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arXiv:0809.5222 · New Journal of Physics

Entangled light from Bose–Einstein condensates

H T Ng, Sougato Bose

Published Apr 3, 2009• 4 citations
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Abstract

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.

DOI
10.1088/1367-2630/11/4/043009

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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.
We analyze a scheme for generating entanglement between two spinor Bose-Einstein condensates (BECs). The BECs are off-resonantly coupled to a common photon mode and are controlled by external lasers to induce a SzSz{S}^{z}{S}^{z}SzSz interaction, where Sz{S}^{z}Sz is the total spin of the BEC. We directly simulate the scheme numerically for small systems and show the performance of the scheme. The scaling of the entanglement to large-scale systems under realistic conditions of spontaneous emission and cavity photon loss is analyzed. It is shown that both entanglement in the beyond-continuous-variable regime can be generated, where the entanglement is of the order of the maximal entanglement between the systems.
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.
In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser, and a strong classical coupling laser, which form a three-level $\ensuremath{\Lambda}$-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and interatomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.
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.