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arXiv:2310.00849 · Physical Review Research

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

Huan-Kuang Wu, Takafumi Suzuki, Naoki Kawashima, Wei-Lin Tu

Published Jun 20, 2024• 0 citations
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Abstract

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S = 1 / 2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J , is considered, and the overall model becomes an effective X X Z model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023297

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In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S = 1 / 2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J , is considered, and the overall model becomes an effective X X Z model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024
Different quantum phases of a hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from the cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\ensuremath{\phi}=\ensuremath{\pi}/4$. Using the mean-field analysis where the quantum spin operators are replaced by ccc numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where a first-order transition takes place in between them. With the help of the CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.
Strongly interacting ultracold dipolar molecules are a rich platform for quantum information and quantum simulation of phenomena relevant to condensed matter systems. This dissertation presents novel theoretical and computational studies of ultracold dipolar molecules relevant to these areas in three broad categories.First, the path integral ground state quantum Monte Carlo method is extended to simulations with both translational and rotational degrees of freedom, including the development of a novel estimator of the elementary excitation energies of a system with these degrees of freedom based on the well known Feynman-Bijl approximation. This is then used to study dipolar molecular ensembles confined to one-dimensional optical lattices. The ground state phase diagram is characterized with both a mean-field method and the aforementioned quantum Monte Carlo method. A quantum phase transition is found for very short optical lattice spacings or very large dipole moments. The prospects for experimentally realizing a system which exhibits this phase transition are discussed.Second, the path integral ground state quantum Monte Carlo method is utilized to study the ground state of dipole molecules confined to two-dimensional optical lattices. On square lattices a crossover from a weakly interacting disordered phase to a strongly interacting striped phase is found for short lattice spacings or large dipole moments. On triangular lattices a crossover between a disordered phase and a completely polarized phase is found, also for short lattice spacings or large dipole moments. The relevance of such simulations to self-assembled dipolar crystals in two dimensions is discussed and simulation results of these systems are presented. Simulations of polarized and harmonically confined molecular systems in two dimensions with translations and rotations are also presented and a realistic interaction potential using highly accurate ab initio quantum chemistry techniques is calculated for LiH--LiH interactions as a preliminary step toward developing a high quality trial wave function for the simulation of systems possessing both translational and rotational degrees of freedom.Finally, several novel applications for dipolar molecules confined to optical lattices are proposed. An experimental realization of a topological phase using 2Sigma^2\\Sigma2Sigma ground state molecules with applied near resonant microwave fields and transverse magnetic fields is proposed. A method to create an array of dipole-coupled two-level molecules exhibiting superradiance and possessing novel spectroscopic properties using 1Sigma^1\\Sigma1Sigma ground state molecules in the combination of a far off-resonant laser field and a moderate magnetic field is proposed. Additionally, a method to create entangled pairs of molecules using closed-shell dipolar molecules immersed in an intense far off-resonant laser field is reviewed and an extension in which parallel optical lattices are merged and molecules are allowed to collide in the presence of a far off-resonant laser field is proposed. Simulation results are presented indicating that a significant amount of entanglement may be generated in such a way in realistic molecular systems.
Microwave-dressed polar molecules offer a route to lattice quantum simulators in which the angular form of long-range dipolar interactions, not only their overall strength, can be engineered. We study this setting in a minimal hard-core Bose lattice model on a square optical lattice, with particles interacting through a sign-changing non-axisymmetric dipolar tail \mathcal V(\mathbf r)\propto (x^2-y^2)/(x^2+y^2)^{5/2} that is repulsive along one lattice axis and attractive along the other. Using worm-algorithm path-integral quantum Monte Carlo simulations, supported by a hard-core spin mapping and a Gutzwiller soft-mode diagnostic, we find two regimes controlled by t/V: at larger t/V the system remains superfluid but develops a pronounced directional stiffness anisotropy, while at smaller t/V it forms a stripe solid selected in the (q,0) axial family, corresponding to real-space stripes parallel to y. The leading ordering wave vector remains in this axial family but reorganizes with filling, showing that the robust ordered object is a family of stripe states rather than one fixed commensurate Bragg peak. Near the closure of the stripe lobe, averaged observables can mimic a narrow supersolid signal; measurement-resolved stripe structure-factor histograms instead reveal first-order switching between superfluid and stripe-solid sectors. NaCs lattice estimates place the relevant V/t window within reach of modest effective dressed dipole moments, linking the predicted stripe-family order and its experimental diagnostics to accessible molecular quantum-simulation scales.
Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J_{1}-J_{2} model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study, by means of quantum Monte Carlo, the ground-state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the xzxzxz plane. We present ground-state phase diagrams of the above system at different tilt angles. We find that as the dipolar interaction increases, the superfluid phase at half-filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle $\ensuremath{\theta}\ensuremath{\lesssim}{30}^{\ensuremath{\circ}}$ or $\ensuremath{\theta}\ensuremath{\gtrsim}{30}^{\ensuremath{\circ}}$, respectively. More interesting physics happens at tilt angles $\ensuremath{\theta}\ensuremath{\gtrsim}{58}^{\ensuremath{\circ}}$, where we find that as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.5. Moreover, unlike what is observed at lower tilt angles, we find that at half filling, a stripe supersolid intervenes between the superfluid and stripe solid phase.
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional square optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid (SF) at all tilt angles θ provided that the strength of dipolar interaction is below a critical value . Upon increasing the interaction strength while keeping θ fixed, the SF phase is destabilized in favor of a checkerboard or a stripe solid (SS) depending on the tilt angle. We explore the nature of the phase transition between the two solid phases, identifying a region of metastable emulsion states intervening between the two solid lobes. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the SS is the most robust, making it the best candidate for experimental observation.