Bosonic Systems Research Articles

Bosonic quantum integrable systems and gauge theories

Bosonic quantum integrable systems and gauge theories

Crosstalk-robust quantum control in multimode bosonic systems

Crosstalk-robust quantum control in multimode bosonic systems

SU(N) magnetism with ultracold molecules

Abstract Quantum systems with SU(N) symmetry are paradigmatic settings for quantum many-body physics. They have been studied for the insights they provide into complex materials and their ability to stabilize exotic ground states. Ultracold alkaline-earth atoms were predicted to exhibit SU(N) symmetry for N = 2I +1 = 1, 2, . . . , 10, where I is the nuclear spin. Subsequent experiments have revealed rich many-body physics. However, alkaline-earth atoms realize this symmetry only for fermions with repulsive interactions. In this paper, we predict that ultracold molecules shielded from destructive collisions with static electric fields or microwaves exhibit SU(N) symmetry, which holds because deviations of the s-wave scattering length from the spin-free values are only about 3% for CaF with static-field shielding and are estimated to be even smaller for bialkali molecules. They open the door to N as large as 32 for bosons and 36 for fermions. They offer important features unachievable with atoms, including bosonic systems and attractive interactions.

Floquet Flux Attachment in Cold Atomic Systems.

Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably the fractional quantum Hall effect. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically driven (Floquet) system of either spins or hard-core bosons. We demonstrate that such a system naturally realizes correlated hopping interactions and provides a sharp connection between such interactions and flux attachment. Starting with a simple, nearest-neighbor, free boson model, we find evidence-from both a coupled-wire analysis and large-scale density matrix renormalization group simulations-that Floquet flux attachment stabilizes the bosonic integer quantum Hall state at 1/4 filling (on a square lattice), and the Halperin-221 fractional quantum Hall state at 1/6 filling (on a honeycomb lattice). At 1/2 filling on the square lattice, time-reversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an optical-lattice-based implementation of our model on a square lattice and discuss prospects for adiabatic preparation as well as effects of Floquet heating.

Excitonic Bose Polarons in Electron-Hole Bilayers.

Bose polarons are mobile particles of one kind dressed by excitations of the surrounding degenerate Bose gas of particles of another kind. These many-body objects have been realized in ultracold atomic gases and become a subject of intensive studies. In this work, we show that excitons in electron-hole bilayers offer new opportunities for exploring polarons in strongly interacting, highly tunable bosonic systems. We found that Bose polarons are formed by spatially direct excitons immersed in degenerate Bose gases of spatially indirect excitons (IXs). We detected both attractive and repulsive Bose polarons by measuring photoluminescence excitation spectra. We controlled the density of IX Bose gas by optical excitation and observed an enhancement of the energy splitting between attractive and repulsive Bose polarons with increasing IX density, in agreement with our theoretical calculations.

Infinite cycles of interacting bosons

Abstract In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity
in the thermodynamic quantities
which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

Specialising neural-network quantum states for the Bose Hubbard model

Abstract Projected variational wavefunctions such as the Gutzwiller, many-body correlator and Jastrow ansatzes have provided crucial insight into the nature of superfluid-Mott insulator transition in the Bose Hubbard model (BHM) in two or more spatial dimensions. However, these ansatzes have no obvious tractable and systematic way of being improved. A promising alternative is to use Neural-network quantum states (NQS) based on Restricted Boltzmann Machines (RBMs). With binary visible and hidden units NQS have proven to be a highly effective at describing quantum states of interacting spin- 1 2 lattice systems. The application of NQS to bosonic systems has so far been based on one-hot encoding from machine learning where the multi-valued site occupation is distributed across several binary-valued visible units of an RBM. Compared to spin- 1 2 systems one-hot encoding greatly increases the number of variational parameters whilst also making their physical interpretation opaque. Here we revisit the construction of NQS for bosonic systems by reformulating a one-hot encoded RBM into a correlation operator applied to a reference state, analogous to the structure of the projected variational ansatzes. In this form we then propose a number of specialisations of the RBM motivated by the physics of the BHM and the ability to capture exactly the projected variational ansatzes. We analyse in detail the variational performance of these new RBM variants for a 10 × 10 BHM, using both a standard Bose condensate state and a pre-optimised Jastrow + many-body correlator state as the reference state of the calculation. Several of our new ansatzes give robust results as nearly good as one-hot encoding across the regimes of the BHM, but at a substantially reduced cost. Such specialised NQS are thus primed tackle bosonic lattice problems beyond the accuracy of classic variational wavefunctions.

