Shortcuts to adiabatic rotation of a two-ion chain

Tobalina, A.; Muga, J. G.; Lizuain, I.; Palmero, M.

doi:10.1088/2058-9565/ac1e01

Cited by 2 publications

(3 citation statements)

References 43 publications

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“…This effect is well known in fast STA expansion or compression processes [11] and may or may not represent a problem to implement it in the laboratory depending on the physical setting. The detailed discussion of specific implementations goes beyond the scope of the present article, but we point out that in a trapped ion setting, the rotation of the trap with varying frequencies and controlled angular speed are possible with "point harmonic traps" making use of concentric rings to implement a ponderomotive potentials and a rotating electrostatic quadrupole potential [20,18,31]. Different (two particle) implementations may be based on two ions in controllable double wells [32].…”

Section: Discussionmentioning

confidence: 99%

“…In essence, a point transformation (i.e., one that does not mix positions and momenta) cannot separate the dynamics into independent normal dynamical modes, so that simple inverse-engineering methods known for the one-dimensional modes and the corresponding 1D invariants cannot be used to find a fast, excitationless rotation protocol [6]. Several wayouts have been investigated, such as purely numerical optimizations [20], or mode separations using more complicated transformations mixing positions and momenta [5]. However, numerical optimizations need specific calculations for each particular state and process, and the approach based on non-point transformations was limited by singularities in the protocol and conditions on the rotation times and commensurate normal frequencies [5].…”

Section: Introductionmentioning

confidence: 99%

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Inverse engineering of fast state transfer among coupled oscillators

Lizuain

Muga

2022

Quantum

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We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a two-dimensional invariant recently proposed in S. Simsek and F. Mintert, Quantum 5 (2021) 409, and involves both rotation and transient scaling of the principal axes of the potential in a Cartesian representation. Importantly, this invariant is degenerate except for the subspace spanned by its ground state. Such degeneracy, in general, allows for infidelities of the final states with respect to ideal target eigenstates. However, the value of a single control parameter can be chosen so that the state switching is perfect for arbitrary (not necessarily known) initial eigenstates. Additional 2D linear invariants are used to find easily the parameter values needed and to provide generic expressions for the final states and final energies. In particular we find time-dependent transformations of a two-dimensional harmonic trap for a particle (such as an ion or neutral atom) so that the final trap is rotated with respect to the initial one, and eigenstates of the initial trap are converted into rotated replicas at final time, in some chosen time and rotation angle.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse engineering of fast state transfer among coupled oscillators

Lizuain

Muga

2022

Quantum

Self Cite

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show abstract

“…This effect well known in fast STA expansion or compression processes [11] and may or may not represent a problem to implement it in the laboratory depending on the physical setting. The detailed discussion of specific implementations goes beyond the scope of the present article, but we point out that in a trapped ion setting, the rotation of the trap with varying frequencies and controlled angular speed are possible with "point harmonic traps" making use of concentric rings to implement a ponderomotive potentials and a rotating electrostatic quadrupole potential [18,20,31]. Different (two particle) implementations may be based on two ions in controllable double wells [32].…”

Section: Discussionmentioning

confidence: 99%

Inverse engineering of fast state transfer among coupled oscillators

Lu,

Lizuain,

Muga

2022

Preprint

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We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a twodimensional invariant recently proposed in S. Simsek and F. Mintert, Quantum 5 (2021) 409, and involves both rotation and transient scaling of the principal axes of the potential in a Cartesian representation. Importantly, this invariant is degenerate except for the subspace spanned by its ground state. Such degeneracy, in general, allows for infidelities of the final states with respect to ideal target eigenstates. However, the value of a single control parameter can be chosen so that the state switching is perfect for arbitrary (not necessarily known) initial eigenstates. Additional 2D linear invariants are used to find easily the parameter values needed and to provide generic expressions for the final states and final energies. In particular we find time-dependent transformations of a two-dimensional harmonic trap for a particle (such as an ion or neutral atom) so that the final trap is rotated with respect to the initial one, and eigenstates of the initial trap are converted into rotated replicas at final time, in some chosen time and rotation angle.

show abstract

Shortcuts to adiabatic rotation of a two-ion chain

Cited by 2 publications

References 43 publications

Inverse engineering of fast state transfer among coupled oscillators

Inverse engineering of fast state transfer among coupled oscillators

Inverse engineering of fast state transfer among coupled oscillators

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