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arXiv:2110.08990 · Journal of Physics B Atomic Molecular and Optical Physics

Decoherence effects in quantum nondemolition measurement induced entanglement between Bose–Einstein condensates

Shuai Gao, Ebubechukwu O. Ilo-Okeke, Yuping Mao, Manikandan Kondappan, Juan E Aristizabal-Zuluaga, Valentin Ivannikov, Tim Byrnes

Published Jul 4, 2022• 7 citations
arXivHTMLPDF

Abstract

Abstract We study the robustness of quantum nondemolition (QND) measurement induced entanglement between Bose–Einstein condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach–Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement and correlation criteria. Our analysis does not use the Holstein–Primakoff approximation, and is capable of modelling long light–atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than 1 / N , where N is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show a remarkable robustness that makes the scheme promising for various quantum information applications.

DOI
10.1088/1361-6455/ac7e0f

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Abstract We study the robustness of quantum nondemolition (QND) measurement induced entanglement between Bose–Einstein condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach–Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement and correlation criteria. Our analysis does not use the Holstein–Primakoff approximation, and is capable of modelling long light–atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than 1 / N , where N is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show a remarkable robustness that makes the scheme promising for various quantum information applications.
We study the robustness of quantum nondemolition (QND) measurement induced entanglement between Bose-Einstein Condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach-Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement, and correlation criteria. Our analysis does not use the Holstein-Primakoff approximation and is capable of modeling long light-atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than $ 1/\sqrt{N}$, where $ N $ is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show a remarkable robustness that makes the scheme promising for various quantum information applications.
We study the effects of optical and atomic decoherence in entangled atomic ensembles produced via quantum nondemolition (QND) measurements. We examine potentially experimentally detrimental effects, such as optical phase diffusion, photon loss and gain, and atomic dephasing. For the optical decoherence channels, we use the technique of integration within ordered operators to obtain the associated Kraus operators. We analyze the effect of different decoherence channels on various quantities, such as the variances of the spin operators, entanglement and correlation criteria, logarithmic negativity, and the Bell–CHSH inequality. We generally find a smooth decay of correlations and entanglement in the presence of decoherence. In the short interaction time range, we find that various quantities show signals consistent with, and showing that entanglement exists under all three types of decoherence. Our results show that QND measurements are one of the most promising methods for entanglement generation between two Bose–Einstein condensates.
Abstract We theoretically study a scheme for generating entanglement between two Bose–Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach–Zehnder interferometer, where the coherent light interacts with the atoms due to a quantum nondemolition Hamiltonian. In contrast to standard approaches where a Holstein–Primakoff approximation is used, we use an exact wavefunction approach where the atoms can be initialized in an arbitrary state and the light–atom interaction times can be arbitrary. In the short time regime, it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein–Podolsky–Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.
The theory of quantum information processing for macroscopic qubits is based on the fact that every macroscopic qubit has a conserved number of particles. However, from an experimental point of view, every such qubit experiences processes of decoherence that impact the possibilities for entanglement generation between such qubits and use in quantum information processing efficiently. One of the most prospective methods for generating entanglement between distant atomic BECs is quantum nondemolition measurements. Here, we study how the effects of photon measurement impact the entanglement when photon loss decoherence is included. We employ the thermally entangled state representation (TESR) and integral within the ordered operator(IWOP) approach to obtain the accurate density matrix in a photon loss channel. We demonstrate that varying outcomes of photon number measurements lead to the generation of distinct entangled states, each exhibiting unique characteristics. We find that using the Hofmann-Takeuchi and Duan-Giedke-Cirac-Zoller criterion provides advantages in entanglement detection compared to the Wineland squeezing and EPR steering criterion in such settings.
Abstract The theory of quantum information processing for macroscopic qubits is based on the fact that every macroscopic qubit has a conserved number of particles. However, from an experimental point of view, every such qubit experiences decoherence that impacts the possibilities for entanglement generation between such qubits to be used in quantum information processing efficiently. One of the most prospective methods for generating entanglement between distant atomic BECs is quantum nondemolition measurements. Here, we study how the effects of photon measurement impact the entanglement when photon loss decoherence is included. We employ the thermally entangled state representation (TESR) and integral within the ordered operator (IWOP) approach to obtain the accurate density matrix in a photon loss channel. We demonstrate that varying outcomes of photon number measurements lead to the generation of distinct entangled states, each exhibiting unique characteristics. In the scenario where two photoelectric detectors detect the same number of photons n c = n d , we observe that the entangled state demonstrates greater robustness compared to cases with unequal photon counts, providing a reliable resource for better performance with post-processing. We have used Hofmann-Takeuchi and Duan-Giedke-Cirac-Zoller criteria to detect entanglement and find that these methods offer significant benefits in detecting entanglement compared to the Wineland squeezing and EPR steering criteria, when evaluating the regions of detectable entanglement time in these contexts.
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in the presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits of high-QQQ cavity and bad cavity, the latter corresponding to the so-called superradiant regime, both in the quasiclassical and quantum regimes. We found that three-mode entanglement as well as two-mode atom-atom and atom-radiation entanglement is generally robust against losses and decoherence, thus making the present system a good candidate for the experimental observation of entanglement in condensate systems. In particular, steady-state entanglement may be obtained both between atoms with opposite momenta and between atoms and photons.