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arXiv:quant-ph/0603088 · Physical Review Letters

Quantum Temporal Correlations and Entanglement via Adiabatic Control of Vector Solitons

Mankei Tsang

Published Jul 11, 2006• 14 citations
arXivHTMLPDF

Abstract

It is shown that optical pulses with an average position accuracy beyond the standard quantum limit can be produced by adiabatically expanding an optical vector soliton followed by classical dispersion management. The proposed scheme is also capable of entangling positions of optical pulses and can potentially be used for general continuous-variable quantum-information processing.

DOI
10.1103/physrevlett.97.023902

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Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2

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It is shown that optical pulses with an average position accuracy beyond the standard quantum limit can be produced by adiabatically expanding an optical vector soliton followed by classical dispersion management. The proposed scheme is also capable of entangling positions of optical pulses and can potentially be used for general continuous-variable quantum-information processing.
Quantum correlations play a prominent role in numerous applications, from quantum communications and networking to enhanced sensing. I propose using optical soliton splitting and inelastic soliton collision to generate pulse pairs with highly correlated photon number fluctuations. The fluctuations are studied using the linearized quantum fluctuation theory of vector solitons. I show that the interpulse correlations arise in the process of inelastic soliton interactions initiated by the polarization mode dispersion and modulation of the fiber dispersion. The inelastic soliton interactions produce pulses with highly correlated quantum fluctuations in the orthogonal polarization components of the field. In the time domain, the pulses have a four-lobe correlation pattern. In the frequency domain, the correlation functions acquire a ``checkerboard'' structure with alternating positive and negative regions. Correlations between the separated pulses arise only with appropriate pulse width, group velocity dispersion, and polarization mode dispersion. The generation of pulses with high intrapulse correlations offers the possibility of producing entangled sources for continuous-variable quantum communication and computation.
Two simple schemes for generating macroscopic (many-photon) continuous-variable entangled states by means of continuous interactions (rather than collisions) between solitons in optical fibers are proposed. First, quantum fluctuations around two time-separated single-component temporal solitons are considered. Almost perfect correlation between the photon-number fluctuations can be achieved after passing a certain distance, with a suitable initial separation between the solitons. The photon-number correlation can also be achieved in a pair of vectorial solitons with two polarization components. In the latter case, the photon-number-entangled pulses can be easily separated by a polarization beam splitter. These results offer possibilities to produce entangled sources for quantum communication and computation.
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Abstract We propose a new approach to generate quantum-correlated pulse pairs using fission of chirped Manakov solitons. Quantum correlations are studied using linearized quantum fluctuation theory. The fission of chirped solitons produces both intra-pulse and inter-pulse high-level correlations. We found that the collision of vector solitons induces nonzero correlations in orthogonal polarization components of the pulse field. The fission of solitons and subsequent collision of the resulting pulses allow a pulse train with complex correlation pattern to be produced. The generation of pulses with correlated quantum fluctuations offers the possibility of engineering new entangled sources for continuous-variable quantum communication and computation.
The equations that govern the temporal evolution of two photons in the Schr\"odinger picture are derived, taking into account the effects of loss, group-velocity dispersion, temporal phase modulation, linear coupling among different optical modes, and four-wave mixing. Inspired by the formalism, we propose the concept of quantum temporal imaging, which uses dispersive elements and temporal phase modulators to manipulate the temporal correlation of two entangled photons. We also present the exact solution of a two-photon vector soliton, in order to demonstrate the ease of use and intuitiveness of the proposed formulation.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2