Quantum solitons as possible qubits

Abstract

In a recent article [1] Izo Abram, of the Centre National d’Etudes des Telecommunlcations (CNET), Bagneux, France suggested that quantum solitons in optical fibres could both be ‘squeezed’ below the short noise level, thus reducing quantum noise, and that they could be used as natural ‘qubits’ for quantum information, quantum computing, logic gates, etc. The point here is that multi-quantum solitons are more easily realised experimentally (in an optical fibre) than are the current realisations of qubits using spin-1/2 systems or as in [2] using 2-level atoms and/or single photons in the context of cavity q.e.d, The ‘quantum soliton’ as described by Abram [1] is the 1-soliton solution of the well known classical one-dimensional attractive Nonlinear Schrodinger (NLS) equation which solution can be put in the form [3] $$ \langle {(\Delta \hat{A})^2}\rangle \langle {(\Delta \hat{B})^2}\rangle \geqslant \frac{1}{4}|\langle \psi |[\hat{A}\hat{B}] - |\psi \rangle {|^2} $$ (1) $$ P\{ \phi (t) = \psi (t)\} = 1 $$ (1.2) Inline 1\( \geqslant \frac{{p - 1}}{m} \) where the oscillatory phase exp iФ(x, t) is determined by where ξ, η θ0 are all real valued parameters: c〈0 is the coupling constant of the NLS equation. Quantum features on this classical soliton are then introduced ([1, 4, 5] and see [6]) by imposing momentum-position uncertainly or number phase uncertainly, the latter in particular satisfying ΔnΔφ≥1/2, a Heisenberg bound for the fluctuations in particle number n and phase φ. For large enough n (a ‘photon number’) [Nφ]=−i for operators Nφ hence the bound: N has eigenvalues n. Because of the well-known stability of classical NLS solitons in optical fibres for very long distance optical communication (especially in the presence of amplifiers at distance separations ∼100 km), and because such classical ‘bits’ must in fact be quantum ‘bits’, and therefore ‘qubits’, the quantum soliton solutions of the quantum attractive NLS equation seem worth investigating as such and in these terms — and this is what we shall do in this paper.