Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of inter- and intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.
Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of inter- and intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.
We present the numerical results of the structure and dynamics of the self-bound ground state arising solely because of the presence of beyond-mean-field quantum fluctuation in spin-orbit- (SO-) coupled binary Bose-Einstein condensates in one dimension. We obtain an analytical soliton solution for nonzero SO coupling that matches quite well with the numerical results. Further, we investigate the dynamical stability of these solitons by adopting three protocols, such as (i) adding initial velocity to each component, (ii) quenching the SO- and Rabi-coupling parameters at initial and finite time, and (iii) allowing collision between the two spin components by giving equal and opposite direction velocity to them. For small velocity perturbation, the soliton has the presence of the breathing oscillation, while large velocity perturbations transform the soliton into moving solitons. The maximum breathing frequency exhibits power-law dependence on the Rabi-coupling frequency with an exponent $\ensuremath{\sim}0.16$. The quenching of SO and Rabi couplings results in several interesting dynamical features, such as dynamical phase transition from plane to stripe phase, dynamical flipping of the spin state, and secondary solitonic modes. In the absence of the SO and Rabi couplings, depending upon the velocity of the up- and down-spin components, the collision between them is either elastic or inelastic, which is consistent with the earlier numerical and experimental observations. However, in the presence of coupling parameters, the collision appears to be inelastic and quasielastic in nature.
We study the formation of stable bright solitons in quasi-one-dimensional (quasi-1D) spin-orbit- (SO-) and Rabi-coupled two pseudospinor dipolar Bose-Einstein condensates (BECs) of 164Dy atoms in the presence of repulsive contact interactions. As a result of the combined attraction-repulsion effect of both interactions and the addition of SO and Rabi couplings, two kinds of ground states in the form of self-trapped bright solitons can be formed, a plane-wave soliton (PWS) and a stripe soliton (SS). These quasi-1D solitons cannot exist in a condensate with purely repulsive contact interactions and SO and Rabi couplings (no dipole). Neglecting the repulsive contact interactions, our findings also show the possibility of creating PWSs and SSs. When the strengths of the two interactions are close to each other, the SS develops an oscillatory instability indicating a possibility of a breather solution, eventually leading to its destruction. We also obtain a phase diagram showing regions where the solution is a PWS or SS.
Abstract We investigate the stability and nonlinear dynamics of dark–bright (DB) solitons in a one-dimensional binary Bose–Einstein condensate subjected to synthetic spin–orbit(SO) and Rabi couplings. In the absence of SO coupling, we map the coupled Gross–Pitaevskii equations onto the integrable Manakov model to obtain exact DB soliton solutions, providing a rigorous theoretical benchmark. We demonstrate that finite SO coupling breaks integrability by inducing spin-dependent phase gradients that drive component-wise spatial separation and intrinsic density oscillations. By contrast, coherent Rabi driving enforces phase locking between spin components and supports robust breather-like excitations. Furthermore, we derive analytical continuity relations for mass and spin current densities, mapping the internal spin dynamics onto an internal Josephson-junction framework in which the gauge field acts as a continuous spatial momentum bias. Using imaginary-time propagation together with Bogoliubov–de Gennes analysis, we systematically characterise ground-state phases and excitation spectra for both symmetric and asymmetric interaction regimes in homogeneous and harmonically trapped systems. Real-time simulations further demonstrate that synthetic gauge fields and interaction quenches drive the system far from equilibrium, triggering modulational-instability-induced multi-soliton fragmentation, breathing stripe patterns, and non-equilibrium transport. Our results highlight the interplay of synthetic gauge fields, external confinement, and interaction engineering as powerful tools for controlling the stability and internal dynamics of multicomponent quantum fluids.
We investigate a dilute mixture of bosons and spin-polarized fermions in one dimension. With an attractive Bose-Fermi scattering length the ground state is a self-bound droplet, i.e., a Bose-Fermi bright soliton where the Bose and Fermi clouds are superimposed. We find that the quantum fluctuations stabilize the Bose-Fermi soliton such that the one-dimensional bright soliton exists for any finite attractive Bose-Fermi scattering length. We study density profile and collective excitations of the atomic bright soliton showing that they depend on the bosonic regime involved: mean-field or Tonks-Girardeau.
These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross-Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov-Kolokolov (VK) criterion and are found stable.