Hybrid Matter-Wave–Microwave Solitons Produced by the Local-Field Effect

It was recently found that the electric local-field effect (LFE) can lead to a strong coupling of atomic Bose-Einstein condensates (BECs) to off-resonant optical fields. We demonstrate that the magnetic LFE gives rise to a previously unexplored mechanism for coupling a (pseudo-) spinor BEC or fermion gas to microwaves (MWs). We present a theory for the magnetic LFE and find that it gives rise to a short-range attractive interaction between two components of the (pseudo) spinor, and a long-range interaction between them. The latter interaction, resulting from deformation of the magnetic field, is locally repulsive but globally attractive, in sharp contrast with its counterpart for the optical LFE, produced by phase modulation of the electric field. Our analytical results, confirmed by the numerical computations, show that the long-range interaction gives rise to modulational instability of the spatially uniform state, and it creates stable ground states in the form of hybrid matter-wave–microwave solitons (which seem like one-dimensional magnetic monopoles), with a size much smaller than the MW wavelength, even in the presence of arbitrarily strong contact intercomponent repulsion. The setting is somewhat similar to exciton-polaritonic condensates in semiconductor microcavities. The release of matter waves from the soliton may be used for the realization of an atom laser. The analysis also applies to molecular BECs with rotational states coupled by the electric MW field.

Figure 1

(a) The GS wave function, $\phi (x)$, along with its Fourier transform, $\varphi (k_x)$, and magnetic field, $\mathcal{H}(x)$, for $\beta =0$, with $\tilde{\mu }=4.26$. (b) Comparison of the GS, as predicted by the TFA [Eqs. (8), (9), and (10)] (the dashed curves) and found numerically (the solid lines) for $\beta =-5$ with $\mu =0.079$. In both plots, $\eta =0$, $H_0=0$, and $\gamma ={10}^{-3}$.

Figure 2

Numerically found profiles of the GS wave functions and magnetic field in the system with $\eta =1$, $\beta =0$, and $\gamma ={10}^{-3}$, for ${\mathcal{H}}_0=0.5$ (a), 1.5 (b), 6.0 (c). The respective chemical potentials are $\mu =-1.12$ (a), $-1.80$ (b), $-6.079$ (c). For the strongly asymmetric soliton in (a), the analytical approximation predicts the amplitude ratio of the two components 0.250, while its numerically found counterpart is 0.235.

Figure 3

The relative share of the total norm of each component in the system with $\gamma ={10}^{-3}$, $\beta =0$, $\eta =1$ vs the background magnetic field, ${\mathcal{H}}_0$. The inset shows the dependence for $N_{\downarrow }$ at small values of ${\mathcal{H}}_0$ (the stars) vis-à-vis the analytical prediction.