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Measuring Interactions in a Bose-Einstein Condensate Using Imbalanced Dynamical Decoupling

Hagai Edri, Boaz Raz, Gavriel Fleurov, Roee Ozeri, Nir Davidson

Published Mar 29, 2020• 1 citation
OpenAlex

Abstract

We measure inter-state interactions in a Bose-Einstein Condensate (BEC) set in a superposition of two states, using microwave spectroscopy. We introduce a population imbalanced dynamic-decoupling scheme that accumulates a phase due to inter-state interactions while canceling intra-state density shifts and external noise sources. Uncertainties of the measured scattering lengths were 0.02$a_{0}$ (where $a_{0}$ is the Bohr radius) for both magnetic sensitive and insensitive transitions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is twisted by the nonlinear interactions, as predicted by Harber et. al and that the twist rate depends on the difference between inter-state and intra-state scattering lengths $a_{22}+a_{11}-2a_{12}$. Our results allow for a better understanding of inter-atomic potentials in $^{87}Rb$. Our scheme can be used for spin squeezing and observing polaron physics close to a Feshbach resonance, where interactions diverge, and strong magnetic noises are ever present.

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We study the evolution of a Bose–Einstein condensate in a two-state superposition due to inter-state interactions. Using a population imbalanced dynamic decoupling scheme, we measure inter-state interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive and insensitive superpositions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is 'twisted' by inter-state interactions, as predicted in [ 1 , 2 ] and the twist rate depends on the difference between inter-state and intra-state scattering lengths a 22 + a 11 − 2 a 12 . We use the non-linear spin dynamics to demonstrate squeezing of Gaussian noise, showing 2.79 ± 0.43 dB squeezing when starting with a noisy state and applying 160 echo pulses, which can be used to increase sensitivity when there are errors in state preparation. Our results allow for a better understanding of inter-atomic potentials in 87 Rb. Our scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics close to Feshbach resonances, where interactions diverge, and strong magnetic noises are ever present.

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The role of interactions in atom interferometry with Bose-Condensed atoms

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In recent years, atom interferometry has become established as an indispensable tool in both fundamental and applied physics. With present state-of-the-art devices based on thermal atoms reaching limits imposed by the momentum spread of the initial atomic wavepacket, it seems natural to ask whether colder sources such as Bose-Einstein condensates may prove beneficial in advancing the precision of interferometric measurements. The thesis at hand aims to inform this question, specifically by examining the role played by atomic interactions in interferometers based on Bose-condensed atoms. Interactions can have both advantageous and deleterious consequences in the context of atom interferometry. They provide a means to control the momentum width of the condensate, and facilitate the generation of nonclassical squeezed states which may enhance the phase sensitivity beyond the shot noise limit. Conversely, the condensate self-interaction causes mean-field shifts, multimode excitations and phase diffusion which can erode both the precision and the accuracy of an interferometric measurement. The question of when and in which systems the detrimental effects of interactions outweigh the advantages of using Bose-Einstein condensates is an important one, and warrants investigation. This thesis presents experimental studies into the role of interactions in both internal- and external-state atom interferometers. As a foundation for these investigations, we describe the design and construction of an apparatus for creating Bose-Einstein condensates of the two stable rubidium isotopes in an optical trap. By sympathetic cooling with a rubidium-87 reservoir, we are able to produce condensates of rubidium-85 in which the interactions may be adjusted by means of a magnetic Feshbach resonance. The tunability afforded by the Feshbach resonance is used to study inelastic losses in ultracold rubidium-85 clouds, as well as the effect of interactions on condensate stability and on the ground state of dual-species mixtures. In particular, we offer new experimental data on the dynamics of collapsing condensates with attractive interactions, over which some controversy has existed since the first experiments more than a decade ago. Good agreement is found between the measured collapse times and a simple mean-field model. Proceeding to interferometry, we present results from Ramsey interferometers operating on the clock transition of rubidium-87 Bose-Einstein condensates. In free-space operation with Raman beamsplitters, we demonstrate projection-noise-limited performance, an important prerequisite for the realisation of squeezing-enhanced sensitivity. Using large condensates of up to 10⁶ atoms and microwave coupling, we study the effect of interactions on the Ramsey fringe contrast. The dominant source of decoherence is found to be spatial dynamics driven by the difference in interparticle interaction strengths, which are analysed using the spin-echo technique and numerical simulations of the Gross-Pitaevskii equation. Finally, we turn our attention to external-state interferometry, implementing a Mach-Zehnder gravimeter using Bragg transitions in a freely falling rubidium-87 condensate. Large-momentum-transfer beamsplitters composed of higher-order Bragg diffraction and Bloch oscillations are used to increase the accumulated phase and thus the sensitivity of the interferometer. The role of interactions in this system is examined, and we canvass methods for achieving further increases in sensitivity.

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Saad J Ansari

Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .

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Interferometric measurement of interhyperfine scattering lengths in Rb87

Pau Gomez, Chiara Mazzinghi, Ferran Martin Ciurana +3 more

We present interferometeric measurements of the $f=1$ to $f=2$ interhyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of $^{87}\mathrm{Rb}$. The interhyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a noninteracting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of interhyperfine scattering length differences, calibrated to intrahyperfine scattering length differences. We report $({a}_{3}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.27(15)$ and $({a}_{1}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.31(13)$, limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of $\ensuremath{\approx}0.3%$ should be possible with this technique.

