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Soliton interferometry with very narrow barriers obtained from spatially dependent dressed states [dataset]

Callum L. Grimshaw

Published Apr 9, 2021• 0 citations
Publisher

Abstract

Bright solitons in atomic Bose-Einstein condensates are a strong candidate for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. One analog to a beam splitter for these solitons is a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but the width in a typical realisation, using a blue-detuned optical dipole potential, is limited by the wavelength of the laser light. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal.

DOI
10.15128/r11j92g749r

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Soliton Interferometry with Very Narrow Barriers Obtained from Spatially Dependent Dressed States

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Bright solitons in atomic Bose-Einstein condensates are strong candidates for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. An analog to a beam splitter is then a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but in a typical realization using a blue-detuned optical dipole potential, the width is limited by the laser wavelength. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal configuration.

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Dynamics of bright solitons in Bose–Einstein condensates: investigations of soliton behaviour in the vector Gross–Pitaevskii equation and applications to enhanced matter-wave interferometry

Callum L. Grimshaw

Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.

•Jan 1, 2021•0 citations

Splitting and recombination of bright-solitary-matter waves

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Communications Physics•Mar 13, 2020•35 citations

Splitting and recombination of bright-solitary-matter waves

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arXiv:1906.06083•May 9, 2019•2 citations

Soliton dynamics in the Gross–Pitaevskii equation : splitting, collisions and interferometry

J. L. Helm

Bose–Einstein condensates with attractive interactions have stable 1D solutions in the form of bright solitary-waves. These solitary waves behave, in the absence of external potentials, like macroscopic quantum particles. This opens up a wide array of applications for the testing of quantum mechanical behaviours and precision measurement. Here we investigate these applications with particular focus on the interactions of bright solitary-waves with narrow potential barriers. We first study bright solitons in the Gross–Pitaevskii equation as they are split on Gaussian and δ-function barriers, and then on Gaussian barriers in a low energy system. We present analytic and numerical results determining the general region in which a soliton may not be split on a finite width potential barrier. Furthermore, we test the sensitivity of the system to quantum fluctuations. We then study fast-moving bright solitons colliding at a narrow Gaussian potential barrier. In the limiting case of a δ-function barrier, we show analytically that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and determine whether the outgoing waves are bright solitons. We use numerical simulations to show that outside the high velocity limit nonlinear effects introduce a skew to the phase-dependence. Finally, we use these results to analyse the process of soliton interferometry. We develop analyses of both toroidal and harmonic trapping geometries for Mach–Zehnder interferometry, and then two implementations of a toroidal Sagnac inter- ferometer, also giving the analytical determination of the Sagnac phase in such systems. These results are again verified numerically. In the Mach–Zehnder case, we again probe the systems sensitivity to quantum fluctuations.

•Jan 1, 2014•0 citations
Bright solitons in atomic Bose-Einstein condensates are a strong candidate for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. One analog to a beam splitter for these solitons is a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but the width in a typical realisation, using a blue-detuned optical dipole potential, is limited by the wavelength of the laser light. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal.
Bright solitons in atomic Bose-Einstein condensates are strong candidates for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. An analog to a beam splitter is then a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but in a typical realization using a blue-detuned optical dipole potential, the width is limited by the laser wavelength. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal configuration.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.
© 2020, The Author(s).Atomic Bose–Einstein condensates confined in quasi-1D waveguides can support bright-solitary-matter waves when interatomic interactions are sufficiently attractive to cancel dispersion. Such solitary-matter waves are excellent candidates for highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-wave interferometers. In this work, we demonstrate experimentally the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, realizing the fundamental components of an interferometer. We show that for a sufficiently narrow barrier, interference-mediated recombination can dominate over velocity-filtering effects. Our theoretical analysis shows that interference-mediated recombination is extremely sensitive to the barrier position, predicting strong oscillations in the interferometer output as the barrier position is adjusted over just a few micrometres. These results highlight the potential of soliton interferometry, while putting tight constraints on the barrier stability needed in future experimental implementations.
Abstract Atomic Bose–Einstein condensates confined in quasi-1D waveguides can support bright-solitary-matter waves when interatomic interactions are sufficiently attractive to cancel dispersion. Such solitary-matter waves are excellent candidates for highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-wave interferometers. In this work, we demonstrate experimentally the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, realizing the fundamental components of an interferometer. We show that for a sufficiently narrow barrier, interference-mediated recombination can dominate over velocity-filtering effects. Our theoretical analysis shows that interference-mediated recombination is extremely sensitive to the barrier position, predicting strong oscillations in the interferometer output as the barrier position is adjusted over just a few micrometres. These results highlight the potential of soliton interferometry, while putting tight constraints on the barrier stability needed in future experimental implementations.
Solitons are long-lived wavepackets that propagate without dispersion and exist in a wide range of one-dimensional (1D) nonlinear systems. A Bose-Einstein condensate trapped in a quasi-1D waveguide can support bright-solitary-matter waves (3D analogues of solitons) when interatomic interactions are sufficiently attractive that they cancel dispersion. Solitary-matter waves are excellent candidates for a new generation of highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-waves interferometers. However, such an interferometer is yet to be realised experimentally. In this work, we demonstrate the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, which brings together the fundamental components of an interferometer. We show that both interference-mediated recombination and classical velocity filtering effects are important, but for a sufficiently narrow barrier interference-mediated recombination can dominate. We reveal the extreme sensitivity of interference-mediated recombination to the experimental parameters, highlighting the potential of soliton interferometry.
Bose–Einstein condensates with attractive interactions have stable 1D solutions in the form of bright solitary-waves. These solitary waves behave, in the absence of external potentials, like macroscopic quantum particles. This opens up a wide array of applications for the testing of quantum mechanical behaviours and precision measurement. Here we investigate these applications with particular focus on the interactions of bright solitary-waves with narrow potential barriers. We first study bright solitons in the Gross–Pitaevskii equation as they are split on Gaussian and δ-function barriers, and then on Gaussian barriers in a low energy system. We present analytic and numerical results determining the general region in which a soliton may not be split on a finite width potential barrier. Furthermore, we test the sensitivity of the system to quantum fluctuations. We then study fast-moving bright solitons colliding at a narrow Gaussian potential barrier. In the limiting case of a δ-function barrier, we show analytically that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and determine whether the outgoing waves are bright solitons. We use numerical simulations to show that outside the high velocity limit nonlinear effects introduce a skew to the phase-dependence. Finally, we use these results to analyse the process of soliton interferometry. We develop analyses of both toroidal and harmonic trapping geometries for Mach–Zehnder interferometry, and then two implementations of a toroidal Sagnac inter- ferometer, also giving the analytical determination of the Sagnac phase in such systems. These results are again verified numerically. In the Mach–Zehnder case, we again probe the systems sensitivity to quantum fluctuations.