Geometric quantum complexity of bosonic oscillator systems

According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the original concept of complexity based on the minimal number of gates required to construct the desired operation as a product, this geometrical approach amounts to a more concrete and computable definition, but its evaluation is nontrivial in systems with a high-dimensional Hilbert space. The geometrical formulation can more easily be evaluated by considering the geometry associated with a suitable finite-dimensional group generated by a small number of relevant operators of the system. In this way, the method has been applied in particular to the harmonic oscillator, which is also of interest in the present paper. However, subtle and previously unrecognized issues of group theory can lead to unforeseen complications, motivating a new formulation that remains on the level of the underlying Lie algebras for most of the required steps. Novel insights about complexity can thereby be found in a low-dimensional setting, with the potential of systematic extensions to higher dimensions as well as interactions. Specific examples include the quantum complexity of various target unitary operators associated with a harmonic oscillator, inverted harmonic oscillator, and coupled harmonic oscillators. The generality of this approach is demonstrated by an application to an anharmonic oscillator with a cubic term.

Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion

Abstract Quasicondensation in one dimension is known to occur for equilibrium systems of hard-core bosons (HCBs) at zero temperature. This phenomenon arises due to the off-diagonal long-range order in the ground state, characterized by a power-law decay of the one-particle density matrix $g_1(x,y)\sim |x-y|^{-1/2}$~--~a well-known outcome of Luttinger liquid theory. 
Remarkably, HCBs, when allowed to freely expand from an initial product state (i.e., characterized by initial zero correlation), exhibit quasicondensation and demonstrate the emergence of off-diagonal long-range order during nonequilibrium dynamics. 
This phenomenon has been substantiated by numerical and experimental investigations in the early 2000s.
In this work, we revisit the dynamical quasicondensation of HCBs, providing a fully analytical treatment of the issue. 
In particular, we derive an exact asymptotic formula for the equal-time one-particle density matrix by borrowing ideas from the framework of quantum Generalized Hydrodynamics. 
Our findings elucidate the phenomenology of quasicondensation and of dynamical fermionization occurring at different stages of the time evolution, as well as the crossover between the two. 

Phase Diagrams of a Relativistic Self-Interacting Boson System

Within the Canonical Ensemble, we investigate a system of interacting relativistic bosons at finite temperatures and finite isospin densities in a mean-field approach. The mean field contains both attractive and repulsive terms. Temperature and isospin density dependences of thermodynamic quantities are obtained. It is shown that, in the case of attraction between particles in a bosonic system, a liquid-gas phase transition develops against the background of the Bose–Einstein condensate. The corresponding phase diagrams are given. We explain the reasons for why the presence of a Bose condensate significantly increases the critical temperature of the liquid-gas phase transition compared to that obtained for the same system within the framework of Boltzmann statistics. Our results may have implications for the interpretation of experimental data, in particular, how sensitive the critical point of the mixed phase is to the presence of the Bose–Einstein condensate.

Diffusion coefficients preserving long-time correlations: consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system

Abstract We analytically derive the diffusion coefficients that drive a system of N coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients provided that the physical constraints are fulfilled. We also investigate entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down sudden death of the entanglement, and for initially separable states entanglement generation may occur.

Phases and coherence of strongly interacting finite bosonic systems in shallow optical lattice

We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between short-range contact interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth. For the dipolar interaction, the many-body features become more distinct and true Mott state can appear even in a shallow lattice. Whereas, for incommensurate fraction of particles, incomplete localization happens that exhibits distinct features in the measure of two-body coherence.

Classifications of bosonic supersymmetric third and fifth order systems

This manuscript explores the extensions and classifications of the bosonic supersymmetric systems. For the third order bosonic superfield equations, four types of integrable supersymmetric extensions are identified, including the B-type (trivial) supersymmetric modified Korteweg–de Vries equation, the supersymmetric Sharma–Tasso–Olver equation, and an A-type (non-trivial) supersymmetric potential Korteweg–de Vries equation. In the case of the fifth order bosonic supersymmetric systems, nine kinds of extensions are discovered, with six being B-type and three being A-type. Notably, several equations such as the supersymmetric Sawada–Kotera equation, the supersymmetric Kaup–Kupershmidt equation and the supersymmetric Fordy–Gibbons equation are classified as B-type extensions. Despite this classification, these supersymmetric systems are shown to be connected to linear integrable couplings. The findings have implications for various fields including string theory and dark matter and highlight the importance of understanding bosonic supersymmetric systems. The obtained supersymmetric systems are solved via bosonization method. Applying the bosonization procedure to every one of supersymmetric systems, one can find various dark equation systems. These dark equation systems can be solved by means of the solutions of the classical equations and some graded linear couplings including homogeneous and nonhomogeneous symmetry equations.

