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Communications in Theoretical Physics

Fast Generation of GHZ States with Bose—Einstein Condensate in a Cavity*

Gang Zhang, Jian Zhou, Zheng‐Yuan Xue

Published May 1, 2015• 0 citations
Publisher

Abstract

Abstract It is shown that strong coupling of Bose—Einstein condensates to an optical cavity can be realized experimentally. With an additional driven microwave field, we show that a highly nonlinear coupling among atoms in a Bose—Einstein condensate can be induced with the assistance of the cavity mode. With such interaction, we can investigate the generation of many body entangled states. In particularly, we show that multipartite entangled GHZ states can be obtained in such architecture with current available techniques.

DOI
10.1088/0253-6102/63/5/588

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Abstract It is shown that strong coupling of Bose—Einstein condensates to an optical cavity can be realized experimentally. With an additional driven microwave field, we show that a highly nonlinear coupling among atoms in a Bose—Einstein condensate can be induced with the assistance of the cavity mode. With such interaction, we can investigate the generation of many body entangled states. In particularly, we show that multipartite entangled GHZ states can be obtained in such architecture with current available techniques.
We consider the model of a weakly driven optical cavity containing two clouds of atomic Bose–Einstein condensates (BECs). Nonclassical photon correlations and correlations between the two atomic BECs are investigated under different cavity conditions including strong atom-field coupling and bad cavity regime. We show that the nonlinear interatom collisional interactions in BEC leads to a significant loss of cavity light coherence. Various types of nonclassical properties are investigated such as sub-Poissonian statistics, antibunching and entanglement. We show that the entanglement can be generated between BECs and the cavity field. The time evolution of entanglement is also numerically studied.
We propose a method to generate entangled light with a Bose-Einstein condensate trapped in a cavity, a system realized in recent experiments. The atoms of the condensate are trapped in a periodic potential generated by a cavity mode. The condensate is continuously pumped by a laser and spontaneously emits a pair of photons of different frequencies in two distinct cavity modes. In this way, the condensate mediates entanglement between two cavity modes, which leak out and can be separated and exhibit continuous variable entanglement. The scheme exploits the experimentally demonstrated strong, steady and collective coupling of condensate atoms to a cavity field.
We propose a method to generate entangled light with a Bose–Einstein condensate trapped in a cavity, a system realized in recent experiments. The atoms of the condensate are trapped in a periodic potential generated by a cavity mode. The condensate is continuously pumped by a laser and spontaneously emits a pair of photons of different frequencies in two distinct cavity modes. In this way, the condensate mediates entanglement between two cavity modes, which leak out and can be separated and exhibit continuous variable entanglement. The scheme exploits the experimentally demonstrated strong, steady and collective coupling of condensate atoms to a cavity field.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.
Prospects for reaching persistent entanglement between two spatially-separated atomic Bose–Einstein condensates are outlined. The system setup comprises two condensates loaded in an optical lattice, which, in return, is confined within a high-Q optical resonator. The system is driven by an external laser that illuminates the atoms, such that photons can scatter into the cavity. In the superradiant phase, a cavity field is established, and we show that the emerging cavity-mediated interactions between the two condensates is capable of entangling them despite photon losses. This macroscopic atomic entanglement is sustained throughout the time-evolution apart from occasions of sudden deaths/births. Using an auxiliary photon mode and coupling it to a collective quadrature of the two condensates, we demonstrate that the auxiliary mode’s squeezing is proportional to the atomic entanglement, and as such, it can serve as a probe field of the macroscopic entanglement.
Prospects for reaching persistent entanglement between two spatially-separated atomic Bose-Einstein condensates are outlined. The system setup comprises two condensates loaded in an optical lattice, which, in return, is confined within a high-Q optical resonator. The system is driven by an external laser that illuminates the atoms, such that photons can scatter into the cavity. In the superradiant phase, a cavity field is established, and we show that the emerging cavity-mediated interactions between the two condensates is capable of entangling them despite photon losses. This macroscopic atomic entanglement is sustained throughout the time-evolution apart from occasions of sudden deaths/births. Using an auxiliary photon mode and coupling it to a collective quadrature of the two condensates, we demonstrate that the auxiliary mode's squeezing is proportional to the atomic entanglement, and as such, it can serve as a probe field of the macroscopic entanglement.