Generation of photon-number-entangled soliton pairs through interactions

Lee, Ray-Kuang; Lai, Yinchieh; Malomed, Boris A.

doi:10.1103/physreva.71.013816

Cited by 18 publications

(10 citation statements)

References 41 publications

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“…Some of the important theoretical approaches for solving QNLSE and other more complicated quantum nonlinear pulse propagation problems include the quantum stochastic simulation method [2], the Bethe's ansatz method [3], the quantum perturbation theory [7], the back-propagation method [8], and the cumulant expansion technique [9]. Some of the important experiments include the quantum nondemolition measurement using solitons [10], the generation of amplitude squeezed states through optical filtering [11,12] or imbalanced nonlinear interference [13], the intrasoliton photon number quantum correlation in both the spectra and time domain [14,15], and the generation of continuous variable Einstein-Podolsky-Rosen entangled states by adiabatically expanding an optical vector soliton [16]. Among them, the generation of entangled states using nonlinear Schrödinger solitons is of particular interest for possible quantum information applications.…”

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confidence: 99%

“…The photon number noises of one soliton can be encoded to the phase noises of the other soliton through the cross-phase modulation and thus create quantum correlation between the two solitons. Recently we have also shown that the photon number correlation of two time-multiplex solitons can be directly established through nonlinear interaction [15]. The whole system is a pure state of infinite modes if no optical loss is assumed.…”

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Entangled Quantum Nonlinear Schrödinger Solitons

Lai

Lee

2009

Phys. Rev. Lett.

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Considered as a multipartite quantum system, time-multiplexed nonlinear Schrödinger solitons after collision are rigorously proved to become quantum entangled in the sense that their quadrature components of suitably selected internal modes satisfy the inseparability criterion. Clear physical insights for the origin of entanglement are given, and the required homodyne local oscillator pulse shape for optimum entanglement detection is determined.

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Entangled Quantum Nonlinear Schrödinger Solitons

Lai

Lee

2009

Phys. Rev. Lett.

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“…The Heisenberg equations of motion derived from this Hamiltonian are analyzed using perturbative techniques by Rand et al [19], who study the specific case of Manakov solitons, and by Lantz et al [20] and Lee et al [21], who numerically investigate the photon number entanglement in higher-order vector solitons. As opposed to these previous studies, in this Letter the exact quantum vector soliton solution is derived in the Schrödinger picture, in the spirit of the scalar soliton analyses in Refs.…”

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Quantum Temporal Correlations and Entanglement via Adiabatic Control of Vector Solitons

Tsang

2006

Phys. Rev. Lett.

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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. DOI: 10.1103/PhysRevLett.97.023902 PACS numbers: 42.65.Tg, 42.50.Dv If an optical pulse consists of N independent photons, then the uncertainty in the pulse-center position is the pulse width divided by N p , the so-called standard quantum limit [1]. The ultimate limit permissible by quantum mechanics, however, is determined by the Heisenberg uncertainty principle and is smaller than the standard quantum limit by another factor of N p , resulting in a quantum-enhanced accuracy useful for positioning and clock synchronization applications [2]. To do better than the standard quantum limit, a multiphoton state with positive frequency correlations and, equivalently, negative time correlations is needed [2]. Consequently, significant theoretical [3,4] and experimental [5] efforts have been made to create such a nonclassical multiphoton state. All previous efforts were based on the phenomenon of spontaneous photon pair generation in parametric processes, limiting N to 2 only. The resultant enhancement can be regarded only as a proof of concept and is too small to be useful, considering that a large number of uncorrelated photons can easily be obtained, with a standard quantum limit orders of magnitude lower than the ultimate limit achievable by two photons. It is hence much more desirable in practice to be able to enhance the position accuracy of a large number of photons. In this Letter, for the first time to the author's knowledge, a scheme that produces a multiphoton state with positive frequency correlations among an arbitrary number of photons is proposed, thus enabling quantum position accuracy enhancement for macroscopic pulses as well. The scheme set forth therefore represents a major step forward towards the use of quantum enhancement in future positioning and clock synchronization applications.The proposed scheme exploits the quantum properties of a vector soliton, in which photons in different optical modes are bound together by the combined effects of group-velocity dispersion, self-phase modulation, and cross-phase modulation [6]. A quantum analysis shows that the average position of the photons in a vector soliton is insensitive to the optical nonlinearities and only subject to quantum dispersive spreading, while the separations among the photons is controlled by the balance between dispersion and nonlinearities. These properties are, in fact, very similar to those of scalar solitons [7,8], so the idea of adiabatically compressing scalar solitons for momentum squeezing [9] can be similarly applied to vector solitons. To produce negative time correlations, however, adiabatic soliton expansion should be performed instead. Giv...

