Quantum Solitons Research Articles

Analogue Hawking radiation and quantum soliton evaporation in a superconducting circuit

Hawking radiation is one of the most intriguing and elusive predictions of quantum field theory in curved spacetime. Previous works simulating Hawking radiation have been mostly based on Unruh’s scenario, where the propagation of quantum field in classical gravitational background is mimicked. Here, guided by the duality between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in sine-Gordon (SG) field theory, we propose the use of a superconducting circuit for investigating analogue Hawking radiation. 1+1 dimensional black holes can be realized as solitons of the SG equation of superconducting phase. It is found despite the absence of field theoretic dynamical modes, the analogue Hawking radiation is emitted in terms of the quantum soliton evaporation as a result of quantum perturbation of the black hole metric. Our theoretical proposal could not only facilitate the observation of relativistic quantum effects in lab, but also contribute to experimentally exploring the quantum mechanics of solitons, especially to the deep relationship between such mechanics and black hole physics.

Manifestly finite derivation of the quantum kink mass

In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar ϕ4 theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Pöschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.

Asynchronous Ballistic Reversible Fluxon Logic

In a previous paper, we described a new abstract circuit model for reversible computation called asynchronous ballistic reversible computing (ABRC), in which localized information-bearing pulses propagate ballistically along signal paths between stateful abstract devices and elastically scatter off those devices serially, while updating the device state in a logically-reversible and deterministic fashion. The ABRC model has been shown to be capable of universal computation. In the research reported here, we begin exploring how the ABRC model might be realized in practice using single flux quantum solitons (fluxons) in superconducting Josephson junction (JJ) circuits. One natural family of realizations could utilize fluxon polarity to represent binary data in individual pulses propagating near-ballistically, along discrete or continuous long Josephson junctions or microstrip passive transmission lines, and utilize the flux charge (-1, 0, +1) of a JJ-containing superconducting loop with Φ 0 <; I c L <; 2Φ 0 to encode a ternary state variable internal to a device. A natural question then arises as to which of the definable abstract ABRC device functionalities using this data representation might be implementable using a JJ circuit that dissipates only a small fraction of the input fluxon energy. We discuss conservation rules and symmetries considered as constraints to be obeyed in these circuits, and begin the process of classifying the possible ABRC devices in this family having up to three bidirectional I/O terminals, and up to three internal states.

Coupling of optical spatial solitons in photorefractive multiple quantum well planar waveguide

A comprehensive theory predicting the existence of both incoherently coupled and coherently coupled grey and dark optical spatial solitons in multiple quantum well planar (MQW) waveguides is presented. In addition, we also show the existence of dark Manakov soliton pair and the bright-dark Manakov soliton pair in such Multiple Quantum well waveguides for the first time. In the case of a coherently coupled soliton pair, the mutual phase difference, the overlap of the optical mode on the waveguide, the external bias field and beam intensity ratio have a profound effect on the FWHM of the soliton pairs. As a general case, a theory for the interesting and hitherto uninvestigated case of coherently coupled multicomponent solitons has been presented and analyzed for the first time. The effect of the mutual phase difference, the overlap of the optical mode on the waveguide(overlap parameter), the external bias field and beam intensity ratio on the FWHM is studied for these coherently coupled multicomponent solitons also. The Manakov soliton solutions are found analytically and they exist in the limit of low total intensity of the beams. We find that the dark-dark and bright-dark Manakov soliton pairs exist in such MQW waveguides whereas bright-bright Manakov soliton pair does not exist. The Manakov solitons’ spatial profile depends upon the overlap parameter, the intensity of the components, and the external electric field.

Rise and Fall of a Bright Soliton in an Optical Lattice.

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to N-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value of the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable nonergodic to nonintegrable ergodic dynamics, through nonintegrable-nonergodic regimes.

A supersymmetric exotic field theory in (1+1) dimensions: one loop soliton quantum mass corrections

We consider one loop quantum corrections to soliton mass for the mathcal{N}=1 supersymmetric extension of the (1+1)-dimensional scalar field theory with the potential U (ϕ) = ϕ2 cos2 (ln ϕ2). First, we compute the one loop quantum soliton mass correction of the bosonic sector. To do that, we regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution, and use the renormalization prescription that the added term vanishes with the corresponding counterterms. As a result we get a finite unambiguous formula for the soliton quantum mass corrections up to one loop order. Afterwards, the computation for the supersymmetric case is extended straightforwardly and we obtain for the one loop quantum correction of the SUSY kink mass the expected value previously derived for the SUSY sine-Gordon and ϕ4 models. However, we also have found that for a particular value of the parameters, contrary to what was expected, the introduction of supersymmetry in this model worsens ultraviolet divergences rather than improving them.

