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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Entanglement in multimode bosonic systems

Yumang Jing, Olov Pettersson, Qiongyi He, Tim Byrnes

Published Nov 3, 2016• 0 citations
Publisher

Abstract

Entanglement generation between atomic ensembles is typically modeled using the framework of continuous variables (CV) which approximates discrete spin operators as canonical position and momentum operators. Although hugely successful with many applications, this approximation is valid only for small deviations in spin. Here we investigate entanglement generation between two atomic ensemble qubits using a measurement based scheme of a common light mode. Various methods of entanglement detection of the entangled state is discussed. We propose a entanglement witness for this state and discuss its further applications to optical states.

DOI
10.1117/12.2245926

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Entanglement generation between atomic ensembles is typically modeled using the framework of continuous variables (CV) which approximates discrete spin operators as canonical position and momentum operators. Although hugely successful with many applications, this approximation is valid only for small deviations in spin. Here we investigate entanglement generation between two atomic ensemble qubits using a measurement based scheme of a common light mode. Various methods of entanglement detection of the entangled state is discussed. We propose a entanglement witness for this state and discuss its further applications to optical states.
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Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.
Summary form only given. A new approach to the problem of the quantum interface between light and atoms has been recently developed. The method utilizes free space dispersive interaction between pulses of light and spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in a certain polarization basis. In the first demonstration of this approach we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state paving the road towards realization of the quantum memory for light. Recently we have also extended the free space light-atoms interface beyond the continuous variables in the proposal, where a coherent superposition "cat" state of an atomic ensemble is generated by a measurement sequence. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented.
We consider the optical generation and characterization of entanglement in atomic ensembles under nonuniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of nonuniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the average total spin remains large, and the detection does not resolve single spins. Furthermore, we derive an analytic formula for determining the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.
We discuss some of the main features of a recently-generated form of hybrid entanglement between discrete- and continuous-variable states of light. Ideally, such a kind of entanglement should involve single-photon and coherent states as key representatives of the respective categories of states. Here we investigate the characteristics and limits of a scheme that, relying on a superposition of photon-creation operators onto two distinct modes, realizes the above ideal form of hybrid entanglement in an approximate way.
We present an entanglement criterion for two mode squeezed states which relies on particle counting only. The proposed inequality is optimal for the state under consideration and robust against particle losses up to 2/3. As it does not involve measurements of quadratures - which is typically very challenging for atomic modes - it renders the detection of atomic many-particle entanglement feasible in many different settings. Moreover it bridges the gap between entanglement verification for a qubit and criteria for continuous variables measured by homodyne detection. We illustrate its application in the context of superradiant light scattering from Bose Einstein condensates by considering the creation of entanglement between atoms and light as well as between two condensates in different momentum states. The latter scheme takes advantage of leaving the Gaussian realm and features probabilistic entanglement distillation.