Observing the two-dimensional Bose glass in an optical quasicrystal

The presence of disorder substantially influences the behaviour of physical systems. It can give rise to slow or glassy dynamics, or to a complete suppression of transport as in Anderson insulators1, where normally extended wavefunctions such as light fields or electronic Bloch waves become exponentially localized. The combined effect of disorder and interactions is central to the richness of condensed-matter physics2. In bosonic systems, it can also lead to additional quantum states such as the Bose glass3,4—an insulating but compressible state without long-range phase coherence that emerges in disordered bosonic systems and is distinct from the well-known superfluid and Mott insulating ground states of interacting bosons. Here we report the experimental realization of the two-dimensional Bose glass using ultracold atoms in an eight-fold symmetric quasicrystalline optical lattice5. By probing the coherence properties of the system, we observe a Bose-glass-to-superfluid transition and map out the phase diagram in the weakly interacting regime. We furthermore demonstrate that it is not possible to adiabatically traverse the Bose glass on typical experimental timescales by examining the capability to restore coherence and discuss the connection to the expected non-ergodicity of the Bose glass. Our observations are in good agreement with recent quantum Monte Carlo predictions6 and pave the way for experimentally testing the connection between the Bose glass, many-body localization and glassy dynamics more generally7,8.

Thermodynamic properties and performance improvements of fractional Otto heat engine with repulsive bosons

This study presents calculations of a multiparticle system within the framework of fractional quantum mechanics. We specifically explore the energy levels of a bosonic system with repulsive interactions confined in a hard-wall box. The impacts of fractional parameters on the system’s thermodynamic properties are meticulously analyzed. Furthermore, utilizing this model, we construct a quantum Otto cycle and discover that the system exhibits Bose–Fermi duality under varying fractional parameters. Intriguingly, the introduction of fractional parameters enables to optimize the performance of the quantum heat engine, edging it closer to the Carnot efficiency.

Universality of Efimov states in highly mass-imbalanced cold-atom mixtures with van der Waals and dipole interactions

We study three-body systems in a mass-imbalanced, two-component, cold-atom mixture, and we investigate the three-body parameter of their Efimov states for both bosonic and fermionic systems, with a major focus on the Er-Er-Li Efimov states. For a system interacting solely via van der Waals interactions, the van der Waals universality of the three-body parameter is analytically derived using the quantum defect theory. With the addition of a perturbative dipole interaction between the heavy atoms, the three-body parameters of the bosonic and fermionic Efimov states are found to behave differently. When the dipole interaction is as strong as the van der Waals interaction, corresponding to realistic Er-Er-Li Efimov states, we show that the van der Waals universality persists once the effects of the nonperturbative dipole interaction are into the s-wave and p-wave scattering parameters between the heavy atoms. For a dipole interaction much stronger than the van der Waals interaction, we find that the universality of the Efimov states can be alternatively characterized by a quasi-one-dimensional scattering parameter due to a strong anisotropic deformation of the Efimov wave functions. Our work thus clarifies the interplay of isotropic and anisotropic forces in the universality of the Efimov states. Based on the renormalized van der Waals universality, the three-body parameter is estimated for specific isotopes of Er-Li cold-atom mixtures. Published by the American Physical Society 2024

Power-law correlation in the homogeneous disordered state of anisotropically self-propelled systems

Self-propelled particles display unique collective phenomena, due to the intrinsic coupling of density and polarity. For instance, the giant number fluctuation appears in the orientationally ordered state, and the motility-induced phase separation appears in systems with repulsion. Effects of strong noise typically lead to a homogeneous disordered state, in which the coupling of density and polarity can still play a significant role. Here we study universal properties of the homogeneous disordered state in two-dimensional systems with uniaxially anisotropic self-propulsion. Using hydrodynamic arguments, we propose that the density correlation and polarity correlation generically exhibit power-law decay with distinct exponents (−2 and −4, respectively) through the coupling of density and polarity. Simulations of self-propelled lattice gas models indeed show the predicted power-law correlations, regardless of whether the interaction type is repulsion or alignment. Further, by mapping the model to a two-component boson system and employing non-Hermitian perturbation theory, we obtain the analytical expression for the structure factors, the Fourier transform of the correlation functions. This reveals that even the first order of the interaction strength induces the power-law correlations. Published by the American Physical Society 2024

Liquid-Liquid Transition in a Bose Fluid near Collapse.

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this Letter, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum MonteCarlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter η describing its strength. If η exceeds a characteristic value η_{c}, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for η≲η_{c}, finding-in addition to a liquid-vapor transition-a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As η approaches η_{c}, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for η larger than η_{c} our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

Symmetry-resolved entanglement entropy for local and non-local QFTs

In this paper, we investigate symmetry-resolved entanglement entropy (SREE) in free bosonic quantum many-body systems. Utilizing a lattice regularization scheme, we compute symmetry-resolved Rényi entropies for free complex scalar fields and a specific class of non-local field theories, where entanglement entropy (EE) exhibits volume-law scaling. We present effective and approximate eigenvalues for the correlation matrix used in computing SREE and demonstrate their consistency with numerical results. Furthermore, we explore the equipartition of EE, verifying its effective behavior in the massless limit. Finally, we comment on EE in non-local quantum field theories and provide an explicit expression for the symmetry-resolved Rényi entropies.