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arXiv:2312.12695 · Physical Review A

Excitations and phase ordering of the spin-stripe phase of a binary dipolar condensate

Au-Chen Lee, D. Baillie, P. B. Blakie

Published Feb 20, 2024• 5 citations
arXivHTMLPDF

Abstract

We consider the ground states, excitations, and dynamics of a quasi-two-dimensional binary dipolar Bose-Einstein condensate. Our focus is on the transition to a spin-stripe ground state in which the translational invariance is spontaneously broken by a striped immiscible pattern of the alternating components. We develop a ground-state phase diagram showing the parameter regime where the spin-stripe state occurs. Using Bogoliubov theory, we calculate the excitation spectrum and structure factors. We identify a balanced regime where the system has a ${\mathbb{Z}}_{2}$ symmetry, and in the spin-stripe state this yields a nonsymmorphic symmetry. We consider the evolution of the system following a quench from the uniform to spin-stripe state, revealing ordering dynamics involving defects of the stripe order. Using an order parameter to characterize the orientational order of the stripes, we show that the phase ordering exhibits dynamic scaling.

DOI
10.1103/physreva.109.023323

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We consider the ground states, excitations, and dynamics of a quasi-two-dimensional binary dipolar Bose-Einstein condensate. Our focus is on the transition to a spin-stripe ground state in which the translational invariance is spontaneously broken by a striped immiscible pattern of the alternating components. We develop a ground-state phase diagram showing the parameter regime where the spin-stripe state occurs. Using Bogoliubov theory, we calculate the excitation spectrum and structure factors. We identify a balanced regime where the system has a Z2{\mathbb{Z}}_{2}Z2​ symmetry, and in the spin-stripe state this yields a nonsymmorphic symmetry. We consider the evolution of the system following a quench from the uniform to spin-stripe state, revealing ordering dynamics involving defects of the stripe order. Using an order parameter to characterize the orientational order of the stripes, we show that the phase ordering exhibits dynamic scaling.
This work concerns a theoretical study of a two-component ultra-cold bosonic gas of polarised magnetic dipolar atoms. The atoms interact by short-ranged contact interactions and long-ranged dipole-dipole interactions. The two components can correspond to two different spin-states of a single atomic species or two different atomic species, as realised in recent experiments. Here, we develop a general theory for the ground states and excitations of a two-component dipolar Bose-Einstein condensate. The ground states are described by dipolar Gross-Pitaevskii equations and Bogoliubov-de Gennes equations describe the excitations. We apply these theories to systems in 3D harmonic traps and a uniform planar potential. Specialised numerical methods are developed to provide accurate solutions of these equations, and to deal with the singular dipole-dipole interaction kernel. These methods involve spectral representations based on plane waves and Bessel functions. We also discuss the methods we used for obtaining ground state solutions of the nonlinear Gross-Pitaevskii energy functional. Dipole-dipole interactions can favour spatial structure, as demonstrated in the recent observation of supersolid states of matter in a single-component dipolar gas. In the two-component system these interactions can also favour a ground state with a periodic order in the pseudo-spin density. A two-component system can be either miscible (components overlap) or immiscible (components are separated). Our focus here is in the spin-stripe state, which occurs in a flattened trap geometry and involves an immiscible stripe pattern along one of the weakly trapped or untrapped directions. We examine the dynamical stability conditions of the uniform miscible state in planar confinement, and produce an associated stability phase diagram. We identify the various instabilities and analytical criteria for estimating these. We focus on the occurrence of, and conditions that favour, density-roton or spin-roton excitations, anticipating that the softening of these excitations will lead to structured ground states. To characterize these excitations we introduce density and spin dynamical structure factors, which can be measured in experiments using Bragg spectroscopy. Building on the stability phase diagram we compute ground states where the immiscible state is unstable to spin-rotons, finding triangular and stripe immiscible states with a length scale set by the confinement and interactions. We find that the transition to the stripe state is continuous and coincides with the spin-roton softening in the uniform miscible state. We study the excitations of the spin stripe state which exhibits three gapless excitation branches arising from the spontaneous broken symmetries. We identify a balanced parameter regime, where the excitations exhibit a nonsymmorphic symmetry (a symmetry is nonsymmorphic when it is a combination of point-group operations with nonprimitive lattice translations, i.e. not an integer multiple of lattice constants), which is revealed in the density and spin dynamical structure factors. We also consider the dynamics of the system following a quench from the uniform to immiscible stripe states. In the early time dynamics, a spin-stripe state is formed in a such way that the stripe order only extends over small domains. In subsequent dynamics, these domain sizes grow as the system phase-orders towards its equilibrium state. We identify the relevant topological defects such as disclinations, dislocations and grain boundaries. Using ensembles of large scale simulations we show that dynamical scaling holds for the growth of order.
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Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with an equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of 23Na^{23}\mathrm{Na}23Na could be a candidate for observing the stripe condensate with high contrast fringes.
In the last decade, considerable advances have been made in the investigation of dipolar quantum gases. Previous theoretical investigations of a rotating binary dipolar Bose-Einstein condensate, where only one component possesses dipole moment, were mainly focused on two special orientations of the dipoles: perpendicular or parallel to the plane of motion. Here we study the ground-state and rotational properties of such a system for an arbitrary orientation of the dipoles. We demonstrate the ground-state vortex structures depend strongly on the relative strength between dipolar and contact interactions and the rotation frequency, as well as on the orientation of the dipoles. In the absence of rotation, the tunable dipolar interaction can be used to induce the squeezing or expansion of the cloud, and to derive the phase transition between phase coexistence and separation. Under finite rotation, the system is found to exhibit exotic ground-state vortex configurations, such as kernel-shell, vortex necklace, and compensating stripe vortex structures. We also check the validity of the Feynman relation, and find no significant deviations from it. The obtained results open up alternate ways for the quantum control of dipolar quantum gases.