0000000000025471
AUTHOR
Andrei Rybin
showing 20 related works from this author
Manipulation of optical solitons in Bose-Einstein condensates
2004
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 $\Lambda$-type medium points to a possibility to create optical gates as well as to a possibility to store optical information.
Exact Solution of Quantum Optical Models by Algebraic Bethe Ansatz Methods
1996
From long standing interests in solitons and integrable systems, e.g. SIT (1968– 74)1,2, “optical solitons” CQ04 (1977)3, we solve exactly, by algebraic Bettie ansatz (= quantum inverse) methods4, models of importance to quantum optics including the quantum Maxwell-Bloch envelope equations for plane-wave quantum self-induced transparency (SIT) in one space variable (x) and one time (t)2; and in the one tinte (t)5 a family of models surrounding and extending the Tavis-Cummings model6 of N 2-level atoms coupled to one cavity mode for ideal cavity (Q = ∞) QED. Additional Kerr type nonlinearities or Stark shifted levels can he incorporated into the Hamiltonian H of one of the most general model…
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light
2004
We consider $\Lambda$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the condensate can achieve large and negative values providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the "slow" and "fast" light propagating without absorption becomes achievable due to strong nonlinearity. An effective two-level quantum model of the system is derived and studied based on the su(2) polynomial deformation approach. We propose an efficient way for generation of subpoissonian fields in the Bose-Einstein condensate at time-scales much sho…
Solitons ofq-deformed quantum lattices and the quantum soliton
2001
We use the classical N-soliton solution of a q-deformed lattice, the Maxwell-Bloch (MB) lattice, which we reported recently (Rybin A V, Varzugin G G, Timonen J and Bullough R K Year 2001 J. Phys. A: Math. Gen. 34 157) in order, ultimately, to fully comprehend the `quantum soliton'. This object may be the source of a new information technology (Abram I 1999 Quantum solitons Phys. World 21-4). We suggested in Rybin et al 2001 that a natural quantum mechanical matrix element of the q-deformed quantum MB lattice becomes in a suitable limit the classical 1-soliton solution of the classical q-deformed MB lattice explicitly derived by a variant of the Darboux-Backlund method. The classical q-defor…
q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice
2000
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed lattice for which in continuum limit the equations of motion become the envelope Maxwell-Bloch (or SIT) equations describing the resonant interaction of light with a nonlinear dielectric. Thus the N-soliton solutions we here report are the natural q-deformations, necessary for a lattice, of the well-known multi-soliton and breather solutions of self-induced transparency (SIT). The method we use to find these solutions is a generalization of the Darboux-Backl…
Collapse in the symmetric Gross–Pitaevskii equation
2004
A generic mechanism of collapse in the Gross–Pitaevskii equation with attractive interparticle interactions is gained by reformulating this equation as Newton's equation of motion for a system of particles with a constraint. 'Quantum pressure' effects give rise to formation of a potential barrier around the emerging singularity, which prevents a fraction of the particles from falling into the singularity. For reasonable initial widths of the condensate, the fraction of collapsing particles for spherically symmetric traps is found to be consistently about 0.7.
Slow-light solitons
2007
We investigate propagation of slow-light solitons in atomic media described by the nonlinear � -model. Under a physical assumption, appropriate to the slow light propagation, we reduce the � -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.
Stopping a slow-light soliton: an exact solution
2005
We investigate propagation of a slow-light soliton in Λ-type media such as atomic vapours and Bose–Einstein condensates. 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. In the strongly nonlinear regime we find an explicit exact solution describing the whole process.
Singularity formation in the Gross-Pitaevskii equation and collapse in Bose-Einstein condensates
2004
We study the mechanisms of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for a flux of particles, and introduce the collapsing fraction of particles. We assume that this collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the collapse behavior on the initial conditions. We find that, for a properly chosen negative scattering length, the remnant fraction of atoms becomes larger when the initial aspect ratio of the condensate is increased.
The su(1,1) Tavis-Cummings model
1998
A generic su(1,1) Tavis-Cummings model is solved both by the quantum inverse method and within a conventional quantum-mechanical approach. Examples of corresponding quantum dynamics including squeezing properties of the su(1,1) Perelomov coherent states for the multiatom case are given.
Driving slow-light solitons by a controlling laser field
2005
In the framework of the nonlinear Λ-model we investigate propagation of a slow-light soliton in atomic vapours 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 location and shape of the spatially localized memory bit imprinted into the medium. We show that the pr…
Theory of slow-light solitons
2005
In the framework of the nonlinear $\Lambda$-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 $\Lambda$-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the $\Lambda$-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 generated by an auxiliary laser. For a rather general time dependence of the fiel…
<title>Multiatom microlaser: a stable source of photons with subpoissonian statistics</title>
2000
We studied a multi-atom model of microlaser. As initial conditions we took diagonal density matrix of atoms in the basis of symmetrized collective states. Under diagnonal invariance taking a place for such initial conditions, we considered peculiarities of dynamics of the field reduced density matrix comparing it with the one-atom case. The field possesses subpoissonian distributions in a quasistationare, which are stable with respect to relaxation and number of atoms fluctuations in a packet. When one does not measure the atomic state on output of the cavity, it is possible to observe a macroscopic superposition of few such subpoissonian distributions. Simulating a measuring process of the…
Non-adiabatic manipulation of slow-light solitons
2005
We provide an exact analytic description of decelerating, stopping and reaccelerating optical solitons in atomic media in the non-adiabatic regime. Dynamical control over slow-light pulses is realized via a nonlinear interplay between the solitons and the controlling field generated by an auxiliary laser. This leads to recovery of optical information. We discuss physically interesting features of our solution, which are in good agreement with recent experiments.
Slow-light solitons: Influence of relaxation
2008
We have applied the transformation of the slow-light equations to the 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 information processing. We also demonstrate that relaxation plays a role of resistance to the sol…
Slow-light soliton dynamics with relaxation
2007
We solved the problem of soliton dynamics in the presence of relaxation. We demonstrate that the spontaneous emission of atoms is strongly suppressed due to nonlinearity. The spatial shape of the soliton is well preserved.
Nonlinear theory of slow light.
2011
In the framework of the nonlinear Λ model, propagation of solitons was analysed in atomic vapours and Bose–Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a Λ -type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled wi…
Quantum dynamics of the intensity-dependent Tavis-Cummings model
1999
An exactly solvable generalization of the intensity-dependent Jaynes-Cummings model to the case of N0 atoms is introduced together with its solution. The quantum dynamics of the model including the squeezing properties of the su(1,1) Perelomov and Glauber coherent states is investigated. The cases of one and two atoms present in the cavity are analysed in detail. These two cases are compared in the situation when the atomic subsystem is initially prepared in the ground state, the Dicke state and the state of thermal equilibrium.
An algebraic approach to the Tavis-Cummings problem
2002
An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.