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arXiv:2309.01969

Multi-mode quantum correlation generated from an unbalanced SU(1,1) interferometer using ultra-short laser pulses as pump

Xueshi Guo, Wen Zhao, Xiaoying Li, Z. Y. Ou

Published Sep 5, 2023• 0 citations
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Abstract

Multi-mode entanglement is one of the critical resource in quantum information technology. Generating large scale multi-mode entanglement state by coherently combining time-delayed continuous variables Einstein-Podolsky-Rosen pairs with linear beam-splitters has been widely studied recently. Here we theoretically investigate the multi-mode quantum correlation property of the optical fields generated from an unbalanced SU(1,1) interferometer pumped ultra-short pulses, which generates multi-mode entangled state by using a non-degenerate parametric processes to coherently combine delayed Einstein-Podolsky-Rosen pairs in different frequency band. The covariance matrix of the generated multi-mode state is derived analytically for arbitrary mode number $M$ within adjacent timing slot, which shows a given mode is maximally correlated to 5 other modes. Based on the derived covariance matrix, both photon number correlation and quadrature amplitude correlation of the generated state is analyzed. We also extend our analyzing method to the scheme of generating entangled state by using linear beam splitter as a coherent combiner of delayed EPR pairs, and compare the states generated by the two coherently combining schemes. Our result provides a comprehensive theoretical description on the quantum correlations generated from an unbalanced SU(1,1) interferometer within Gaussian system range, and will offer more perspectives to quantum information technology.

DOI
10.48550/arxiv.2309.01969

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Multi-mode entanglement is one of the critical resource in quantum information technology. Generating large scale multi-mode entanglement state by coherently combining time-delayed continuous variables Einstein-Podolsky-Rosen pairs with linear beam-splitters has been widely studied recently. Here we theoretically investigate the multi-mode quantum correlation property of the optical fields generated from an unbalanced SU(1,1) interferometer pumped ultra-short pulses, which generates multi-mode entangled state by using a non-degenerate parametric processes to coherently combine delayed Einstein-Podolsky-Rosen pairs in different frequency band. The covariance matrix of the generated multi-mode state is derived analytically for arbitrary mode number MMM within adjacent timing slot, which shows a given mode is maximally correlated to 5 other modes. Based on the derived covariance matrix, both photon number correlation and quadrature amplitude correlation of the generated state is analyzed. We also extend our analyzing method to the scheme of generating entangled state by using linear beam splitter as a coherent combiner of delayed EPR pairs, and compare the states generated by the two coherently combining schemes. Our result provides a comprehensive theoretical description on the quantum correlations generated from an unbalanced SU(1,1) interferometer within Gaussian system range, and will offer more perspectives to quantum information technology.
Quantum entanglement shared by more than two partites is the essential bases for developing quantum communication networks and quantum computation. The multipartite entanglement of continuous variables can be generated by distributing or combining squeezed states of light using linear optics. We experimentally obtained a tripartite entangled state of bright optical field by means of a nondegenerate optical parametric amplifier (NOPA) and optical beam-splitters. The NOPA is operated in the state of parametric deamplification by locking the relative phase between the pump laser and the injected seed wave to (2n+1)π, so the generated Einstein-Podolsky-Rosen (EPR) beam for continuous variables is an entangled state of light with the quantum correlation of phase quadratures and the quantum anticorrelation of amplitude quadratures [1]. The output EPR beam consists of two frequency-degenerate optical modes with horizontal and vertical polarizations which are distributed to three parties with two linear beam-splitters. We have theoretically and experimentally demonstrated the three parties are in a tripartite entangled state with three-mode “position” (amplitude quadrature) correlation and relative “momentum” (phase quadrature) correlation [2]-[4]. The obtained GHZ-like state is a fully inseparable tripartite continuous-variables state violating the three inequalities used for the criterion of the inseparability [5][6]. The controlled dense coding quantum communication is experimentally accomplished by exploiting the tripartite entanglement. The three entangled modes are sent to a sender (Alice), a receiver (Bob) and a controller (Claire), respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity completed under Claire’s help is always larger than that without her help.
Quantum entanglement is an indispensable resource for implementing quantum information processing. The scale of quantum entanglement directly determines its quantum information processing capability. Therefore, it is of great importance to generate ultra-large-scale (ULS) quantum entanglement for the development of quantum information science and technology. Many efforts have been made to increase the scale of quantum entanglement. Recently, time-domain multiplexing has been introduced into continuous-variable (CV) quantum systems to greatly enlarge the scale of quantum entanglement. In this Letter, based on a time-delayed quantum interferometer, we theoretically propose and experimentally demonstrate a scheme for generating an ULS CV deterministic entanglement containing 2×20 400 optical modes. In addition, such ULS entanglement contains 81 596 squeezed modes. Our results provide a new platform for implementing ULS CV quantum information processing.
Time-domain multiplexed continuous-variable quantum states provide a promising route toward large-scale quantum networks. Existing platforms are based on continuous-wave pumped optical parametric systems, where the durations of temporal modes are on the order of nanoseconds. Here we demonstrate the time-domain multiplexed squeezing localized in a train of ultrashort pulses by exploiting unbalanced SU(1,1) interferometer (USUI) with a mode-locked laser serving as pump. Using the pulse-resolved measurement, we reveal the correlation structure of the state is unique and fundamentally different from previous approaches. To reach the ideal intensity squeezing, in principle, both the gain of USUI and mode number MMM involved in joint measurement should tend to infinity, illustrating the feature of global multimode squeezing. We conduct proof-of-principle experiments, in which the temporal mode duration is down to 10 ps. We verify the intensity squeezing degree RdR_dRd​ depends on both the gain of USUI and MMM. The results show RdR_dRd​ improves with the increase of MMM for M<10M<10M<10 and RdR_dRd​ is lower than shot noise level by ∼0.9\sim0.9∼0.9 dB for M>10M>10M>10 when the gain of USUI is fixed. Our investigations demonstrate the emission from high gain USUI is novel, which not only possesses the unique coherent feature but also enables the realization of ultra-large-scale quantum states.
We experimentally demonstrate the creation and characterization of Einstein-Podolsky-Rosen (EPR) correlation between optical beams in a time-gated fashion. The correlated beams are created with two independent continuous-wave optical parametric oscillators and a half beam splitter. We define the temporal modes using a square temporal filter with duration TTT and make time-resolved measurements on the generated state. We observe correlations between the relevant conjugate variables in the temporal mode which correspond to EPR correlation. Our scheme is extendable to continuous-variable quantum teleportation of a non-Gaussian state defined in the time domain such as a superposition of coherent states.
We study theoretically and experimentally the quantum properties of a type-II frequency-degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode Gaussian states, illustrated in terms of the covariance matrix. We report on the experimental generation of a two-mode squeezed vacuum on nonorthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e., quantum correlations and anticorrelations on orthogonal quadratures. A half sum of squeezed variances as low as $0.33\ifmmode\pm\else\textpm\fi{}0.02$, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.