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arXiv:2505.09553 · Physical Review A

Phase domain walls in coherently driven Bose-Einstein condensates

Sergei S. Gavrilov

Published Feb 13, 2026• 0 citations
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Abstract

We consider coherent states of weakly interacting bosons under the conditions of external resonant excitation, with a focus on a two-dimensional polariton fluid driven by a plane electromagnetic wave near the ground state. The coherent driving breaks the U(1) symmetry explicitly, which prevents the occurrence of quantum vortices in a uniform scalar condensate. Surprisingly, a spinor (two-component) system of the same kind admits topological excitations, such as domain walls of relative phase or confined half-vortex molecules, typical of a freely evolving spinor Bose system. Opposite-phase domains arise from the spontaneous breakdown of the spin symmetry $(\mathbb{Z}_2)$. Domain walls form with time even when the initial state of the system is uniform or completely disordered; they fall into different topological types distinguished by the total phase variation in the transverse direction. One type of domain walls is similar to ``magnetic'' solitons in Bose-Einstein condensates and exhibits nonzero spin polarization whose sign depends on the direction of motion. Domain walls of the second type, by contrast, behave like monopoles with broken spatiotemporal symmetry and tend to move in certain preferred directions. The interaction of vortices and domain walls results in a long-range ordering of the system.

DOI
10.1103/tqbc-32nf

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We consider coherent states of weakly interacting bosons under the conditions of external resonant excitation, with a focus on a two-dimensional polariton fluid driven by a plane electromagnetic wave near the ground state. The coherent driving breaks the U(1) symmetry explicitly, which prevents the occurrence of quantum vortices in a uniform scalar condensate. Surprisingly, a spinor (two-component) system of the same kind admits topological excitations, such as domain walls of relative phase or confined half-vortex molecules, typical of a freely evolving spinor Bose system. Opposite-phase domains arise from the spontaneous breakdown of the spin symmetry (Z2)(\mathbb{Z}_2)(Z2​). Domain walls form with time even when the initial state of the system is uniform or completely disordered; they fall into different topological types distinguished by the total phase variation in the transverse direction. One type of domain walls is similar to ``magnetic'' solitons in Bose-Einstein condensates and exhibits nonzero spin polarization whose sign depends on the direction of motion. Domain walls of the second type, by contrast, behave like monopoles with broken spatiotemporal symmetry and tend to move in certain preferred directions. The interaction of vortices and domain walls results in a long-range ordering of the system.
Spinorial or multi-component Bose-Einstein condensates may sustain fractional quanta of circulation, vorticant topological excitations with half integer windings of phase and polarization. Matter-light quantum fluids, such as microcavity polaritons, represent a unique test bed for realising strongly interacting and out-of-equilibrium condensates. The direct access to the phase of their wavefunction enables us to pursue the quest of whether half vortices ---rather than full integer vortices--- are the fundamental topological excitations of a spinor polariton fluid. Here, we are able to directly generate by resonant pulsed excitations, a polariton fluid carrying either the half or full vortex states as initial condition, and to follow their coherent evolution using ultrafast holography. Surprisingly we observe a rich phenomenology that shows a stable evolution of a phase singularity in a single component as well as in the full vortex state, spiraling, splitting and branching of the initial cores under different regimes and the proliferation of many vortex anti-vortex pairs in self generated circular ripples. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the phase singularities dynamics
We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate (BEC) from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature (London) 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.
We report the observation of spin domain walls bounded by half-quantum vortices (HQVs) in a spin-1 Bose-Einstein condensate with antiferromagnetic interactions. A spinor condensate is initially prepared in the easy-plane polar phase, and then, suddenly quenched into the easy-axis polar phase. Domain walls are created via the spontaneous Z_{2} symmetry breaking in the phase transition and the walls dynamically split into composite defects due to snake instability. The end points of the defects are identified as HQVs for the polar order parameter and the mass supercurrent in their proximity is demonstrated using Bragg scattering. In a strong quench regime, we observe that singly charged quantum vortices are formed with the relaxation of free wall-vortex composite defects. Our results demonstrate a nucleation mechanism for composite defects via phase transition dynamics.
A new mechanism of parity breakdown in a spinor Bose gas is predicted; it causes a single-mode state of polaritons to be spontaneously divided into different polarization domains which annihilate each other at the interface areas. In a polariton wire, such interface is a dark soliton that can run in space without dissipation. In a planar cavity, quantized vortices arise in which phase difference of orthogonally polarized components makes one complete turn around the core. Coupled vortex-antivortex pairs and straight filaments can form in analogy to Bose-Einstein condensates and superconductors. However, the rotational symmetry is broken even for individual vortices, which makes them interact on a large scale and form internally ordered structures. These states come into being under resonant excitation if the spin coupling rate significantly exceeds the decay rate.
We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a Z2{\mathbb{Z}}_{2}Z2​ symmetry-breaking phase transition in a shaken optical lattice. We derive a generic model to describe the dispersion and to compute the wave functions and energies of the domain walls. We find two distinct regimes which demand different physical pictures. In the weak-coupling regime, where interactions are weak compared to the kinetic-energy barrier, ``density-wave domain walls'' form that support an extended density wave and a series of phase steps. These features can be understood as the quantum interference between domains with distinct momenta. In the strong-coupling regime where interaction dominates, the system forms ``phase domain walls'' which have the minimum width allowed by the uncertainty principle and suppressed density modulation. Analytic results for the domain-wall wave functions are obtained in the two regimes. The energy of domain walls behaves similarly to that of topological defects in paradigmatic field theories.
We discuss some recent advances in the spin dynamics in photonic systems and polariton superfluids. In particular, we describe how the spin degree of freedom affects the collective behaviour of the half-soliton gas. First, we demonstrate that the anisotropy in the intra- and interspin interaction leads to the formation of a one-dimensional ordered phase: the topologicalWigner crystal. Second, we show that half-solitons behave as magnetic monopoles in effective magnetic fields. We study the transport properties and demonstrate a deviation from the usual Ohm's law for moderate values of the magnetic field. Introduction Photonic systems offer great opportunities for the study of quantum fluids, due to the possibility of creation of macroscopically occupied states with well-controlled properties by coherent excitation with lasers, and the full access to the wavefunction of the quantum fluid by well-established optical methods [1]. The main distinctive feature of quantum fluids as compared with classical ones are the topological defects, which, once created, cannot be removed by a continuous transformation. The most well-known example of such defect is a quantum vortex, which can appear in two-dimensional (2D) and three-dimensional (3D) systems. Its analog in one-dimensional (1D) Bose-Einstein condensates (BECs) is a soliton [2]. In fact, solitons are ubiquitous in systems described by the self-defocussing nonlinear Schrödinger equations. Specifically, for Bose gases, they are associated with the excitations of type II of the Lieb and Liniger theory. Spinor BECs (particularly with two pseudospin projections) offer a plethora of nonlinear spin effects, including half-integer topological defects possible in BECs with spin-anisotropic interactions [3]. Recent experimental work reports on the emergent monopole behaviour of half-solitons in the presence of an effective magnetic field [4]. In this chapter, we highlight some theoretical advances concerning not only the dynamics but also the many-body aspects of the physics of half-solitons. A Topological Wigner Crystal It is commonly accepted that the Wigner crystal is one of the most simple yet dramatic many-body effects. In the seminal work published in 1931 [5], Wigner showed that as a result of the competition between the long-ranged potential and kinetic energies, electrons spontaneously form a self-organized crystal at low densities, in a state that strongly differs from the Fermi gas. Experimental observations of this effect have been reported in carbon nanotubes [6].