Optical computing with soliton trains in Bose–Einstein condensates

Abstract

Optical computing devices can be implemented based on controlled generation of soliton trains in single and multicomponent Bose-Einstein condensates (BEC). Our concepts utilize the phenomenon that the frequency of soliton trains in BEC can be governed by changing interactions within the atom cloud [1]. We use this property to store numbers in terms of those frequencies for a short time until observation. The properties of soliton trains can be changed in an intended way by other components of BEC occupying comparable states or via phase engineering. We elucidate in which sense such an additional degree of freedom can be regarded as a tool for controlled manipulation of data. Finally the outcome of any manipulation made is read out by observing the signature within the density profile.

Bright solitons in non-equilibrium coherent quantum matter

“…Effective mechanisms to generate excitations in general BEC within the Gross-Pitaevskii (GP) mean-field parameter regime [2,4] are important tools for investigations on their properties both experimentally and theoretically [31] and carry the possibility for applications, e.g. in optical computing [16,32]. Vortices with quantized circulation in superfluids are a key example of a topologically stable excitation in a two-dimensional BEC system guided by a nonlinear Schrödinger-type equation.…”

Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates

“…However, the theoretical description in the mean-field regime is more complicated due to the non-conservative character of the underlying partial differential equations, and so far effective and simple methods to analyze solutions have been lacking. BEC have been studied for decades particularly due to their intrinsic nonlinearity and relatively simple mathematical description, particularly because these states of coherent quantum matter support excitations such as solitons [5][6][7][8], quantum vortices, vortex rings or giant vortices [9][10][11][12][13], which essentially require such nonlinearities [14]. It turns out that these excitations depend significantly on the unique features of the underlying particles forming the BEC.…”

Nonlinear eigenmodes of a non-equilibrium harmonic oscillator

“…The output will be the quantum harmonic oscillator patterns observed, iff both pump spots are equal 0. So we can identify all the harmonic oscillator patterns with an output 1, and thus we have established a simple feasible NOR gate by means of topologically stable excitations carried by a non-equilibrium polariton condensate within a semiconductor microcavity which stand in the tradition of optical computing [17].…”

“…The output will be the quantum harmonic oscillator patterns observed, if both pump spots are equal to 0. So we can identify all the harmonic oscillator patterns with an output 1, and thus we have established a simple feasible NOR gate by means of topologically stable excitations carried by a non-equilibrium polariton condensate within a semiconductor microcavity which stand in the tradition of optical computing [17,38]. This NOR gate can be generalized in the sense that we do not solely distinguish between 'on' corresponding to 0 and 'off' associated with 1 of both pump spots, but in addition include the experimental and numerical observation that different pump strengths lead to different numbers of density lobes.…”

“…Polaritons in semiconductor microcavities are superpositions between excitons (electron-hole pairs) and cavity photons, and as such the combination of the components determines the particle statistics [2,15]. These quasi-particles in a dilute regime show distinctive properties such as Bose-Einstein condensation, superfluidity, a finite non-zero speed of sound owing to the nonlinearity and the emergence of elementary topologically stable excitations such as solitons or quantum vortices [2,6,13,16,17]. In their very nature, polariton BECs are nonequilibrium systems-polaritons can be created via a local light field and decay after 1-100 ps mainly owing to leaking of the cavity photons [6,11,18].…”