Nonlinear Entanglement and its Application to Generating Cat States

Shen, Yong; Assad, Syed M.; Grosse, Nicolai B.; Li, X. Y.; Reid, M. D.; Lam, Ping Koy

doi:10.1103/physrevlett.114.100403

Cited by 33 publications

(31 citation statements)

References 38 publications

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“…Two-state oscillation of the BEC has been experimentally observed [26]. We present in Figure 6 predictions for this type of oscillation with N = 20 and n L = 2 where the solutions indicate states (38) with a separation of n = 16 atoms. The question becomes how to certify the quantum coherence of the embedded cat-states (38) that may be generated in the experiment where such oscillation is observed.…”

Section: Creation Of N-scopic Quantum Superpositionsmentioning

confidence: 82%

“…In a separate paper, we examine a third criterion based on uncertainty relations and Einstein-Podolsky-Rosen steering [31]. Previous studies have proposed signatures (criteria or measures) for mesoscopic "cat" states (see for instance [3,4,22,25,[29][30][31][32][33][34][35][36][37][38][39]). These include proposals based on interference fringes, entanglement measures, uncertainty relations, negative Wigner functions and state fidelity.…”

Section: Introductionmentioning

confidence: 99%

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Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

et al. 2016

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We examine how to signify and quantify the mesoscopic quantum coherence of approximate twomode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by n. These criteria negate certain mixtures of quantum states, thereby signifying a generalised n-scopic Schrodinger cat-type paradox. The first criterion is the correlation â †nbn = 0 (hereâ andb are the boson operators for each mode). The correlation manifests as interference fringes in n-particle detection probabilities and is also measurable via quadrature phase amplitude and spin squeezing measurements. Measurement of â †nbn enables a quantification of the overall n-th order quantum coherence, thus providing an avenue for high efficiency verification of a high-fidelity photonic NOON states. The second criterion is based on a quantification of the measurable spin-squeezing parameter ξN . We apply the criteria to theoretical models of NOON states in lossy interferometers and doublewell trapped BECs. By analysing existing BEC experiments, we demonstrate generalised atomic "kitten" states and atomic quantum coherence with n 10 atoms.

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Section: Creation Of N-scopic Quantum Superpositionsmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

et al. 2016

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“…In a fully degenerate configuration, the Wigner function of the TPS exhibits negativities [30,32,33], a clear signature of SG statistics, which is impossible to achieve by second-order down-conversion (SODC) and linear optics. Nonlinear steering has been proposed and verified based on a partially degenerate configuration [34]. González et al revealed the relationship between Gaussian entanglement and both number of seeded modes and intensity in the nondegenerate case [35].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian nature and entanglement of spontaneous parametric nondegenerate triple-photon generation

et al. 2021

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We theoretically demonstrate through numerical methods that the triple-photon state generated by threephoton spontaneous parametric down-conversion is a non-Gaussian Greenberger-Horne-Zeilinger state, showing super-Gaussian statistics. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, we propose a model to prepare two-mode sub-Gaussian entangled states with a tunable negative Wigner function based on quadrature projection measurements. We find that these Gaussian projection measurements with outcomes X 1 not only improve the entanglement of the residual two modes but also introduce a Gaussian component, resulting in the coexistence of Gaussian and non-Gaussian entanglement.

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“…The superposition state (1.1) giving rise to this paradox has motivated much research. This includes experiments that realize different forms of cat states [3][4][5][6][7][8][9][10][11], proposals to generate and detect cat states [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], alternative interpretations of quantum mechanics and of the cat state [29][30][31][32][33][34][35][36][37], and theories that modify quantum mechanics [38,39]. In this paper, we present criteria for mesoscopic quantum coherence (MQC) and mesoscopic quantum entanglement (MQE).…”

Section: Introductionmentioning

confidence: 99%

Criteria to detect macroscopic quantum coherence, macroscopic quantum entanglement, and an Einstein-Podolsky-Rosen paradox for macroscopic superposition states

Reid

2019

Phys. Rev. A

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According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schrödinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system C is entangled with a second system S, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems C and S are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schrödinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.

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Nonlinear Entanglement and its Application to Generating Cat States

Cited by 33 publications

References 38 publications

Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

Non-Gaussian nature and entanglement of spontaneous parametric nondegenerate triple-photon generation

Criteria to detect macroscopic quantum coherence, macroscopic quantum entanglement, and an Einstein-Podolsky-Rosen paradox for macroscopic superposition states

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