Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

Manju, P.; Hardman, Kyle; Sooriyabandara, M. A.; Wigley, P. B.; Close, John; Robins, Nicholas; Hush, Michael; Szigeti, Stuart S.

doi:10.1103/physreva.98.053629

“…Interestingly, the steep energy dependence of the measured transmission functions produces a velocity filtering effect, whereby the transmitted soliton always has a higher centre of mass kinetic energy than the reflected soliton 18,22,33 . This causes the transmitted soliton to have a larger oscillation amplitude than the reflected soliton, which we directly observe in the trajectories of the daughter solitons (see Extended Data Fig.…”

Section: Controllable Splittingmentioning

confidence: 99%

Splitting and recombination of bright-solitary-matter waves

Wales

¹

,

Rakonjac

²

,

Billam

³

et al. 2020

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Solitons are long-lived wavepackets that propagate without dispersion and exist in a wide range of onedimensional (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.Bright-solitary waves, referred to as solitons in this work, are wavepackets that propagate in a quasi-1D geometry without dispersion, owing to a self-focussing nonlinearity. They are of fundamental interest in a broad range of settings due to their ubiquity in nonlinear systems, which occur prolifically in nature 1, 2 . In Bose-Einstein 1 arXiv:1906.06083v1 [cond-mat.quant-gas] 14 Jun 2019 condensates (BECs) the nonlinearity is provided by interatomic interactions governed by the s-wave scattering length, which can be tuned using a magnetic Feshbach resonance 3 . Bright solitons in BECs of 7 Li, 85 Rb, 39 K and 133 Cs have so far been experimentally demonstrated 4-10 . Understanding and probing the coherent phase carried by matter-wave solitons is an area of particular relevance for BEC physics, both because it is important in determining the stability of soliton-soliton collisions 10-14 and because there is a great interest in using solitons for atom interferometry 15-22 .Matter-wave interferometers have emerged as a means of achieving unprecedented sensitivity in interferometric measurements 23-26 . However, they have typically been limited by either interatomic collisions or dispersion of the atomic wavepackets, which cause dephasing and a reduced signal to noise, respectively 27 . Previous works have successfully reduced the impact of interatomic collisions through the control of interatomic interactions 28, 29 , or by generating squeezed states 30, 31 . However, dispersion remains a limitation. A soliton-based interferometer has the potential to overcome dispersion, allowing for much longer phase-accumulation times, albeit for an increased quantum noise 32 . To date, only one experiment has demonstrated interferometry with a soliton 8 , in which Bragg pulses were used for splitting and recombination. However, interferom...

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“…Furthermore, BECs are finite momentum width sources that typically have nonnegligible inter-atomic interactions. These inter-atomic interactions couple different momentum components of the cloud and also have a non-trivial effect on the transmission dynamics [48][49][50][51] . Therefore, although the analytic study can guide our parameter choice, it cannot provide detailed modelling of an interacting BEC's transmission dynamics through double Gaussian barriers.…”

Section: Fabry-perot Interferometrymentioning

confidence: 99%

“…Specifically, as the scattering length goes from positive to negative, the three-body recombination loss increases due to the difference in the propagation dynamics of the BEC as it approaches the barrier. Condensates with positive and negative scattering lengths undergo expanding or focussing, respectively, under free propagation 50,58,59 . These dynamics modify the cloud density and therefore the overall three-body loss as well.…”

Section: Analysis Of Resonant Transmissionmentioning

confidence: 99%

“…In the presence of inter-atomic interactions the peaks are either further suppressed or not well-defined, as compared to the non-interacting cloud. This reduction in contrast is caused by the additional interaction-induced expansion of the BEC's momentum distribution, scattering-length-dependent distortions in the momentum distribution that occur during interaction with barriers 50 , and non-trivial intra-cavity dynamics due to the presence of inter-atomic interactions.…”

Section: Analysis Of Resonant Transmissionmentioning

confidence: 99%

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An atomic Fabry–Perot interferometer using a pulsed interacting Bose–Einstein condensate

Manju

¹

,

Hardman

²

,

Wigley

³

et al. 2020

Sci Rep

Self Cite

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We numerically demonstrate atomic Fabry–Perot resonances for a pulsed interacting Bose–Einstein condensate (BEC) source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice, which we determined using a previously-developed analytical model for a plane matter-wave incident on a double rectangular barrier system. Through numerical simulations using the non-polynomial Schödinger equation—an effective one-dimensional Gross–Pitaevskii equation—we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For $$^{85}$$ 85 Rb atomic sources with the current experimentally-achievable momentum width of $$0.02 \hbar k_0$$ 0.02 ħ k 0 [$$k_0 = 2\pi /(780~\text {nm})$$ k 0 = 2 π / ( 780 nm ) ], we show that reasonably high contrast Fabry–Perot resonant transmission peaks can be observed using (a) non-interacting BECs, (b) interacting BECs of $$5 \times 10^4$$ 5 × 10 4 atoms with s-wave scattering lengths $$a_s=\pm 0.1a_0$$ a s = ± 0.1 a 0 ($$a_0$$ a 0 is the Bohr radius), and (c) interacting BECs of $$10^3$$ 10 3 atoms with $$a_s=\pm 1.0a_0$$ a s = ± 1.0 a 0 . Our theoretical investigation impacts any future experimental realization of an atomic Fabry–Perot interferometer with an ultracold atomic source.

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“…Soliton interferometers have been elaborated theoretically in various configurations [11][12][13][14][15][16][17][18][19][20] (including the case when the splitter is inserted as a localized self-repulsive nonlinearity, or its combination with the usual potential barrier [21]) and realized in experiment [9]. Interactions of matter-wave solitons with local potentials have also been studied in other contexts, such as an analytical treatment of the collisions [22], rebound from potential wells [23,24], dynamics of solitons in a dipolar BEC [12], and probing effects of interparticle interactions on tunneling [25,26]. However, the splitting of a fundamental soliton by a linear and/or nonlinear potential barrier implies, in a sense, the application of "brute force" to a soliton, as its intrinsic structure does not resonate with the action of the splitter.…”

Section: Introductionmentioning

confidence: 99%

Splitting of two-component solitary waves from collisions with narrow potential barriers

Grimshaw

¹

,

Gardiner

²

,

Malomed

³

2020

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We consider the interaction of two component bright-bright solitons with a narrow potential barrier (splitter) in the framework of the two-component Gross-Pitaevskii (nonlinear-Schrödinger) system, with self-attraction within each component and cross-attraction between the components, motivated by the splitting of composite solitons facilitating the design of two-component soliton-interferometer schemes. We determine approximate analytic results by assuming a weak potential barrier and applying perturbation theory to the limit where the system becomes integrable. We do this for the case of negligible interspecies interactions, and also when the nonlinearities are strongly asymmetric, such that the wavefunction for the component with a smaller population is solved by neglecting its self-interaction term and the other component constitutes a bright soliton. We use numerical simulations to find the transmissions of both components in regions outside of these approximations and to compare with the approximate analytics, finding that there is an appreciable parameter range where one component is essentially entirely transmitted and the other reflected.

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Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

Cited by 17 publications

References 55 publications

Splitting and recombination of bright-solitary-matter waves

Splitting and recombination of bright-solitary-matter waves

An atomic Fabry–Perot interferometer using a pulsed interacting Bose–Einstein condensate

Splitting of two-component solitary waves from collisions with narrow potential barriers

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