arXiv:1904.07617•Physical Review A•Sep 10, 2019•5 citations
We measure inter-state interactions in a Bose-Einstein Condensate (BEC) set in a superposition of two states, using microwave spectroscopy. We introduce a population imbalanced dynamic-decoupling scheme that accumulates a phase due to inter-state interactions while canceling intra-state density shifts and external noise sources. Uncertainties of the measured scattering lengths were 0.02a0a_{0}a0​ (where a0a_{0}a0​ is the Bohr radius) for both magnetic sensitive and insensitive transitions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is twisted by the nonlinear interactions, as predicted by Harber et. al and that the twist rate depends on the difference between inter-state and intra-state scattering lengths a22+a11−2a12a_{22}+a_{11}-2a_{12}a22​+a11​−2a12​. Our results allow for a better understanding of inter-atomic potentials in 87Rb^{87}Rb87Rb. Our scheme can be used for spin squeezing and observing polaron physics close to a Feshbach resonance, where interactions diverge, and strong magnetic noises are ever present.
We study the evolution of a Bose–Einstein condensate in a two-state superposition due to inter-state interactions. Using a population imbalanced dynamic decoupling scheme, we measure inter-state interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive and insensitive superpositions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is 'twisted' by inter-state interactions, as predicted in [ 1 , 2 ] and the twist rate depends on the difference between inter-state and intra-state scattering lengths a 22 + a 11 − 2 a 12 . We use the non-linear spin dynamics to demonstrate squeezing of Gaussian noise, showing 2.79 ± 0.43 dB squeezing when starting with a noisy state and applying 160 echo pulses, which can be used to increase sensitivity when there are errors in state preparation. Our results allow for a better understanding of inter-atomic potentials in 87 Rb. Our scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics close to Feshbach resonances, where interactions diverge, and strong magnetic noises are ever present.
In recent years, atom interferometry has become established as an indispensable tool in both fundamental and applied physics. With present state-of-the-art devices based on thermal atoms reaching limits imposed by the momentum spread of the initial atomic wavepacket, it seems natural to ask whether colder sources such as Bose-Einstein condensates may prove beneficial in advancing the precision of interferometric measurements. The thesis at hand aims to inform this question, specifically by examining the role played by atomic interactions in interferometers based on Bose-condensed atoms. Interactions can have both advantageous and deleterious consequences in the context of atom interferometry. They provide a means to control the momentum width of the condensate, and facilitate the generation of nonclassical squeezed states which may enhance the phase sensitivity beyond the shot noise limit. Conversely, the condensate self-interaction causes mean-field shifts, multimode excitations and phase diffusion which can erode both the precision and the accuracy of an interferometric measurement. The question of when and in which systems the detrimental effects of interactions outweigh the advantages of using Bose-Einstein condensates is an important one, and warrants investigation. This thesis presents experimental studies into the role of interactions in both internal- and external-state atom interferometers. As a foundation for these investigations, we describe the design and construction of an apparatus for creating Bose-Einstein condensates of the two stable rubidium isotopes in an optical trap. By sympathetic cooling with a rubidium-87 reservoir, we are able to produce condensates of rubidium-85 in which the interactions may be adjusted by means of a magnetic Feshbach resonance. The tunability afforded by the Feshbach resonance is used to study inelastic losses in ultracold rubidium-85 clouds, as well as the effect of interactions on condensate stability and on the ground state of dual-species mixtures. In particular, we offer new experimental data on the dynamics of collapsing condensates with attractive interactions, over which some controversy has existed since the first experiments more than a decade ago. Good agreement is found between the measured collapse times and a simple mean-field model. Proceeding to interferometry, we present results from Ramsey interferometers operating on the clock transition of rubidium-87 Bose-Einstein condensates. In free-space operation with Raman beamsplitters, we demonstrate projection-noise-limited performance, an important prerequisite for the realisation of squeezing-enhanced sensitivity. Using large condensates of up to 10⁶ atoms and microwave coupling, we study the effect of interactions on the Ramsey fringe contrast. The dominant source of decoherence is found to be spatial dynamics driven by the difference in interparticle interaction strengths, which are analysed using the spin-echo technique and numerical simulations of the Gross-Pitaevskii equation. Finally, we turn our attention to external-state interferometry, implementing a Mach-Zehnder gravimeter using Bragg transitions in a freely falling rubidium-87 condensate. Large-momentum-transfer beamsplitters composed of higher-order Bragg diffraction and Bloch oscillations are used to increase the accumulated phase and thus the sensitivity of the interferometer. The role of interactions in this system is examined, and we canvass methods for achieving further increases in sensitivity.
Precision measurement of spin-dependent inter-hyperfine scattering lengths in 87^{87}87Rb
We present precision measurements of the f=1f=1f=1 to f=2f=2f=2 inter-hyperfine scattering lengths in a single-domain 87^{87}87Rb spinor Bose-Einstein condensate. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a co-magnetometer strategy to cancel laboratory magnetic noise. We find the scattering length ratios a32(12)/a20(1)=−1.27(15)a_{32}^{(12)}/a_{20}^{(1)}=-1.27(15)a32(12)​/a20(1)​=−1.27(15) and a12(12)/a20(1)=−1.31(13)a_{12}^{(12)}/a_{20}^{(1)}=-1.31(13)a12(12)​/a20(1)​=−1.31(13), limited by atom number fluctuations. Using better control of atom number, we estimate precisions of ∼0.3%\sim 0.3\%∼0.3% should be possible with this technique.
A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.
Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .
We present interferometeric measurements of the f=1f=1f=1 to f=2f=2f=2 interhyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb. The interhyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a noninteracting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of interhyperfine scattering length differences, calibrated to intrahyperfine scattering length differences. We report $({a}_{3}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.27(15)$ and $({a}_{1}^{(12)}\ensuremath{-}{a}_{2}^{(12)})/({a}_{2}^{(1)}\ensuremath{-}{a}_{0}^{(1)})=\ensuremath{-}1.31(13)$, limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of $\ensuremath{\approx}0.3%$ should be possible with this technique.