Counterdiabatic vortex pump in spinor Bose-Einstein condensates

Ollikainen, Tuomas; Masuda, S.; Möttönen, Mikko; Nakahara, Mikio

doi:10.1103/physreva.95.013615

Cited by 13 publications

(15 citation statements)

References 51 publications

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“…Here, in contrast, we show that the knot configuration can be created using a dynamic magnetic field control obtained from the CD scheme [39,40]. In the CD scheme, we first select the reference adiabatic dynamics of the spin degree of freedom corresponding to the instantaneous eigenstates of the Zeeman Hamiltonian…”

Section: B Topological Considerationsmentioning

confidence: 99%

“…We further employ the unitary transformation introduced in Refs. [39,40] to obtain a CD field which can be experimentally implemented using a single pair of quadrupole coils. The transformation is given by U (t) = e −iα(t)Fz , where α(t) = arctan [|B CD |/ (b q ρ)].…”

Section: B Topological Considerationsmentioning

confidence: 99%

“…As a result, the Zeeman part of the Hamiltonian for the unitarytransformed order parameter is rotated by α(t) and an additional time-dependent magnetic field is introduced along z. The resulting magnetic field giving rise to the knot structure is [40]…”

Section: B Topological Considerationsmentioning

confidence: 99%

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Quantum knots in Bose-Einstein condensates created by counterdiabatic control

et al. 2017

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We study theoretically the creation of knot structures in the polar phase of spin-1 Bose-Einstein condensates using the counterdiabatic protocol in an unusual fashion. We provide an analytic solution to the evolution of the external magnetic field that is used to imprint the knots. As confirmed by our simulations using the full three-dimensional spin-1 Gross-Pitaevskii equation, our method allows for the precise control of the Hopf charge as well as the creation time of the knots. The knots with Hopf charge exceeding unity display multiple nested Hopf links.

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Section: B Topological Considerationsmentioning

confidence: 99%

Section: B Topological Considerationsmentioning

confidence: 99%

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Quantum knots in Bose-Einstein condensates created by counterdiabatic control

et al. 2017

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“…In this paper, we study phase imprinting on the order parameter of BECs with the fast-forward scaling theory showing the nontrivial scaling property. In contrast to the various phase imprinting protocols previously proposed or demonstrated, e.g., [45][46][47][48][49][50][51][52][53][54][55][56], our phase imprinting protocol is based on the nontrivial scaling property of quantum dynamics. The theory is applied to derive the driving potential for creation of a peculiar state, a wave packet with uniform momentum density (WPUM), which is introduced in this paper.…”

Section: Introductionmentioning

confidence: 99%

Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance

2018

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We study phase imprinting on Bose-Einstein condensates (BECs) with the fast-forward scaling theory revealing a nontrivial scaling property in quantum dynamics. We introduce a wave packet with uniform momentum density (WPUM) which has peculiar properties but is short-lived. The fastforward scaling theory is applied to derive the driving potential for creation of the WPUMs in a predetermined time. Fast manipulation is essential for the creation of WPUMs because of the instability of the state. We also study loading of a BEC into a predetermined Bloch state in the lowest band from the ground state of a periodic potential. Controlled linear potential is not sufficient for creation of the Bloch state with large wavenumber because the change in the amplitude of the order parameter is not negligible. We derive the exact driving potential for creation of predetermined Bloch states using the obtained theory.

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“…Alternative methods to create knots were theoretically proposed in Refs. [23,24]. During its evolution, the knot is predicted to facilitate the decay of the underlying polar magnetic phase into the ferromagnetic phase [20].…”

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Decay of a Quantum Knot

et al. 2019

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We experimentally study the dynamics of quantum knots in a uniform magnetic field in spin-1 Bose-Einstein condensates. The knot is created in the polar magnetic phase, which rapidly undergoes a transition towards the ferromagnetic phase in the presence of the knot. The magnetic order becomes scrambled as the system evolves, and the knot disappears. Strikingly, over long evolution times, the knot decays into a polar-core spin vortex, which is a member of a class of singular SO(3) vortices. The polar-core spin vortex is stable with an observed lifetime comparable to that of the condensate itself. The structure is similar to that predicted to appear in the evolution of an isolated monopole defect, suggesting a possible universality in the observed topological transition.Topological defects and textures provide intriguing conceptual links between many otherwise distant branches of science [1,2]. They appear in various contexts ranging from condensed matter to high-energy physics and cosmology, and can be highly stable against weak perturbations. However, there can be mechanisms leading to the decay of the defects despite their topological stability. The decay can be induced by, for example, changes to the underlying symmetries or the finite size of the system [3].Spinor Bose-Einstein condensates (BECs) are one of the most fascinating systems available for the study of topological defects due to the diverse range of broken symmetries associated with the different magnetic phases of the system. In the scalar case, the spin degrees of freedom are inaccessible and the topology of the BEC is simply described by the broken U(1) symmetry, yielding one-dimensional solitons and vortex lines as the only possible topological defects of the system. Upon including the spin degrees of freedom, the internal symmetries of the gas become plentiful, allowing for a diverse set of excitations. For example, in spinor BECs there can be several types of vortices [4][5][6][7][8][9], skyrmions [10][11][12][13][14], monopoles [15][16][17][18][19], and quantum knots [20,21].Topologically stable knots are classified by a linking number (or Hopf charge) Q, which counts the number of times each preimage loop of the order parameter is linked with every other such loop [22]. In Ref. [21], the experimental creation of knots with Q = 1 was reported in the polar magnetic phase of spin-1 BECs. Alternative methods to create knots were theoretically proposed in Refs. [23,24]. During its evolution, the knot is predicted to facilitate the decay of the underlying polar magnetic phase into the ferromagnetic phase [20]. Prior to the present study, however, neither this nor any other prediction involving the temporal evolution of the knot has been experimentally tested beyond the preliminary investigations of Ref. [21]. * tuomas.ollikainen@aalto.fiIn this Letter, we report experimental observations of the evolution of the quantum knot in spin-1 87 Rb BECs in a uniform external magnetic field. We show that the knot structure begins to decay rapidly on a time sc...

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Counterdiabatic vortex pump in spinor Bose-Einstein condensates

Cited by 13 publications

References 51 publications

Quantum knots in Bose-Einstein condensates created by counterdiabatic control

Quantum knots in Bose-Einstein condensates created by counterdiabatic control

Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance

Decay of a Quantum Knot

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