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Physical Review A

Spatial soliton pairs of the vectorial Thirring model realized in a coherent atomic system via electromagnetically induced transparency

Hui‐jun Li, Kun Zhang

Published Jan 20, 2017• 7 citations
Publisher

Abstract

We propose a scheme to realize a (2+1)-dimensional vectorial Thirring model in a coherent atomic system via electromagnetically induced transparency (EIT). We show that under EIT conditions the probe field envelopes obey coupled nonlinear Schr\"odinger equations, which are reduced to a Thirring model when system parameters are suitably chosen. We present spatial soliton-pair solutions exhibiting many interesting features, including controllability (i.e., the soliton property of one component can be adjusted by the propagation constant of another component in which the soliton remains unchanged), diversity (i.e., many different types of soliton-pair solutions can be found, including bright-bright, dark-bright, dark-dark, darklike-dark, dark-dipole, darklike-multidark, and high-dimensional bright-bright, dark-darklike soliton pairs), and stability. Furthermore, we demonstrate that the stability of soliton pairs in the system can be strengthened by adjusting the propagation constant. Comparing with previous studies, in addition to supporting much more stable (1+1)-dimensional and (2+1)-dimensional spatial soliton-pair solutions, the present scheme needs only a single atomic species and hence is easy to realize experimentally.

DOI
10.1103/physreva.95.013829

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We propose a scheme to realize a (2+1)-dimensional vectorial Thirring model in a coherent atomic system via electromagnetically induced transparency (EIT). We show that under EIT conditions the probe field envelopes obey coupled nonlinear Schr"odinger equations, which are reduced to a Thirring model when system parameters are suitably chosen. We present spatial soliton-pair solutions exhibiting many interesting features, including controllability (i.e., the soliton property of one component can be adjusted by the propagation constant of another component in which the soliton remains unchanged), diversity (i.e., many different types of soliton-pair solutions can be found, including bright-bright, dark-bright, dark-dark, darklike-dark, dark-dipole, darklike-multidark, and high-dimensional bright-bright, dark-darklike soliton pairs), and stability. Furthermore, we demonstrate that the stability of soliton pairs in the system can be strengthened by adjusting the propagation constant. Comparing with previous studies, in addition to supporting much more stable (1+1)-dimensional and (2+1)-dimensional spatial soliton-pair solutions, the present scheme needs only a single atomic species and hence is easy to realize experimentally.
We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having $\mathrm{\ensuremath{\Lambda}}$ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schr\"odinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.
We propose a scheme to exhibit a Stern–Gerlach effect of n-component (n>2) high-dimensional ultraslow optical solitons in a coherent atomic system with (n+1)-pod level configuration via electromagnetically induced transparency (EIT). Based on Maxwell–Bloch equations, we derive coupled (3+1)-dimensional nonlinear Schrödinger equations governing the spatial-temporal evolution of n probe-field envelopes. We show that under EIT conditions significant deflections of the n components of coupled ultraslow optical solitons can be achieved by using a Stern–Gerlach gradient magnetic field. The stability of the ultraslow optical solitons can be realized by an optical lattice potential contributed from a far-detuned laser field.
We propose a scheme to realize an optical Thirring model and create temporal optical Thirring solitons in a tripod-type atomic gas via double electromagnetically induced transparency (EIT). We show that giant enhancement of the cross-phase modulation for the two polarization components of the probe pulse can be obtained under the condition of the double EIT, and hence the optical Thirring model can be realized. We also show that the system supports stable temporal optical Thirring solitons, which have ultralow generation power and ultraslow propagation velocity. In particular, these temporal optical Thirring solitons may experience a significant Stern-Gerlach deflection when a gradient magnetic field is applied to the system. The results reported here are useful not only for extending the research realm of nonlinear magneto-optics but also for the application in precision measurements, such as the detection of microgradient magnetic fields.
We propose a scheme to construct a two-dimensional Aubry-Andr\'e (AA) model and realize two-dimensional AA localization of light waves via electromagnetically induced transparency (EIT). The system we suggest is a cold, resonant atomic gas with an NNN-type level configuration and interacting with probe, control, assisted, and far-detuned laser fields. We show that under EIT conditions the probe-field envelope obeys a modified nonlinear Schr\"odinger equation with a quasiperiodic potential, which becomes a two-dimensional nonlinear AA model when the system parameters are suitably chosen. The quasiperiodic potential is obtained by the cross-phase modulation of the assisted field and the Stark shift of the far-detuned laser field. In addition, the cubic nonlinearity term appearing in the model is contributed by the self-phase modulation of the probe field. We demonstrate that the system can be used to not only realize various two-dimensional AA localizations of light waves, but also to display nonlinearity and dimensionality effects on the AA localizations.
We propose a scheme to generate stable ultraslow three-dimensional spatiotemporal optical solitons, or ultraslow optical bullets, at very low light levels via atomic coherence. The system we consider is an ensemble of resonant, lifetime-broadened NNN-type four-level atoms, working in a regime of electromagnetically induced transparency. Due to the quantum interference effect induced by a control field, the absorption of a probe field is largely suppressed. Moreover, the Kerr nonlinearity is greatly enhanced, and the dispersion property of the probe field is drastically changed. Using a method of multiple scales, we derive two coupled nonlinear envelope equations controlling the evolution of the envelopes of the probe field and an assisted field. We show that under certain conditions the envelope of the probe field satisfies a three-dimensional nonlinear Schr\"odinger equation and the envelope of the assisted field obeys a linear Helmholtz equation. We obtain various optical bullet solutions for the probe-field envelope and demonstrate that such optical bullets have many novel features, including very slow propagating velocity and very low generation power. In addition, they can be actively controlled and manipulated by adjusting system parameters. The stabilization of the optical bullets obtained can be easily realized by the trapping potential contributed by the assisted field, which is also investigated in detail.