Quantum Solitons Research Articles

Weakly nonlocal matter-wave droplets and soliton trains engineering in a Bose-Einstein condensate

We propose a comprehensive analysis of the modulational instability (MI) phenomenon in one-dimensional Bose-Einstein condensate (BEC) in the context of mutually symmetric components in the binary mixture. The proposed model considers weak nonlocal cubic mean-field and quadratic beyond mean-field interactions arising from quantum fluctuations. The instability regions are analyzed using linear stability analysis of a continuous wave, considering maximum perturbation wavenumber and growth rate. The regions for quantum droplets (QDs) and solitons are identified by varying the nonlocality parameter. Numerical simulations confirm analytical predictions, revealing that nonlocality influences the formation of various QD profiles and instability time. Furthermore, solitonic patterns exhibit nonlocality-dependent behavior. Our study opens new doors to a better characterization of QDs in binary mixtures in the presence of higher-order beyond mean-field effects.

Perturbative approach to time-dependent quantum solitons

Recently we have introduced a lightweight, perturbative approach to quantum solitons. Thus far, our approach has been largely limited to configurations consisting of a single soliton plus a finite number of mesons, whose classical limit is an isolated stationary or rigidly moving soliton. In this paper, with an eye to soliton collisions and oscillons, we generalize this approach to quantum states whose classical limits are genuinely time-dependent. More precisely, we use a unitary operator, inspired by the coherent state approach to solitons, to factor out the nonperturbative part of the state, which includes the classical motion. The solution for the quantum state and its evolution is then reduced to an entirely perturbative problem.

Hyper-entangling mesoscopic bound states

We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose–Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented. Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.

Equations of Quantum Relativistic Hydrodynamics and Soliton Solutions in Describing Nucleus–Nucleus Collisions

Equations of Quantum Relativistic Hydrodynamics and Soliton Solutions in Describing Nucleus–Nucleus Collisions

Quantum-behaved particle swarm optimization based on solitons

This paper introduces a novel variant of the quantum particle swarm optimization algorithm based on the quantum concept of particle-like solitons as the most common solutions of the quantum nonlinear Schrödinger equation. Soliton adaptation in external potentials is one of their most remarkable features which allows them to be stabilized even without a trapping potential, while the potential must be bounded for quantum particles to be localized. So we consider the motion scenario of the present algorithm based on the corresponding probability density function of quantum solitons. To evaluate the efficiency, we examine the proposed algorithm over a set of known benchmark functions, including a selection of test functions with different modalities and dimensions. Moreover, to achieve a more comprehensive conclusion about the performance, we compare it with the results obtained by particle swarm optimization (PSO), standard quantum-behaved particle swarm optimization QPSO, improved sine cosine Algorithm (ISCA), and JAYA optimization algorithm. The numerical experiments reveal that the proposed algorithm is an effective approach to solving optimization problems that provides promising results in terms of better global search capability, high accuracy, and faster convergence rate.

Variational quantum algorithm for Gaussian discrete solitons and their boson sampling

In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as self-organized quantum processors. We develop a computational approach that uses a neural network as a variational ansatz for quantum solitons in an array of waveguides. By training the resulting phase space quantum machine-slearning model, we find different soliton solutions, varying the number of particles and interaction strength. We consider Gaussian states that enable measuring the degree of entanglement and sampling the probability distribution of many-particle events. We also determine the probability of generating particle pairs and unveil that soliton bound states emit correlated pairs. These results may have a role in boson sampling with nonlinear systems and in quantum processors for entangled nonlinear waves.

Coherent, time-correlated tunneling of density wave electrons

A growing body of evidence reveals that charge density wave (CDW) transport is a high-temperature cooperative quantum phenomenon. According to the time-correlated soliton tunneling (ST) model, quantum solitons, or electron-phonon correlates within the CDW condensate, act much like electrons tunneling through a Coulomb-blockade tunnel junction. Pair creation of charged fluidic soliton droplets is prevented by their electrostatic energy below a Coulomb-blockade threshold electric field. Above threshold, the quantum fluid flows in a periodic fashion, via a hybrid between Zener-like and coherent Josephson-like tunneling. We summarize the time-correlated ST model and compare model simulations with experiment. The ST model shows excellent agreement with coherent voltage oscillations, and with CDW current-voltage characteristics. Finally, we discuss implications for physics and potential applications.

Coherent-solitonic states for Gross–Pitaevskii equation with parabolic potential

It is shown that Gross–Pitaevskii equation with parabolic potential has solutions in form of localized wave packets, which are self-similar and undergo periodic spatial oscillations. The proposed solutions combine some properties of coherent states of quantum optics and solitons of the nonlinear Schrödinger equation, and are expressed in terms of spatially shifted and phase-modulated solutions of nonlinear second order ordinary differential equation.

