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 Letters

Interferometry below the Standard Quantum Limit with Bose-Einstein Condensates

Jacob Dunningham, Keith R. Burnett, Stephen Mark Barnett

Published Sep 18, 2002• 151 citations
Publisher

Abstract

We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.

DOI
10.1103/physrevlett.89.150401

Related papers

Sub-shot-noise-limited measurements with Bose-Einstein condensates

Jacob Dunningham, Keith R. Burnett

We discuss practical schemes for using entangled Bose-Einstein condensates to detect phase shifts with a resolution better than the shot-noise limit. We begin by outlining a procedure for demonstrating how squeezed matter waves can be used to make measurements by simply lowering and raising a potential barrier between two condensates. The phase shift is read out by a scheme which involves releasing the condensates and studying the collapses and revivals of the visibility of the observed interference fringes. Finally we show how this scheme could be extended to measurements of other quantities such as gravity. All the steps of this process are attainable with current technology and so may provide a practical route for achieving enhanced resolution measurements with matter waves.

Physical Review A•Sep 2, 2004•70 citations

Quantum phase of Bose-Einstein condensates

Jacob Dunningham, Dunningham, Jacob Andrew

The quantum phase of a Bose-Einstein condensate has long been a subject fraught with misunderstanding and confusion. In this thesis we provide a consis- tent description of this phenomenon and, in particular, discuss how phase may be defined, created, manipulated, and controlled. We begin by describing how it is possible to set up a reference condensate against which the phase of other condensates can be compared. This allows us to think of relative phases as if they were absolute and gives a clear and precise definition to 'the phase of a condensate'. A relative phase may also be established by coupling condensates and we show how this can be controlled. We then extend this model to explain how the phase along a chain of coupled condensates can lock naturally without the need for any measurements. The second part of the thesis deals primarily with the link between entangle- ment and phase. We show that, in general, the more entangled a state is, the better its phase resolution. This leads us to consider schemes by which maximally entangled states may be able to be created since these should give the best prac- tical advantages over their classical counterparts. We consider two such states: a number correlated pair of condensates and a Schrodinger cat state. Both schemes are shown to be remarkably robust to loss. A comparison of the merits of these two states, as the inputs to an interferom- eter, reveals very different behaviours. In particular, the number correlated state performs significantly better than the cat state in the presence of loss, which means that it might be useful in interferometry and frequency standard schemes where phase resolution is of the utmost importance. Finally, we propose a scheme for concentrating the entanglement between con- densates, which is an important step in quantum communication protocols. This, along with the ability to manipulate phase and entanglement, suggests that the future for condensates holds not only academic interest but great potential for practical applications.

•Jan 1, 2001•0 citations

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

Phase-resolution limit in the macroscopic interference between Bose-Einstein condensates

Sigmund Kohler, Fernando Sols

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.

arXiv:cond-mat/9912252•Physical Review A•Apr 17, 2001•13 citations

Using quantum interferometers to make measurements at the Heisenberg limit

Jacob Dunningham, T. Kim

In recent work we proposed a quantum interferometer and showed how it could be used to significantly enhance the resolution that could be achieved in measurement schemes. In this paper, we outline a detailed scheme on how these quantum interferometers could be implemented. We also analyze the effects of dissipation and of imperfect detectors and show that this scheme is remarkably robust to both. This suggests that quantum interferometers may provide a promising route for implementing sub-shot-noise limited measurements in the laboratory.

Journal of Modern Optics•Jan 10, 2006•24 citations

Entanglement-Enhanced Atomic Gravimeter

Christophe Cassens, Bernd Meyer-Hoppe, Ernst Maria Rasel +1 more

Interferometers based on ultracold atoms enable an absolute measurement of inertial forces with unprecedented precision. However, their resolution is fundamentally restricted by quantum fluctuations. Improved resolutions with entangled or squeezed atoms were demonstrated in internal-state measurements for thermal and quantum-degenerate atoms and, recently, for momentum-state interferometers with laser-cooled atoms. Here, we present a gravimeter based on Bose-Einstein condensates with a sensitivity of − 1.7 − 0.5 + 0.4 dB beyond the standard quantum limit. Interferometry with Bose-Einstein condensates combined with delta-kick collimation minimizes atom loss in and improves scalability of the interferometer to very-long-baseline atom interferometers.

arXiv:2404.18668•Physical Review X•Feb 11, 2025•30 citations
We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.
We discuss practical schemes for using entangled Bose-Einstein condensates to detect phase shifts with a resolution better than the shot-noise limit. We begin by outlining a procedure for demonstrating how squeezed matter waves can be used to make measurements by simply lowering and raising a potential barrier between two condensates. The phase shift is read out by a scheme which involves releasing the condensates and studying the collapses and revivals of the visibility of the observed interference fringes. Finally we show how this scheme could be extended to measurements of other quantities such as gravity. All the steps of this process are attainable with current technology and so may provide a practical route for achieving enhanced resolution measurements with matter waves.
The quantum phase of a Bose-Einstein condensate has long been a subject fraught with misunderstanding and confusion. In this thesis we provide a consis- tent description of this phenomenon and, in particular, discuss how phase may be defined, created, manipulated, and controlled. We begin by describing how it is possible to set up a reference condensate against which the phase of other condensates can be compared. This allows us to think of relative phases as if they were absolute and gives a clear and precise definition to 'the phase of a condensate'. A relative phase may also be established by coupling condensates and we show how this can be controlled. We then extend this model to explain how the phase along a chain of coupled condensates can lock naturally without the need for any measurements. The second part of the thesis deals primarily with the link between entangle- ment and phase. We show that, in general, the more entangled a state is, the better its phase resolution. This leads us to consider schemes by which maximally entangled states may be able to be created since these should give the best prac- tical advantages over their classical counterparts. We consider two such states: a number correlated pair of condensates and a Schrodinger cat state. Both schemes are shown to be remarkably robust to loss. A comparison of the merits of these two states, as the inputs to an interferom- eter, reveals very different behaviours. In particular, the number correlated state performs significantly better than the cat state in the presence of loss, which means that it might be useful in interferometry and frequency standard schemes where phase resolution is of the utmost importance. Finally, we propose a scheme for concentrating the entanglement between con- densates, which is an important step in quantum communication protocols. This, along with the ability to manipulate phase and entanglement, suggests that the future for condensates holds not only academic interest but great potential for practical applications.
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 study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.
In recent work we proposed a quantum interferometer and showed how it could be used to significantly enhance the resolution that could be achieved in measurement schemes. In this paper, we outline a detailed scheme on how these quantum interferometers could be implemented. We also analyze the effects of dissipation and of imperfect detectors and show that this scheme is remarkably robust to both. This suggests that quantum interferometers may provide a promising route for implementing sub-shot-noise limited measurements in the laboratory.
Interferometers based on ultracold atoms enable an absolute measurement of inertial forces with unprecedented precision. However, their resolution is fundamentally restricted by quantum fluctuations. Improved resolutions with entangled or squeezed atoms were demonstrated in internal-state measurements for thermal and quantum-degenerate atoms and, recently, for momentum-state interferometers with laser-cooled atoms. Here, we present a gravimeter based on Bose-Einstein condensates with a sensitivity of − 1.7 − 0.5 + 0.4 dB beyond the standard quantum limit. Interferometry with Bose-Einstein condensates combined with delta-kick collimation minimizes atom loss in and improves scalability of the interferometer to very-long-baseline atom interferometers.