Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate

N. Piovella, Mary M. Cola, R. Bonifacio

Published Jan 31, 2003• 51 citations
Publisher

Abstract

We present a quantum description of the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser. In the linear regime, the atomic medium is described approximately by two momentum states coupled to the radiation mode. We calculate the evolution of the operators in the Heisenberg picture and their expectation values, such as average and variance of the occupation numbers, atom-atom and atom-field correlations, and two-mode squeezing parameters. Then, we disentangle the evolution operator and obtain the exact evolution of the state vector in the linear regime. This allows us to demostrate that the system can be atom-atom or atom-field thermally entangled. We define the quasiclassical and the quantum recoil limits, for which explicit expressions of the average population numbers are obtained.

DOI
10.1103/physreva.67.013817

Related papers

Entanglement in a Bose–Einstein condensate by collective atomic recoil

Mary M. Cola, Matteo G. A. Paris, N. Piovella +1 more

We address the interaction between a Bose–Einstein condensate and a single-mode quantized radiation field in the presence of a strong far off-resonant pump laser. The generation of atom–atom and atom–field entanglement is demonstrated in the linear regime. The effects of cavity losses are taken into account and an analytic solution of the corresponding master equation is given in terms of the Wigner function of the system.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 24, 2004•5 citations

A condensate in a lossy cavity: Collective atomic recoil and generation of entanglement

Mary M. Cola, Matteo G. A. Paris, N. Piovella +1 more

The interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser generates, in proper regimes, atom-atom and atom-field entanglement. The effects of cavity losses are taken into account and an analytic solution of the corresponding master equation is given in terms of the Wigner function of the system.

Journal of Modern Optics•Apr 1, 2004•0 citations

Robust generation of entanglement in Bose-Einstein condensates by collective atomic recoil

Mary M. Cola, Matteo G. A. Paris, N. Piovella

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-$Q$ 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.

arXiv:quant-ph/0404109•Physical Review A•Oct 13, 2004•30 citations

Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil

Samanta Piano, Gerardo Adesso

We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.

•Jan 1, 2013•5 citations

Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil

Samanta Piano, Gerardo Adesso

We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.

arXiv:1311.5940•Entropy•May 17, 2013•7 citations

Optical control and entanglement of atomic Schrödinger fields

M. G. Moore, Pierre Meystre

We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.

arXiv:quant-ph/9807088•Physical Review A•Mar 1, 1999•64 citations
We present a quantum description of the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser. In the linear regime, the atomic medium is described approximately by two momentum states coupled to the radiation mode. We calculate the evolution of the operators in the Heisenberg picture and their expectation values, such as average and variance of the occupation numbers, atom-atom and atom-field correlations, and two-mode squeezing parameters. Then, we disentangle the evolution operator and obtain the exact evolution of the state vector in the linear regime. This allows us to demostrate that the system can be atom-atom or atom-field thermally entangled. We define the quasiclassical and the quantum recoil limits, for which explicit expressions of the average population numbers are obtained.
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.
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.
We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.