Semicomputational calculation of Bragg shift in stratified materials.

The fiber Bragg grating (FBG) may be viewed as a one dimensional photonic band-gap crystal by virtue of the periodic spatial perturbation imposed on the fiber core dielectric material. Similar to media supporting Bloch waves, the engraved weak index modulation, presenting a periodic "potential" to an incoming guided mode photon of the fiber, yields useful spectral properties that have been the basis for sensing applications and emerging quantum squeezing and solitons. The response of an FBG sensor to arbitrary external stimuli represents a multiphysics problem without a known analytical solution despite the growing use of FBGs in classical and quantum sensing and metrology. Here, we study this problem by first presenting a solid mechanics model for the thermal and elastic states of a stratified material. The model considers an embedded optical material domain that represents the Bragg grating, here in the form of an FBG. Using the output of this model, we then compute the optical modes and their temperature- and stress-induced behavior. The developed model is applicable to media of arbitrary shape and composition, including soft matter and materials with nonlinear elasticity and geometric nonlinearity. Finally, we employ the computed surface stress and temperature distributions along the grating to analytically calculate the Bragg shift, which is found to be in reasonable agreement with our experimental measurements.

Propagation and energy of bright and dark solitons in magnetized quantum semiconductor plasmas in the presence of Bohm potential effect

A theoretical investigation is presented for the bright and dark solitons in GaAs, GaSb, InP, and GaN quantum magnetized semiconductor plasma systems. The plasma system consists of electrons, holes, and ions, all existed in a quantizing magnetic field. The Zakharov–Kuznetsov (ZK) equation is derived by using the reductive perturbation method. The bright and the dark soliton solutions are derived for the ZK equation. The electric field and the soliton energy were also derived. The present results are considered to be beneficial in understanding the waves propagating in quantum semiconductor plasmas on an ultrafast time scale in semiconductors nanostructures that are applicable for quantum computing.

Quantum fluidic charge density wave transport

We discuss charge density wave transport as the periodic flow of a quantum fluid of electron–phonon correlates, viewed as quantum solitons, within the condensate. Pair creation of charged soliton droplets is prevented by their electrostatic energy below a Coulomb-blockade threshold electric field. Above threshold, the quantum fluid flows in drip-like fashion as microscopic entities tunnel coherently from one charging energy macrostate to the next. We summarize the time-correlated soliton tunneling model and compare simulations of coherent oscillations, narrow band noise, and current–voltage characteristics with experiment. We also explore the possibility of collective quantum behavior at room temperature in some materials. Finally, we discuss potential applications in quantum information processing.

Ion-acoustic solitons in negative ion plasma with relativistic degenerate electrons and positrons

In this paper, the oblique propagation of the ion-acoustic quantum soliton in polarized quantum plasma including relativistic degenerate electrons and positrons is studied. By using the reductive perturbation method, we derived the ZK equation for this model. This equation shows that in presence of the negative ion there are two slow and fast ion-acoustic modes. Our numerical results indicate that there are only compressive and refractive solitons for fast and slow modes, respectively. The effect of the negative ion parameters on the amplitude and width of the ion-acoustic quantum soliton are studied, as well.

Droplet under confinement: Competition and coexistence with a soliton bound state

We study the stability of quantum droplet and its associated phase transitions in ultracold Bose-Bose mixtures uniformly confined in quasi-two-dimension. We show that the confinement-induced boundary effect can be significant when increasing the atom number or reducing the confinement length, which destabilizes the quantum droplet towards the formation of a soliton bound state. In particular, as increasing the atom number we find the reentrance of soliton ground state, while the droplet is stabilized only within a finite number window that sensitively depends on the confinement length. Near the droplet-soliton transitions, they can coexist with each other as two local minima in the energy landscape. Take the two-species $^{39}$K bosons for instance, we have mapped out the phase diagram for droplet-soliton transition and coexistence in terms of atom number and confinement length. The revealed intriguing competition between quantum droplet and soliton under confinement can be readily probed in current cold atoms experiments.

