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arXiv:0807.2393 · Physical Review A

Photosolitonic effect

Maxim Khodas, Alex Kamenev, L. I. Glazman

Published Nov 26, 2008• 31 citations
arXivHTMLPDF

Abstract

We show that dark solitons in one-dimensional Bose liquids may be created by absorption of a single quanta of an external ac field, in a close analogy with the Einstein's photoelectric effect. Similarly to the von Lenard's experiment with photoexcited electrons, the external field's photon energy $\ensuremath{\hbar}\ensuremath{\omega}$ should exceed a certain threshold. In our case the latter is given by the soliton energy ${\ensuremath{\epsilon}}_{s}(\ensuremath{\hbar}q)$ with the momentum $\ensuremath{\hbar}q$, where $q$ is photon's wave number. We find the probability of soliton creation to have a power-law dependence on the frequency detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\epsilon}}_{s}∕\ensuremath{\hbar}$. This dependence is a signature of the quantum nature of the absorption process and the orthogonality catastrophe phenomenon associated with it.

DOI
10.1103/physreva.78.053630

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We show that dark solitons in one-dimensional Bose liquids may be created by absorption of a single quanta of an external ac field, in a close analogy with the Einstein's photoelectric effect. Similarly to the von Lenard's experiment with photoexcited electrons, the external field's photon energy \ensuremathℏ\ensuremathω\ensuremath{\hbar}\ensuremath{\omega}\ensuremathℏ\ensuremathω should exceed a certain threshold. In our case the latter is given by the soliton energy \ensuremathϵs(\ensuremathℏq){\ensuremath{\epsilon}}_{s}(\ensuremath{\hbar}q)\ensuremathϵs​(\ensuremathℏq) with the momentum \ensuremathℏq\ensuremath{\hbar}q\ensuremathℏq, where qqq is photon's wave number. We find the probability of soliton creation to have a power-law dependence on the frequency detuning \ensuremathω\ensuremath−\ensuremathϵs∕\ensuremathℏ\ensuremath{\omega}\ensuremath{-}{\ensuremath{\epsilon}}_{s}∕\ensuremath{\hbar}\ensuremathω\ensuremath−\ensuremathϵs​∕\ensuremathℏ. This dependence is a signature of the quantum nature of the absorption process and the orthogonality catastrophe phenomenon associated with it.
We show that dark solitons in 1D bose systems may be excited by resonant absorption of single quanta of an external ac field. The energy of the quantum ℏω\hbarωℏω should be slightly blue-detuned from the energy of a soliton with momentum ℏq\hbar qℏq, where qqq is the external field wavenumber qqq. We calculate the absorption cross-section and show that it has power-law dependence on the frequency detuning. This reflects the quantum nature of the absorption process and the orthogonality catastrophe phenomenon associated with it.
It is well known that high-intensity optical fields with soliton features, both bright and dark solitons, can trap and reshape photon fields of lower intensities into optical solitons by means of cross-phase modulation in optical materials with Kerr nonlinearity. In general the induced photon fields are not arbitrarily given, they are well-defined quantum states |ℓ, m〉 of a discrete spectrum which we refer to as quantum photosoliton modes. In this study we propose a scheme for the generation of quantum photosoliton states, by considering linear photon field propagating coupled to a vector high-intensity optical field with coexisting mutually transparent bright and dark solitons. It is found that features of the probe spectrum, specifically the nature, number and degeneracy of the associate quantum modes, depend on the strengths of couplings of the linear photon field to the bright and dark soliton components of the vector-soliton pump. The competition created by these simultaneous couplings leads to a rich variety of photosoliton modes, including modes that are replica of the soliton pump or translation modes of the two components of the vector-soliton pump. For the context where the optical pump consists of a single bright and a single dark soliton structures, it is found that photosoliton modes are all multiple degenerate in addition to being replica of some other modes. However, when the optical pump is a periodic multiplex of bright-dark solitons, photosoliton quantum states retain their identities (i.e. become non degenerate) but some of them are still either replica or translation modes of components of the optical pump.
We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a ΛΛΛ-coupled three-level system. Numerical simulations of the corresponding two-component system reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. However, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in, which happens after a few tens of milliseconds after the quench of the optical fields.
Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.
Bright solitary-waves may be created in dilute Bose-Einstein condensates of at tractively interacting atoms in one dimensional regimes. In integrable systems, such solitary waves are particle-like objects called solitons. We investigate the consequences of non-integrability on the solitary waves in trapped Bose-Einstein condensates caused by an axial harmonic trap, and non-integrability caused by three dimensional effects. To analyse the soliton-like nature of the solitary-waves in an axial harmonic trap, a particle analogy for the solitary-waves is formulated. Exact Soliton solutions exist in the absence of an external trapping potential, which behave in a particle-like manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the, collision time of the solitons. We find that the collision time of the solions is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carrier over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes. We predict that these chaotic regimes will be an indicator of rapid depletion of the condensate due to quantum transitions of the condensate particles into non-condensate modes. To analyse the residual effects of the three dimensional nature of the solitary waves, we use a nonlinear Schrödinger equation with an additional quintic term. We perform variational calculations, and confirm the collapse of a soliton when the number of particles contained therein is increased past a critical number. We investigate the effects of varying the axial trap frequency and scattering length on the critical number. We propose a method to model particle exchange between solitons by extending the variational treatment to two solitons.
We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.