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“…The unique scale independent properties of the internal modes, specifically their gap separation from the phonon band, their localization to a few ions and their high frequency, suggest that such coherences can be measured and manipulated using existing ion trap techniques. This indicates that trapped-ion solitons may be useful for generating entanglement [11,32,33], and implementing quantum information processing in large systems. …”

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Quantum Coherence of Discrete Kink Solitons in Ion Traps

et al. 2010

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We propose to realize quantized discrete kinks with cold trapped ions. We show that long-lived solitonlike configurations are manifested as deformations of the zigzag structure in the linear Paul trap, and are topologically protected in a circular trap with an odd number of ions. We study the quantum-mechanical time evolution of a high-frequency, gap separated internal mode of a static kink and find long coherence times when the system is cooled to the Doppler limit. The spectral properties of the internal modes make them ideally suited for manipulation using current technology. This suggests that ion traps can be used to test quantum-mechanical effects with solitons and explore ideas for the utilization of the solitonic internal-modes as carriers of quantum information.Solitons are localized configurations of nonlinear systems which are nonperturbative and topologically protected [1]. Quantum-mechanical properties of solitons, such as squeezing, have been predicted and measured in optical systems [2]. Quantum dynamics has been observed with a single Josephson junction soliton [3]. In waveguide arrays [4,5] and Bose-Einstein condensates [6] solitons are mean field solutions, localized to a few sites of a periodic potential. In chains of coupled particles, solitons are discrete spatial configurations, as in the Frenkel-Kontorova (FK) model [7,8].Discrete solitons of the FK model and its generalizations are referred to as kinks. An important property of kinks is the existence of localized modes. One mode is the kink's translational 'zero-mode', whose frequency generally rises above zero. Other localized modes are known as 'internal modes' [9,10]. Physically they describe 'shapechange' excitations of the kink and typically they are separated by an energy gap from other long-wavelength phononic modes. It was suggested to use the internal mode as a carrier of quantum information [11].Quantum information processing in ion traps [12] has dramatically improved over the last decades [13,14]. Recently there has been a considerable interest in using trapped ions for quantum simulation of various systems such as spin-chains [15][16][17] In this Letter we demonstrate that quantum coherence in static discrete kinks can be observed with ordinary Paul traps without external additions. We explore quasi-2D discrete kinks resembling those of the zigzag model [23]. In the linear trap we find local metastable deformations of the zigzag structure [24], as depicted in Fig. 1, which are long-lived already with a moderate number of ions, N 20. In a circular trap with an odd number of ions, similar configurations form the ground state. We study the robustness of a high-frequency internal mode of the kink against decoherence in the thermal environment of all the other modes. With all nonlinear interactions accounted for, we numerically integrate a non-Markovian master equation, which leads us to our main result: already at the standard Doppler cooling limit coherence persists in the internal mode for many oscillations. This could allow ...

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Generation of photon-number-entangled soliton pairs through interactions

Cited by 18 publications

References 41 publications

Entangled Quantum Nonlinear Schrödinger Solitons

Entangled Quantum Nonlinear Schrödinger Solitons

Quantum Temporal Correlations and Entanglement via Adiabatic Control of Vector Solitons

Quantum Coherence of Discrete Kink Solitons in Ion Traps

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