On Bound States in Quantum Field Theory

In this paper, a new method to describe the energy spectrums of bound states in Quantum Field Theory is presented. We point out that the fundamental field and its dual soliton combine together to form bound states and the soliton corresponds to the ghost particle in our regularization scheme which takes advantage of dimensional regularization and Pauli-Villars regularization. Based on this point of view, we discuss the bound states of massive Thirring model, the positronium (e+e−) in QED and the vector meson in QCD. We also give a new way to obtain the mass of soliton (quantum soliton) from the stationary condition (gap equation). Our results agree with experimental data to high precision. We argue that the hypothetic X17 particle in decay of 8Be and 4He is a soliton. For vector meson, we find the squared masses of ρ resonances are \(m^{2}(n)\sim (an^{1/3}-b)^{2}\) (n ∈ N) which coincide well with experiments.

Exactly Solvable System of One-Dimensional Trapped Bosons with Short- and Long-Range Interactions.

We introduce a model of trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. We find the exact ground-state energy and many-body wave function. The density profile and the pair-correlation function are sampled using MonteCarlo method and show a rich variety of regimes with crossovers between them. Strong attraction leads to a trapped McGuire quantum soliton. Weak repulsion results in an incompressible Laughlin-like fluid with flat density, well reproduced by a Gross-Pitaevskii equation with long-range interactions. Stronger repulsion induces Friedel oscillations and the eventual formation of a Wigner crystal.

Quantum soliton scattering manifolds

We consider the quantum multisoliton scattering problem. For BPS theories one truncates the full field theory to the moduli space, a finite dimensional manifold of energy minimising field configurations, and studies the quantum mechanical problem on this. Non-BPS theories — the generic case — have no such obvious truncation. We define a quantum soliton scattering manifold as a configuration space which satisfies asymptotic completeness and respects the underlying classical dynamics of slow moving solitons. Having done this, we present a new method to construct such manifolds. In the BPS case the dimension of the n-soliton moduli space ℳn is n multiplied by the dimension of ℳ1. We show that this scaling is not necessarily valid for scattering manifolds in non-BPS theories, and argue that it is false for the Skyrme and baby-Skyrme models. In these models, we show that a relative phase difference can generate a relative size difference during a soliton collision. Asymptotically, these are zero and non-zero modes respectively and this new mechanism softens the dichotomy between such modes. Using this discovery, we then show that all previous truncations of the 2-Skyrmion configuration space are unsuitable for the quantum scattering problem as they have the wrong dimension. This gives credence to recent numerical work which suggests that the low-energy configuration space is 14- dimensional (rather than 12-dimensional, as previously thought). We suggest some ways to construct a suitable manifold for the 2-Skyrmion problem, and discuss applications of our new definition and construction for general soliton theories.

Engineering a Kerr-Based Deterministic Cubic Phase Gate via Gaussian Operations

We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show how our scheme can be adapted to deterministically generate a nonclassical approximate cubic phase state with high fidelity using a ratio of native nonlinearity to linear loss of only 10^{-4}, indicating that our approach may be experimentally viable in the near term even on all-optical platforms, e.g., using quantum solitons in pulsed nonlinear nanophotonics.

Well-defined quantum soliton masses without supersymmetry

22 years ago, Rebhan and van Nieuwenhuizen showed that loop corrections to the mass of a quantum soliton depend on a choice of matching condition for the regulators of the vacuum and one-soliton sector Hamiltonians. In supersymmetric theories, regulators which preserve supersymmetry yield the correct quantum corrections, as these are dictated by supersymmetry. However, in a general theory it is not known which matching condition yields the correct mass. We use the leading term in the operator that creates the soliton to construct the regulated one-soliton sector Hamiltonian from that of the vacuum sector, providing the correct matching condition. As an application, we derive a simple formula for the one-loop mass of a kink in a large class of 1+1 dimensional scalar field theories and also, at one loop, we diagonalize the Hamiltonian which describes the kink excitations.

A note on one-loop soliton quantum mass corrections

We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1 + 1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution and use the renormalization prescription that such added term vanishes with adequate counterterms. As a result, we get a finite unambiguous formula for the soliton quantum mass corrections up to one-loop order, which turns to be independent of the chosen regularization scheme.

Квантовые флуктуации в лазерном солитоне

In the framework of consistent quantum electrodynamics, derived is the Heisenberg-Langevin equation for spatial laser soliton. Discussed are in detail the canonical variables for the generation field and for a material two-level medium consisting of a medium that forms laser generation and saturated absorption medium. It is assumed that laser generation evolves in time much slower than the atomic medium. This makes it possible to apply adiabatic approximation and construct a closed equation for the amplitude of the laser field. When deriving the equation special attention is paid to the definition of Langevin sources that play a decisive role in the formation of quantum statistical features of solitons. In order to provide a procedure of observation of soliton quantum squeezing, synchronization of laser generation by an external weak electromagnetic beam is introduced.