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

Measuring the quantum state of a Bose-Einstein condensate

Eric L. Bolda, Sze Meng Tan, Daniel F. Walls

Published Jun 1, 1998• 37 citations
Publisher

Abstract

We describe an atomic interferometer based on Raman transitions between two hyperfine states. We show how atom count probabilities at the output of the interferometer can be used to reconstruct the joint multiparticle state of a two-mode Bose-Einstein condensate. Two data collection schemes are compared, via numerical solution for the density matrix from the probability data and analytical estimates of the errors are made. In the first scheme, only the phase of the interferometer is varied. We prove that state reconstruction is impossible for the case of a balanced beam splitter; otherwise, the problem is ill-conditioned. In the second scheme, both the phase and transmission parameters are varied, the $Q$ function can be measured directly, and the reconstruction of the state is well conditioned.

DOI
10.1103/physreva.57.4686

Related papers

Reconstruction of the Joint State of a Two-Mode Bose-Einstein Condensate

Eric L. Bolda, Sze Meng Tan, Daniel F. Walls

We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.

arXiv:quant-ph/9703014•Physical Review Letters•Dec 15, 1997•16 citations

Quantum state reconstruction of a Bose-Einstein condensate

S Mancini, P Tombesi

We propose a tomographic scheme to reconstruct the quantum state of a Bose-Einstein condensate, exploiting the radiation field as a probe and considering the atomic internal degrees of freedom. The density matrix in the number state basis can be directly retrieved from the atom counting probabilities.

arXiv:quant-ph/9710038•Europhysics Letters (EPL)•Nov 15, 1997•16 citations

Quantum State Reconstruction of a Bose-Einstein Condensate

Mancini, S, Tombesi, P

We propose a tomographic scheme to reconstruct the quantum state of a Bose-Einstein condensate, exploiting the radiation field as a probe and considering the atomic internal degrees of freedom. The density matrix in the number state basis can be directly retrieved from the atom counting probabilities.

•Jan 1, 1997•10 citations

Measuring the multiparticle state of a two-mode Bose-Einstein condensate

Eric L. Bolda, S. M. Tan, Daniel F. Walls

Summary form only given. Much recent interest in the new dilute alkali Bose-Einstein condensate sytems from the idea that the multiparticle state may be highly squeezed due to collisions. The internal states of the atoms can serve as a probe of this squeezing. Motivated by the success of homodyne tomography in measuring the quantum state of light, we propose to obtain the complete density matrix of a two-mode condensate from repeated atom-counting measurements.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Information-Recycling Beam Splitters for Quantum Enhanced Atom Interferometry

Simon A. Haine

We propose a scheme to significantly enhance the sensitivity of atom interferometry performed with Bose-Einstein condensates. When an optical two-photon Raman transition is used to split the condensate into two modes, some information about the number of atoms in one of the modes is contained in one of the optical modes. We introduce a simple model to describe this process, and find that by processing this information in an appropriate way, the phase sensitivity of atom interferometry can be enhanced by more than a factor of 10 for realistic parameters.

arXiv:1206.3025•Physical Review Letters•Jan 28, 2013•35 citations

Interferometry and precision measurements with Bose-condensed atoms

D. Döring

Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.

•Jan 1, 2011•0 citations
We describe an atomic interferometer based on Raman transitions between two hyperfine states. We show how atom count probabilities at the output of the interferometer can be used to reconstruct the joint multiparticle state of a two-mode Bose-Einstein condensate. Two data collection schemes are compared, via numerical solution for the density matrix from the probability data and analytical estimates of the errors are made. In the first scheme, only the phase of the interferometer is varied. We prove that state reconstruction is impossible for the case of a balanced beam splitter; otherwise, the problem is ill-conditioned. In the second scheme, both the phase and transmission parameters are varied, the QQQ function can be measured directly, and the reconstruction of the state is well conditioned.
We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.
We propose a scheme to significantly enhance the sensitivity of atom interferometry performed with Bose-Einstein condensates. When an optical two-photon Raman transition is used to split the condensate into two modes, some information about the number of atoms in one of the modes is contained in one of the optical modes. We introduce a simple model to describe this process, and find that by processing this information in an appropriate way, the phase sensitivity of atom interferometry can be enhanced by more than a factor of 10 for realistic parameters.
Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.