Quantum soliton evaporation

Quantum evaporation may occur in a variety of systems such as superfluids, Bose-Einstein condensates, and gravitational black holes (Hawking radiation). However, to date all predictions are based on semiclassical models, e.g., the Einstein equations and classical space-time metric for a black hole and only the fluctuations are quantized. Here we use a fully quantized dynamical equation, the quantum nonlinear Schr\odinger equation, to study the evolution of quantum solitons. As a result of quantum fluctuations in the center-of-mass position, the expectation value of the quantum soliton width increases and concomitantly evaporates through the emission of frequency-entangled photon pairs. The frequency of this emission decreases as the soliton evaporates due to the soliton spreading. In the final phase, the soliton mean field collapses irreversibly into a state with zero mean amplitude. These results may provide insight to quantum evaporation in other systems where a full quantum description is still to be developed and highlights that even classically stable systems may also be subject to quantum evaporation.

Quantum metrology beyond Heisenberg limit with entangled matter wave solitons.

Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.

Sine-Gordon soliton as a model for Hawking radiation of moving black holes and quantum soliton evaporation

The intriguing connection between black holes’ evaporation and physics of solitons is opening novel roads to finding observable phenomena. It is known from the inverse scattering transform that velocity is a fundamental parameter in solitons theory. Taking this into account, the study of Hawking radiation by a moving soliton gets a growing relevance. However, a theoretical context for the description of this phenomenon is still lacking. Here, we adopt a soliton geometrization technique to study the quantum emission of a moving soliton in a one-dimensional model. Representing a black hole by the one soliton solution of the Sine-Gordon equation, we consider Hawking emission spectra of a quantized massless scalar field on the soliton-induced metric. We study the relation between the soliton velocity and the black hole temperature. Our results address a new scenario in the detection of new physics in the quantum gravity panorama.

Quantum treatment of field propagation in a fiber near the zero dispersion wavelength

In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photon-polariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrödinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrödinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term. Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.

One-dimensional Bose gas dynamics: Breather relaxation

One-dimensional Bose gases are a useful testing-ground for quantum dynamics in many-body theory. They allow experimental tests of many-body theory predictions in an exponentially complex quantum system. Here we calculate the dynamics of a higher-order soliton in the mesoscopic case of $N=10^3-10^4$ particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a $1/N$ expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming BEC experiments.

Statics and dynamics of a self-bound matter-wave quantum ball

We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate with a constant velocity in any direction in free space and its stability under a small perturbation is established numerically and variationally. In frontal head-on and angular collisions at large velocities two quantum balls behave like quantum solitons. Such collision is found to be quasi elastic and the quantum balls emerge after collision without any change of direction of motion and velocity and with practically no deformation in shape. When reflected by a hard impenetrable plane, the quantum ball bounces off like a wave obeying the law of reflection without any change of shape or speed. However, in a collision at small velocities two quantum balls coalesce to form a larger ball which we call a quantum-ball breather. We point out the similarity and difference between the collision of two quantum and classical balls. The present study is based on an analytic variational approximation and a full numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of $^7$Li atoms.

Vortex-bright solitons in a spin-orbit-coupled spin-1 condensate

We study the vortex-bright solitons in a quasi-two-dimensional spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein condensate (BEC) using variational method and numerical solution of a mean-field model. The ground state of these vortex-bright solitons is radially symmetric for weak ferromagnetic and polar interactions. For a sufficiently strong ferromagnetic interaction, we observe the emergence of an asymmetric vortex-bright soliton as the ground state. We also numerically investigate stable moving solitons and binary collision between them. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed model for generating the moving solitons. At low velocities, the head-on collision between two {\em in-phase} solitons results either in collapse or fusion of the soliton pair. On the other hand, in head-on collision, the two {\em out-of-phase} solitons strongly repel each other and trace back their trajectories before the actual collision. At low velocities, in a collision with an impact parameter, the {\em out-of-phase} solitons get deflected from their original trajectory like two rigid classical disks. These {\em out-of-phase solitons} behave like classical disks, and their collision dynamics is governed by classical laws of motion. However, at large velocities two SO-coupled spinor solitons, irrespective of phase difference, can pass through each other in a head-on collision like two quantum solitons.

