Anomalous tunneling of collective excitations and effects of superflow in the polar phase of a spin-1 spinor Bose-Einstein condensate

Watabe, Shohei; Kato, Yasuyuki; Ōhashi, Y.

doi:10.1103/physreva.84.013616

Cited by 6 publications

(12 citation statements)

References 19 publications

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“…The corresponding perturbation theory for a large Jordan block is given in Appendix F. We give a general treatment of "massive" NGMs [50,51,52,53] in Bogoliubov theory in Subsec. 7.2.2 and Appendix G. The resulting perfect tunneling properties [54,55,56,57,58,59,60,61] of these NGMs are discussed in Subsec. 7.2.3. This paper is organized as follows.…”

Section: Preprint Submitted To Elseviermentioning

confidence: 99%

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Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

2015

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When continuous symmetry is spontaneously broken, there appear Nambu-Goldstone modes (NGMs) with linear or quadratic dispersion relation, which is called type-I or type-II, respectively. We propose a framework to count these modes including the coefficients of the dispersion relations by applying the standard Gross-Pitaevskii-Bogoliubov theory. Our method is mainly based on (i) zero-mode solutions of the Bogoliubov equation originated from spontaneous symmetry breaking and (ii) their generalized orthogonal relations, which naturally arise from well-known Bogoliubov transformations and are referred to as "σ-orthogonality" in this paper. Unlike previous works, our framework is applicable without any modification to the cases where there are additional zero modes, which do not have a symmetry origin, such as quasi-NGMs, and/or where spacetime symmetry is spontaneously broken in the presence of a topological soliton or a vortex. As a by-product of the formulation, we also give a compact summary for mathematics of bosonic Bogoliubov equations and Bogoliubov transformations, which becomes a foundation for any problem of Bogoliubov quasiparticles. The general results are illustrated by various examples in spinor Bose-Einstein condensates (BECs). In particular, the result on the spin-3 BECs includes new findings such as a type-I-type-II transition and an increase of the type-II dispersion coefficient caused by the presence of a linearly-independent pair of zero modes.

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Section: Preprint Submitted To Elseviermentioning

confidence: 99%

“…Scattering problems of NGMs are extensively studied in Refs. [54,55,56,57,58,59,60,61]. It is known that NGMs show a perfect tunneling in the long-wavelength limit.…”

Section: Ssb-originated Zero-modes As An Origin Of Perfect Tunneling mentioning

confidence: 99%

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

2015

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“…The tunneling of excitations in Bose-Einstein condensates through a potential barrier is referred to as the anomalous tunneling. These have been intensively and extensively studied for scalar Bose-Einstein condensates [29,30,33,[45][46][47][48][49][50][51][52][53], and for Bose-Einstein condensates with internal degrees of freedom [54][55][56][57][58].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Stability criterion for superfluidity based on the density spectral function

Watabe

Kato

2013

Phys. Rev. A

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We study a stability criterion hypothesis for superfluids expressed in terms of the local density spectral function I n (r,ω) that is applicable to both homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive or attractive external potential within Bogoliubov theory, using solutions for the tunneling problem. We also evaluate the local density spectral function using an orthogonal basis, and calculate the autocorrelation function C n (r,t). When superfluids in a d-dimensional system flow below a threshold, I n (r,ω) ∝ ω d holds in the low-energy regime and C n (r,t) ∝ 1/t d+1 holds in the long-time regime. However, when superfluids flow with the critical current, I n (r,ω) ∝ ω β holds in the low-energy regime and C n (r,t) ∝ 1/t β+1 holds in the long-time regime with β < d. These results support the stability criterion hypothesis recently proposed.

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“…Our interest in this paper is how such dynamically unstable modes are reflected or transmitted by the barrier potential. For the case of β ≥ 0, for which the system is dynamically stable, almost the same situation has been discussed in the previous works, 9,10) where the tunneling problem of spin waves in a spin-1 polar state has been investigated and the perfect transmission was observed in the low energy limit. The BdG Eq.…”

Section: Bogoliubov Spectrum In a Uniform Systemmentioning

confidence: 58%

“…So far, the anomalous tunneling has been studied in BECs with supercurrent flow, [4][5][6] at finite temperature, 7) and with spin degrees of freedom. [8][9][10] The relations with Josephson current, 11,12) impedance matching, 13) and scattering at magnetic domain wall and at impurities 14,15) were also discussed. The above works revealed that the anomalous tunneling occurs in the zero-energy limit of the NG mode: The NG boson in the zero-energy limit is identical to the condensed particles, and hence, its wave function extends over the both side of the barrier potential, resulting in the perfect transmission.…”

Section: Introductionmentioning

confidence: 99%

Perfect transmission and perfect reflection of Bogoliubov quasiparticles in a dynamically unstable Bose-Einstein condensate

Ohashi,

Kawaguchi

2020

Preprint

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The Nambu-Goldstone (NG) mode in a Bose-Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multi-component BEC (binary and spin-1 BEC) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave is the NG mode. Here, the mode that exhibits the perfect transmission is the dynamically unstable spin-wave mode, which is a pure-imaginary-eigenvalue solution of the Bogoliubov-de Gennes equation. Hence, we should take the zero-energy limit along not the real axis but the imaginary axis. We also demonstrate the existence of the perfect reflection of a dynamically unstable mode at the point where the imaginary part of the eigenvalue takes its maximum. In this case, the incident and reflected waves destructively interfere, and the amplitude of the quasiparticle wave function is strongly suppressed. We numerically confirm that the perfect reflection is a generic nature of dynamically unstable modes and not related to the NG mode.

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Anomalous tunneling of collective excitations and effects of superflow in the polar phase of a spin-1 spinor Bose-Einstein condensate

Cited by 6 publications

References 19 publications

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

Stability criterion for superfluidity based on the density spectral function

Perfect transmission and perfect reflection of Bogoliubov quasiparticles in a dynamically unstable Bose-Einstein condensate

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