Ulf Leonhardt
A new type of soliton with controllable speed is constructed generalizing the theory of slow-light propagation to an integrable regime of nonlinear dynamics. The scheme would allow the quantum-information transfer between optical solitons and atomic media.
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We investigate propagation of slow-light solitons in atomic media described by the nonlinear $Λ$-model. Under a physical assumption, appropriate to the slow light propagation, we reduce the $Λ$-scheme to a simplified nonlinear model, which is also relevant to 2D dilatonic gravity. Exact solutions describing various regimes of stopping slow-light solitons can then be readily derived.
We have applied the transformation of the slow light equations to Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the presence of relaxation and found that the spontaneous emission from the upper atomic level is strongly suppressed. Our solution proves that the spatial shape of the soliton is well preserved even if the relaxation time is much shorter than the soliton time length. This fact is of great importance for applications of the slow-light soliton concept in optical in…
In the framework of the nonlinear $Λ$-model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the $Λ$-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the $Λ$-type media. We provide an exact analytic description of decelerating, stopping and re-accelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field …
In the framework of the nonlinear $Λ$-model we investigate propagation of a slow-light soliton in atomic vapors and Bose-Einstein condensates. The velocity of the slow-light soliton is controlled by a time-dependent background field created by a controlling laser. For a fairly arbitrary time dependence of the field we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the loc…
We investigate the quantum squeezing of slow-light solitons generated in a $Λ$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.
We investigate propagation of a slow-light soliton in atomic vapors and Bose-Einstein condensates described by the nonlinear Lambda-model. We show that the group velocity of the soliton monotonically decreases with the intensity of the controlling laser field, which decays exponentially after the laser is switched off. The shock wave of the vanishing controlling field overtakes the slow soliton and stops it, while the optical information is recorded in the medium in the form of spatially localized polarization. We find an explicit exact solution describing the whole process within the slowly v…
We show that a weak probe light beam can form spatial solitons in an electro-magnetically induced transparency (EIT) medium composed of four-level atoms and a coupling light field. We find that the coupling light beam can induce a highly controllable nonlinear waveguide and exert very strong effects on the dynamical behavior of the solitons. Hence, in the EIT medium, it is not only possible to produce spatial solitons at very low light intensities but also simultaneously control these solitons by using the coupling-light-induced nonlinear waveguide.
It is shown that bipartition of optical solitons can be used to generate entangled light beams. The achievable amount of entanglement can be substantially larger for N-bound solitons N=2,3 than for the fundamental soliton (N=1). An analysis of the mode structure of the entangled beams shows that just N modes are essentially entangled. In particular, partitioning of the fundamental soliton effectively produces 2-mode squeezed light.
We consider the quantum effect of slow light dark soliton (SLDS) in a cold atomic gas with defocuing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations, and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are bi-orthogonal and constitute a com…
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton "gas" that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenome…
We propose a method to control the optical transparency of a Bose-Einstein condensate with working energy levels of the Lambda-type. The reported effects are essentially nonlinear and are considered in the framework of an exactly solvable model describing the interaction of light with a Lambda-type medium. We show how the complicated nonlinear interplay between fast and slow solitons in the $Λ$-type medium points to a possibility to create optical gates as well as to a possibility to store optical information.
In this Letter we discuss the possibility of producing Bragg solitons in an electromagnetically induced transparency medium. We show that this coherent medium can be engineered to be a Bragg grating with a large Kerr nonlinearity through proper arrangements of light fields. Unlike in previous studies, the parameters of the medium can be easily controlled through adjusting the intensities and detunings of lasers. Thus this scheme may provide an opportunity to study the dynamics of Bragg solitons. And doing experiments with low power lights is possible.
We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables entanglement between the certain pair of waveguides. This entanglement generation process occurs even with a very large number of photons in the laser field used, so it does not require a special material with an extremely high nonlinearity coefficient. Also absorption in the waveguide media does not influence it too much.
It is shown that slow Bragg soliton solutions are possible in nonlinear complex parity-time (PT) symmetric periodic structures. Analysis indicates that the PT-symmetric component of the periodic optical refractive index can modify the grating band structure and hence the effective coupling between the forward and backward waves. Starting from a classical modified massive Thirring model, solitary wave solutions are obtained in closed form. The basic properties of these slow solitary waves and their dependence on their respective PT-symmetric gain/loss profile are then explored via numerical sim…
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a …
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