Creation and Manipulation of Stable Dark Solitons and Vortices in Microcavity Polariton Condensates

Solitons and vortices obtain widespread attention in different physical systems as they offer potential use in information storage, processing, and communication. In exciton-polariton condensates in semiconductor microcavities, solitons and vortices can be created optically. However, dark solitons are unstable and vortices cannot be spatially controlled. In the present work we demonstrate the existence of stable dark solitons and vortices under nonresonant incoherent excitation of a polariton condensate with a simple spatially periodic pump. In one dimension, we show that an additional coherent light pulse can be used to create or destroy a dark soliton in a controlled manner. In two dimensions we demonstrate that a coherent light beam can be used to move a vortex to a specific position on the lattice or be set into motion by simply switching the periodic pump structure from two-dimensional (lattice) to one-dimensional (stripes). Our theoretical results open up exciting possibilities for optical on-demand generation and control of dark solitons and vortices in polariton condensates.

Figure 1

(a) Sketch of a semiconductor microcavity. Two coherent homogenous optical beams create a periodic reservoir. The two panels on the right illustrate the periodic pump profiles in one and two dimensions. The 2D periodic structure is generated by four coherent homogeneous beams. (b) Density distribution of steady state periodic solutions created by periodic pumps in one dimension. Solid lines represent stable solutions, while the dashed line represents unstable solutions. The insets show the solutions at $P=5$ and $P=30$, respectively. Time evolution of (c) the density and (d) the phase of a stable dark soliton in one dimension at $P=30$.

Figure 2

Density of dark solitons for different system parameters. (a) Dependence of the number of dark solitons per number of pump valleys $R$ on the effective polariton mass (scaled with the factor $a$) at $P=30$ for ${\gamma }_c=0.08$, ${\gamma }_c=0.1$, and ${\gamma }_c=0.125{\mathrm{ps}}^{-1}$. (b) Dependence of $R$ on the pump intensity with $a=1$ and ${\gamma }_c=0.1{\mathrm{ps}}^{-1}$. Profiles of dark solitons with (c) ${\gamma }_c=0.1{\mathrm{ps}}^{-1}$, $a=0.5$, and $P=30$, and with (d) ${\gamma }_c=0.1{\mathrm{ps}}^{-1}$, $a=1$, and $P=30$.

Figure 3

Controlled excitation and switching dynamics of dark solitons. (a) Time evolution of the condensate density under homogeneous ($t<1000\mathrm{ps}$) and periodic ($t\ge 1000\mathrm{ps}$) excitation at $P=30$. (b)–(e) Normalized spatial intensity profiles of coherent pulse used for creation and annihilation of dark solitons launched at different times and spatial positions (b) $x=0$, (c) $x=8$, (d) $x=2$, and (e) $x=-16\mu \mathrm{m}$.

Figure 4

Controlling vortices with coherent pulses. Profiles of (a) density and (b) phase of condensate under 2D periodic pump excitation at $P=8$ showing vortices (phase defects) forming from the initial noise. (c) Density profile of condensate at $P=20$. (d) Dependence of number of vortices on pump intensity. (e)–(h) Manipulation of a vortex by a sequence of four coherent pulses at $P=10$. Snapshots of the density profiles are shown at (e) $t=400$, (f) $t=800$, (g) $t=1200$, and (h) $t=1400\mathrm{ps}$. A full movie is included in the Supplemental Material [50]. Arrows indicate the target cell for vortex motion due to application of a coherent pulse.

Figure 5

Controlling vortices through nonresonant excitation. Shown is the manipulation of vortices by switching the excitation from a two-dimensional lattice (with two vortices) in (a) to a stripelike excitation in (b), setting the vortices into motion, back to a two-dimensional lattice confining the vortices in a different place in (c). The panels show snapshots of the condensate density in time for $P=22$ at (a) $t=400$, (b) $t=800$, and (c) $t=1200\mathrm{ps}$. A corresponding movie is included in the Supplemental Material [50].