where the charge motion is restricted to individual layers which remain coupled through spin-exchange. These systems can be directly realized experimentally and we argue that they have a rich phase diagram, potentially including a strongly correlated BEC-to-BCS cross-over and regimes with different superconducting order parameters, as well as complex parton phases and possibly even analogs of tetraquark states. In particular, we propose a novel, strong pairing mechanism in these systems, which puts the formation of hole pairs at experimentally accessible, elevated temperatures within reach. Ultimately we propose to explore how the physics of the mixed-dimensional bilayer system can be connected to the rich phenomenology of the single-layer Hubbard model.

Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.

Transport properties of cold atoms in optical lattice

We investigated the transport properties of cold atoms in a one-dimensional optical lattice under distance selective dissipation and external driving. We analyze how tunneling, on-site interaction, dissipation and external driving affect the transport of cold atoms. We used mean-field theory and the classical phase space method to explain the dynamics of the system. In order to analyze the transport effect of cold atoms, we calculate the relative density of atoms on each site and the standard deviation of relative density. The manipulation transport of cold atoms can be achieved through a step function like interaction in theory. In particular, we study the transport of cold atoms in the double-well with external driving. The steady states of the system are analytically derived.

Gauge-Field Extended k·p Method and Novel Topological Phases

Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i)The little co-group must include the translations with nontrivial algebraic relations. (ii)The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.

Topological Mott transition in a Weyl-Hubbard model: Dynamical mean-field theory study

Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties by means of dynamical mean-field theory (DMFT). We characterize topological phases by numerically evaluating the Chern number via the Ishsikawa-Matsuyama formula for interacting phases. Within our studies, we find that the Chern numbers become trivial when interactions lead to insulating behavior. For a deeper understanding of the Weyl-semimetal-to-Mott-insulator topological phase transition, we evaluate the topological properties of quasiparticle bands as well as so-called blind bands. Our study is complementary to recent studies of Weyl semimetals with DMFT.

Majorana corner pairs in a two-dimensional s -wave cold atomic superfluid

We propose a method to prepare Majorana pairs at the corners of imprinted defects on a two-dimensional cold atom optical lattice with $s$-wave superfluid pairing. Different from previous proposals that manipulate the effective Dirac masses, our scheme relies on the sign flip of the spin-orbit coupling at the corners, which can be tuned in experiments by adjusting the angle of incident Raman lasers. The Majorana corner pairs are found to be located at the interface between two regimes with opposite spin orbit coupling strengths in an anticlockwise direction and are robust against certain symmetry-persevered perturbations. Our work provides a new way for implementing and manipulating Majorana pairs with existing cold-atom techniques.

Quantum simulation of two-dimensional quantum chemistry in optical lattices

Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$_2^+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions. We extend this approach to larger systems by introducing as many mediating atoms as fermions, and derive the effective repulsion law. In all cases, we analyze how the continuous limit is approached for increasing optical lattice sizes.

P Orbital Flat Band and Dirac Cone in the Electronic Honeycomb Lattice.

Theory anticipates that the in-plane px, py orbitals in a honeycomb lattice lead to potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s–p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orbital bands, including the p orbital flat band and Dirac cone.

Dynamics of rotated spin states and magnetic ordering with two-component bosonic atoms in optical lattices

The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focused on experimentally realizing ground or thermal states via adiabatic loading, it would often be more straightforward to prepare specific simple product states and to probe the properties of interacting spins by observing their dynamics. We explore this possibility for spin-1/2 and spin-1 models that can be realized with bosons in optical lattices, and which exhibit $\mathit{XY}$-ferromagnetic (or counterflow spin-superfluid) phases. We consider the dynamics of initial spin-rotated states corresponding to a mean-field version of the phases of interest. Using matrix product state methods in one dimension, we compute both nonequilibrium dynamics and ground and thermal states for these systems. We compare and contrast their behavior in terms of correlation functions and induced spin currents, which should be directly observable with current experimental techniques. We find that although spin correlations decay substantially at large distances and on long timescales, for induction of spin currents, the rotated states behave similarly to the ground states on experimentally observable timescales.

A transient superconductor

Physics Systems of interacting particles occupying a lattice can often be described by the so-called Hubbard model. This model has been studied extensively with cold atoms in optical lattices, where its parameters can be easily tuned. In a complementary approach, Buzzi et al. investigated the organic molecular superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br, which can be described by the model, and used light to modulate the Hubbard parameters. The frequency of the light was tuned to a vibrational mode of the molecular building block of this material. The photoexcitation caused the sample to (briefly) become superconducting at temperatures much higher than the critical temperature. Calculations indicated that this was a consequence of an unusual long-range state of doubly occupied lattice sites. Phys. Rev. X 10 , 031028 (2020).

Supersolid phase of cold atoms

Supersolid phase is a phase of matter that is characterized by the combination of the off-diagonal long-range order of superfluid and the diagonal long-range order of solid. Cold atoms with spin–orbit-coupling, contact interaction and long-range interaction can provide systems for the research of supersolid phase. Under the effect of spin-dependent potential and spin–orbit-coupling, hard-core ultra-cold atoms with contact interaction can be shown to construct supersolid phase. The combination of soft-core long-range interaction and spin–orbit coupling can establish exotic supersolid phase with spontaneous breakdown of chiral symmetry. The optical Bragg scattering of cold atoms in optical lattices can be used to detect supersolid phase. The study of supersolid phase will be helpful to the researches of matter phases.