Controlling of dark or bright soliton type in a cascade-type electromagnetically induced transparency semiconductor quantum well by the coupling longitudinal optical phonons

In the past few years, with developing the technology of electromagnetically induced transparency (EIT) and improving the semiconductor technology, it has become possible to realize the application of optical soliton to communication device. Studies show the reduction of group velocity of the optical soliton in EIT medium under weak driving condition, which possibly realizes the storing of optical pulses in information storage. More importantly, semiconductor quantum wells have the inherent advantages such as large electric dipole moments of the transitions, high nonlinear optical coefficients, small size, easily operating and integrating. So it is considered to be the most potential EIT medium to realize the application of quantum devices. The optical soliton behavior in the semiconductor quantum well is studied, which can provide a certain reference value for the practical application of information transmission and processing together quantum devices. Although there has been a series of researches on both linear and nonlinear optical properties in semiconductor quantum wells structures, few publications report the effects of the cross-coupling longitude-optical phonon (CCLOP) relaxation on its linear and nonlinear optical properties. However, to our knowledge, the electron-longitude-optical phonon scattering rate can be realized experimentally by varying the sub-picosecond range to the order of a picosecond. According to this, we in the paper study the effects of the CCLOP relaxation on its linear and nonlinear optical properties in a cascade-type three-level EIT semiconductor quantum well. According to the current experimental conditions, we first propose a cascade-type three-level EIT semiconductor quantum well model. And in this model we consider the longitudinal optical phonons coupling between the bond state and anti-bond state. Subsequently, by using the multiple-scale method, we analytically study the dynamical properties of solitons in the cascade-type three-level EIT semiconductor quantum well with the CCRLOP. It is shown that when the CCRLOP strength is smaller, there exhibits the dark soliton in the EIT semiconductor quantum well. Only if the strength of the CCRLOP is larger, will in the system there exists bright soliton. That is to say, with increasing the strength of the CCRLOP, the soliton type of the system is converted from dark to bright soliton little by little. So, the temporal soliton type can be effectively controlled by the strength of the CCRLOP. In addition, we also find that the group velocity of the soliton can also be controlled by the strength of CCRLOP and the control light. These results may provide a theoretical basis for manipulating experimentally the dynamics of soliton in semiconductor quantum wells.

Statics and dynamics of a self-bound dipolar matter-wave droplet

We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular collision at large velocities along all directions two droplets behave like quantum solitons. Such a collision is found to be quasi elastic and the droplets emerge undeformed after collision without any change of velocity. However, in a collision at small velocities the axisymmeric dipolar interaction plays a significant role and the collision dynamics is sensitive to the direction of motion. For an encounter along the z direction at small velocities, two droplets, polarized along the z direction, coalesce to form a larger droplet—a droplet molecule. For an encounter along the x direction at small velocities, the same droplets stay apart and never meet each other due to the dipolar repulsion. The present study is based on an analytic variational approximation and a numerical solution of the mean-field Gross–Pitaevskii equation using the parameters of 52Cr atoms.

Quantization of solitons and quantum stability

Nonlinear field theories which are often studied perturbatively can be interpreted also in terms of their soliton solutions. In addition to states related to quantization of free-field modes, a set of various particles will be present. A quantum expansion of the scalar theory is given in terms of a coupling constant. There occur states associated with quantization of the free field modes but also heavy particles. The heavy particles have a new quantum number and will be stable. An interpretation of the stability of the particles as related to a topological property is also described.

Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ϕ(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ϕ 4(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.

Topological protection of multiparticle dissipative transport.

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Generalized guidance equation for peaked quantum solitons and effective gravity

Bouncing oil droplets have been shown to follow de Broglie-Bohm–like trajectories and at the same time they exhibit attractive and repulsive pseudo-gravitation. We propose a model aimed at rendering account of these phenomenological observations. It inspires, in a more speculative approach, a toy model for quantum gravity.