Optical creation of dark-bright soliton lattices in multicomponent Bose-Einstein condensates

Abstract

We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a $Λ$-coupled three-level system. Numerical simulations reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. On the other hand, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in.

Figures (5)

• Figure 1: $\Lambda$ atom-light coupling scheme. (a) Bare-state basis $\{|1\rangle, |2\rangle, |3\rangle\}$: states $|1\rangle$ and $|2\rangle$ of the ground state multiplet are coupled to an excited state $|3\rangle$ via position-dependent Rabi frequencies $\Omega_1(x)$ and $\Omega_2(x)$, with single-photon detuning $\tilde{\Delta}$ and spontaneous emission rate $\Gamma$. (b) Dark--bright basis $\{|\mathrm{B}(x)\rangle, |\mathrm{D}(x)\rangle, |3\rangle\}$: the bright state $|\mathrm{B}(x)\rangle$ couples to $|3\rangle$ with total Rabi frequency $\Omega(x) = \sqrt{|\Omega_1(x)|^2 + |\Omega_2(x)|^2}$, while the dark state $|\mathrm{D}(x)\rangle$ is decoupled from the light field.
• Figure 2: Stationary state of the system interacting with light fields for $x\in[-\pi/2, \pi/2]$. (a) Lowest-energy dark-state wave function $\varphi_{{\rm D}}$ as the stationary solution of Eq. \ref{['eq:ds-gpe']} with $g=g_{11}$. (b) Solid lines: stationary solution of Eqs. \ref{['eq:full-gpe']} representing the lowest-energy state of the dark-state manifold. The wave function $\varphi_3$ is not shown since the population of this component is less than $10^{-5}$. Dashed lines: corresponding stationary solutions of Eqs. \ref{['eq:free']}.
• Figure 3: Evolution of $\Psi_{1}$ and $\Psi_{2}$ [governed by Eqs. \ref{['eq:free']}] starting from $\varphi_{1}$ and $\varphi_{2}$ --- the stationary state of the system interacting with the light-fields, shown in Fig. \ref{['fig:phi_vs_psi_0.5pi']}(b).
• Figure 4: Stationary state of the system interacting with light-fields for $x\in[-\pi, \pi)$ under periodic boundary conditions, and the BdG analysis for an infinite lattice. (a) Solid lines: stationary solution of Eqs. \ref{['eq:full-gpe']} representing the lowest-energy state of the dark-state manifold. The wave function $\varphi_3$ is not shown since the population of this state is less than $10^{-5}$. Dashed lines: corresponding stationary solutions of Eqs. \ref{['eq:free']}. (b) BdG stability spectrum for the case of an infinite periodic soliton lattice, whose single cell is shown in (a). The purely imaginary eigenvalues span the whole of the imaginary axis, but the view is restricted to the interval $[-1, 1]$.
• Figure 5: Evolution of $\Psi_{1}$ and $\Psi_{2}$, governed by Eqs. \ref{['eq:free']} and assuming all nonlinear couplings to equal to the value of $g_{11}$, starting from $\varphi_{1}$ and $\varphi_{2}$. (a) Calculation for a time interval of $\unit[1]{s}$, periodic boundary conditions. (b) A close-up view of the dynamics around the first instability in (a). (c) Same as (a) for hard-wall boundary conditions.