The Jackiw-Rebbi model describes a one-dimensional Dirac field coupled to a soliton field and can be equivalently thought of as a model describing a Dirac field with a spatially dependent mass term. Neglecting the dynamics of the soliton field, a kink in the background soliton profile yields a topologically protected zero-energy mode for the field, which in turn leads to charge fractionalisation. We show here that the model, in the first quantised form, can be realised in a driven slow-light setup, where photons mimic the Dirac field and the soliton field can be implemented–and tuned–by adjusting optical parameters such as the atom-photon detuning. Furthermore, we discuss how the existence of the zero-mode and its topological stability can be probed naturally by studying the transmission spectrum. We conclude by analysing the robustness of our approach against possible experimental errors in engineering the Jackiw-Rebbi Hamiltonian in this optical setup.
In a one dimensional shallow optical lattice, in the presence of both cubic and quintic nonlinearity, a superfluid density wave, is identified in Bose-Einstein condensate. Interestingly, it ceases to exist, when only one of these interaction is operative. We predict the loss of superfluidity through a classical dynamical phase transition, where modulational instability leads to the loss of phase coherence. In certain parameter domain, the competition between lattice potential and the interactions, is shown to give rise to a stripe phase, where atoms are confined in finite domains. In pure two-body case, apart from the known superfluid and insulating phases, a density wave insulating phase is found to exist, possessing two frequency modulations commensurate with the lattice potential.
The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating wave solutions in quasi one dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time dependent coupling and the trap variation on the condensate profile are explicated. The TBEC has also been investigated in presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions. PACS numbers: 03.75. Kk, 03.75.Lm, 03.75.Mn Much theoretical work has already gone into studying the ground state solutions of the coupled GrossPitaevskii (GP) equations describing multi-component BECs [1,2,3,4]. TBEC has been observed, where the two hyperfine levels of 87 Rb [5,6] act as the two components. In this case, a fortuitous coincidence in the triplet and singlet scattering lengths has led to the suppression of exoergic spin-exchange collisions, which lead to heating and resultant loss of atoms. A number of interesting features, like the preservations of the total density profile and coherence for a characteristically long time, in the face of the phase-diffusing couplings to the environment and the complex relative motions [7], point to the extremely interesting dynamics of the TBEC. TBEC has been produced in a system comprising of 41 [12,13,14,15]. In the TBEC, a number of investigations, primarily devoted to the study of localized solitons, have been carried out recently [16,17,18,19,20]. The coincidence of singlettriplet coupling in 87 Rb, leads to the well known Manakov system [21] in weak coupling quasi-one dimensional scenario [22,23]. The rich dynamics of solitons in this integrable system has received considerable attention in the literature [24,25,26,27]. The effect of spatial inhomogeneity, three-dimensional geometry, and dissipation on TBEC have been examined. However, the periodic solitary waves have not received much attention in the literature, particularly in the presence of the harmonic trap [28]. Periodic sinusoidal excitations are natural in linear systems. In nonlinear models periodic cnoidal waves can be present. It is worth mentioning that, in nonlinear resonant atomic media, cnoidal excitations have been experimentally generated [29,30], where relaxation naturally led to the atomic level population necessary for the existence of these nonlinear periodic waves [31].Here we analyze the solutions of a generic TBEC model in a quasi-one dimensional geometry for periodic solutions. Interestingly, we find exact sinusoidal wave solutions in this system in the presence of a harmonic trap, which do not occur in the single component case. The presence of two components leads to these waves, whose energy difference are controlled by the cross phase modulation (XPM). In presence of time dependent trap and sc...
We examine the superradiance of a Bose-Einstein condensate pumped with a Laguerre-Gaussian laser of high winding number, e.g., = ℓ 7. The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ-fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ-fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ-fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
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