Phase diagrams of spin-2 Floquet spinor Bose-Einstein condensates

TL;DR

This work proposes a method to realize spin-2 Floquet spinor Bose-Einstein condensates by Floquet engineering of the quadratic Zeeman energy in the high-frequency limit, which renormalizes all spin-flip interactions via Bessel function factors. The authors derive an effective Hamiltonian $\hat{H}_{\text{eff}}$ that contains Floquet-engineered spin-flip couplings and analyze the ground-state structure within mean-field theory, identifying polar, ferromagnetic, and cyclic states and several Floquet-induced variants (e.g., $\mathbf{P_6}$, $\mathbf{C_1}$, $\mathbf{P_3}$). Phase diagrams in the driving-parameter space reveal that positive $\tilde{c}_2$ yields rich phase behavior with new Floquet polar states and first- or second-order transitions, while negative $\tilde{c}_2$ reduces to the conventional phase structure with feedback from the drive neglected. The results demonstrate that Floquet tuning of spin-dependent interactions can access novel quantum phases and offer experimental pathways to control spin dynamics in spin-2 condensates.

Abstract

We propose the realization of a spin-2 Floquet spinor Bose-Einstein condensate via Floquet engineering of the quadratic Zeeman energy. In the Floquet system, the coupling strengths of all angular-momentum-conserving spin-flip processes are renormalized by driving-parameter-dependent Bessel functions. Such Floquet-engineered interactions significantly enriches possible ground states in homogeneous gases. The resulting phase diagrams, which map the distributions of these possible ground states, are presented in the space of the driving parameters.

Figures (2)

• Figure 1: Phase diagram for a positive $\Tilde{c}_2>0$. (a) Diagram in the parameter space of periodic driving $(q_0,\mathcal{Q}=Q/ (\hbar \omega))$. Vertical dashed lines labeled by b,c,d,e correspond to $\mathcal{Q}=( 0, 0.15, 0.3006,0.45)$ respectively. The energy $E$ (red lines) and derivative of energy $\partial E/\partial q_0$ (green lines) along these labeled lines are demonstrated in (b) ($\mathcal{Q}=0$), (c) ($\mathcal{Q}=0.15$), (d) ($\mathcal{Q}=0.3006$) and (e) ($\mathcal{Q}=0.45$), respectively. The unit of energy is $\left\vert \Tilde{c}_{2}\right\vert$. Other parameters are $\Tilde{c}_{0}=7\left\vert \Tilde{c}_{2}\right\vert$ and $\Tilde{c}_1=0.5\left\vert \Tilde{c}_{2}\right\vert$.
• Figure 2: Phase diagram for the positive $\Tilde{c}_2<0$. (a) Diagram in the parameter space of periodic driving $(q_0,\mathcal{Q}=Q/ (\hbar \omega))$. (b) Evolutions of the energy and the derivative of energy as a function of $q_0$ at $\mathcal{Q}=0.2$. Other parameters are the same as Fig. \ref{['fig1']}.