© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Generation of maximally entangled states of a Bose-Einstein condensate and Heisenberg-limited phase resolution

Christopher C. Gerry, Richard A. Campos

Published Aug 28, 2003• 43 citations

Abstract

We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.

DOI: 10.1103/physreva.68.025602

Related papers

Phase resolution for Bose-Einstein condensates

Jacob Dunningham, Keith R. Burnett

We discuss how the nature of the relative phase between two entangled condensates differs depending on whether the entanglement is established by measurements or by coupling. In the former case, the limit of the resulting phase resolution scales inversely with the square root of the number of atoms. This limit can be surpassed, however, when the condensates are entangled by coupling and can reach the fundamental Heisenberg limit where the phase resolution scales inversely with the number of atoms involved.

Physical Review A•May 3, 2000•18 citations

Fast generation of many-atom maximal entanglement in spin-1 Bose-Einstein condensates

GuangSi Meng, Huiming Xu, Song Yang +4 more

We propose a scheme for generating many-atom maximal entanglement states in spin-1 Bose-Einstein condensates. By applying a far-off-resonate blue-detuned linear-polarized laser to the condensates, the hyperfine level $F=1,m=0$ ground state and the hyperfine $F=0$ excited state are conveniently coupled. Such a configuration is more efficient and provides a fast implementation of the maximally entangled GHZ state, using only half of the time that is required in single-atom Raman-transition-based schemes [You, Phys. Rev. Lett. 90, 030402 (2003)].

Physical Review A•Mar 26, 2012•2 citations

Generation of Entangled Coherent States in Raman-Coupled Bose–Einstein Condensates

Kuang Le-Man, Aihua Zeng, Kuang Zhen-Hua

A method for producing entangled coherent states (ECSs) for atomic Bose–Einstein condensates (BECs) is presented. The proposed method involves a BEC with three internal states and two classical laser beams in a three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulating strengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.

Chinese Physics Letters•May 28, 2004•4 citations

Parity measurements, Heisenberg-limited phase estimation, and beyond

Christopher C. Gerry, Adil Benmoussa, Richard A. Campos

We review the use of parity measurements to obtain Heisenberg-limited phase shift measurements from interferometry performed with maximally path entangled two mode states containing N photons, contrasting this measure with the method of coincidence detection which requires a number of such detections that scales with N. For large N, coincidence measurements will become impractical. In contrast, the parity method we propose is independent of N. In addition, with the parity approach, one can use an entanglement of a coherent state and the vacuum to approach the Heisensberg limit of phase resolution without the requirement of first producing a Fock state of large photon number. We also show in a very simple way, using Maximally entangled states and parity measurements that it is possible to go beyond the Heisenberg limit if the phase shifts are generated by a nonlinear Kerr-like interaction.

Journal of Modern Optics•Sep 10, 2007•24 citations

Generation of Entangled Coherent States in Raman-Coupled Bose-Einstein Condensates

KUANGLe-Man, ZENGAi-Hua, KUANGZhen-Hua

A method for producing entangled coherent states (ECSs) for atomic Bose-Einstein condensates (BECs) ispresented. The proposed method involves a BEC with three internal states and two classical laser beams ina three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulatingstrengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.

Chinese Physics Letters•Jan 1, 2004•0 citations

Quantum entanglement of many atoms in spinor Bose-Einstein condensates

Xu‐Bo Zou, K. Pahlke, Wolfgang M. Mathis

We present a theoretical analysis of the experimental scheme for creating maximally entangled states of many atoms in spin-1 Bose-Einstein condensates by driving single atom Raman transition [Li You, Phys. Rev. Lett. 90, 030402 (2003)]. It is shown that, with the help of strong external laser pulses, the model proposed by You can be greatly simplified. Using this simplified interaction, an analytical expression is given for the entangled states between atoms with hyperfine spin $\ensuremath{-}1$ and 1. We also show how to generate the entangled state between atoms with hyperfine spin 0 and 1.

Physical Review A•May 10, 2004•8 citations

We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.

We discuss how the nature of the relative phase between two entangled condensates differs depending on whether the entanglement is established by measurements or by coupling. In the former case, the limit of the resulting phase resolution scales inversely with the square root of the number of atoms. This limit can be surpassed, however, when the condensates are entangled by coupling and can reach the fundamental Heisenberg limit where the phase resolution scales inversely with the number of atoms involved.

We propose a scheme for generating many-atom maximal entanglement states in spin-1 Bose-Einstein condensates. By applying a far-off-resonate blue-detuned linear-polarized laser to the condensates, the hyperfine level

F=1,m=0

ground state and the hyperfine

F=0

excited state are conveniently coupled. Such a configuration is more efficient and provides a fast implementation of the maximally entangled GHZ state, using only half of the time that is required in single-atom Raman-transition-based schemes [You, Phys. Rev. Lett. 90, 030402 (2003)].

We review the use of parity measurements to obtain Heisenberg-limited phase shift measurements from interferometry performed with maximally path entangled two mode states containing N photons, contrasting this measure with the method of coincidence detection which requires a number of such detections that scales with N. For large N, coincidence measurements will become impractical. In contrast, the parity method we propose is independent of N. In addition, with the parity approach, one can use an entanglement of a coherent state and the vacuum to approach the Heisensberg limit of phase resolution without the requirement of first producing a Fock state of large photon number. We also show in a very simple way, using Maximally entangled states and parity measurements that it is possible to go beyond the Heisenberg limit if the phase shifts are generated by a nonlinear Kerr-like interaction.

We present a theoretical analysis of the experimental scheme for creating maximally entangled states of many atoms in spin-1 Bose-Einstein condensates by driving single atom Raman transition [Li You, Phys. Rev. Lett. 90, 030402 (2003)]. It is shown that, with the help of strong external laser pulses, the model proposed by You can be greatly simplified. Using this simplified interaction, an analytical expression is given for the entangled states between atoms with hyperfine spin $\ensuremath{-}1$ and 1. We also show how to generate the entangled state between atoms with hyperfine spin 0 and 1.