Magnetic-monopole-induced polarons in atomic superlattices

Magnetic monopoles have been realized as emergent quasiparticles in both condensed matter and ultracold atomic platforms, with growing interest in the coupling effects between the monopole and different magnetic quasiparticles. In this work, interaction effects between monopoles and magnons are investigated for an atomic pseudospin chain. We reveal that the monopole can excite a virtual magnon cloud in the paramagnetic chain, thereby giving rise to an unconventional type of polaron, the monopole-cored polaron (MCP). The MCP is composed of the monopole as the impurity core and the virtual magnon excitation as the dressing cloud. The magnon dressing facilitates the Dirac string excitation and impacts the monopole hopping. This induces an antitrapping effect of the MCP, which refers to the fact that the dressing enhances the mobility of the MCP, in contrast to the self-trapping of the common polarons. Moreover, heterogeneous bipolarons are shown to exist under the simultaneous doping of a north and a south monopole. The heterogeneous bipolaron possesses an inner degree of freedom composed of two identical impurities. Our investigation sheds light on the understanding of how the coupling between the impurity core and the dressing cloud can engineer the property of the polaron.

Figure 1

One-to-one correspondence between occupation states (left column) and pseudospin-monopole states (middle column) and between pseudospin-monopole states and magnon-monopole states (right column). The red open circle represents the magnon and the dark and light blue circles represent the south magnetic monopole and north magnetic monopole, respectively.

Figure 2

(a) Magnon density around the SM obtained from the numerical calculation (blue solid lines) and the MCP basis ansatz with a Jordan-Wigner transform (red closed circles) and second-order perturbation treatment (green closed diamonds) for $d=2.5$ in the 11-site pseudospin chain. (b) Binding energy $E_B$ as a function of the monopole (spin)-spin interaction strength $d$. (c) Dispersions of a free SM (black dashed line) and the MCP induced by the SM for $d=1$ (purple solid line), 2 (cyan solid line), and 3 (brown solid line). (d) Hopping amplitude of the MCP $J_{\mathrm{MCP}}$ as a function of $d$.

Figure 3

(a) Four possible hopping channels (CH1–CH4) of the SM: CH1 refers to the tunneling of the SM on the magnon vacuum background, CH2 and CH3 represent the tunneling of the SM with magnon creation and annihilation, and CH4 shows the counterpropagating channel between the SM and the magnon. (b) Contributions of the CH1 (blue solid line), CH2 (purple solid line), CH3 (cyan dashed line), and CH4 (red solid line) to the hopping strength of the MCP.

Figure 4

Temporal evolution of the one-body density of the MCP for linear gradient fields with (a i) $(g_1,g_2)=(J/100,0)$ and (a ii) quadratic gradient fields ($g_1=J/100$ and $g_2=g_1/100$). The red solid lines show $\langle x\rangle$ as a function of time. Above (a i) and (a ii) the superlattice potential under a first-order and a second-order gradient field is shown, respectively. (b) Density spectrum for evolution time $T={10}^6\frac{1}{J}$. In (b i) the standard Bloch oscillation (BO) occurs of MCP with $\omega =2g_1$ under linear gradient fields. (b ii) shows the quadratic BO feature of the MCP, with the center frequency of ${\omega }_0=2g_1+46g_2$ and the internal of peaks ${\delta }_{\omega }\sim 8g_2$ for the pseudospin chain with 11 sites.

Figure 5

(a) Intermediate channels of the second-order coupling for the position exchange of the SMCP and NMCP. (b) Complete SMCP-NMCP interaction potential $V_{\mathrm{int}}\left(r\right)$ for $d=0.2$ (blue) and 0.8 (purple). The spectrum for (c) $d=0.2$ and (e) $d=0.8$ is shown as a function of $k_{\mathrm{c}.\mathrm{m}.}$, and the results based on ${\widehat{H}}_{\text{FH}}$ (solid lines) are compared with those derived for ${\widehat{H}}_{\mathrm{eff}}$ (circles). The inset in (e) shows a close-up of the second bipolaron band. The projection of the bipolaron eigenstates onto the relative coordinate are shown for (d) $d=0.2$ and (f) $d=0.8$, with $k_{\mathrm{c}.\mathrm{m}.}=0$. In (d) the black solid line (red dashed line) refers to the eigenstate with positive (negative) parity of the bipolaron band. In (f) the red dashed line (blue dotted line) shows the eigenstate in the first (second) bipolaron band with negative (positive) parity.

Figure 6

(a) The DSG pseudospin chain with an SM fixed at the first site. (b) Extended pseudospin chain replacing the SM with two auxiliary spins. The auxiliary spins are marked with purple circles.

Figure 7

(a) The DSG pseudospin chain with one SM (NM) fixed at the $i\mathrm{th}$ ($j\mathrm{th}$) site. (b) Two extended subpseudospin chains named chain SN (upper) and chain NS (lower). The auxiliary spins are marked with purple circles.