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arXiv:1507.03771 · Physical Review A

Fast bias inversion of a double well without residual particle excitation

S. Martínez-Garaot, Mikel Palmero, David Guéry-Odelin, Juan Gonzalo Muga

Published Nov 5, 2015• 7 citations
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Abstract

We design fast bias inversions of an asymmetric double well so that the lowest states in each well stay in the same well they started, free from residual motional excitation. This cannot be done adiabatically, and a sudden bias switch produces in general motional excitation. The residual excitation is suppressed by complementing a predetermined fast bias change with a linear ramp whose time-dependent slope compensates for the displacement of the wells. The process, combined with vibrational multiplexing and demultiplexing, can produce vibrational state inversion without exciting internal states, just by deforming the trap.

DOI
10.1103/physreva.92.053406

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We design fast bias inversions of an asymmetric double well so that the lowest states in each well stay in the same well they started, free from residual motional excitation. This cannot be done adiabatically, and a sudden bias switch produces in general motional excitation. The residual excitation is suppressed by complementing a predetermined fast bias change with a linear ramp whose time-dependent slope compensates for the displacement of the wells. The process, combined with vibrational multiplexing and demultiplexing, can produce vibrational state inversion without exciting internal states, just by deforming the trap.
Sending multiple messages on qubits encoded in different vibrational modes of cold atoms or ions along a transmission waveguide requires us to merge first and then separate the modes at input and output ends. Similarly, different qubits can be stored in the modes of a trap and be separated later. We design the fast splitting of a harmonic trap into an asymmetric double well so that the initial ground vibrational state becomes the ground state of one of two final wells, and the initial first excited state becomes the ground state of the other well. This might be done adiabatically by slowly deforming the trap. We speed up the process by inverse engineering a double-function trap using dynamical invariants. The separation (demultiplexing) followed by an inversion of the asymmetric bias and then by the reverse process (multiplexing) provides a population inversion protocol based solely on trap reshaping.
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.
Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.
We show that electronic population can be switched adiabatically between the wells of a biased, asymmetric double quantum well (QW) structure. A time-dependent dc field guides an initial state along a smooth path to a state that is localized in a specified QW. General requirements for adiabaticity are determined that manifest the conditions in which the transfer process is optimal. The time duration of the perturbation is a sensitive parameter that influences strongly the outcome of the adiabatic passage. If the perturbation occurs too rapidly, the states mix, and a time-varying superposition state is created. However, if the requirements of adiabaticity are satisfied at all times during the perturbation, the system remains in a pure state, and evolves adiabatically to the final state. Various forms of the dc field are compared, and their relative performance evaluated. The optimal field for efficient adiabatic passage varies from structure to structure, and depends on the response of the system to the dc field. Complex field shapes can be used to produce multiple shifts in electronic density between the QWs. This procedure provides an effective means to perform adiabatic passage in semiconductor heterostructures, with smooth transitions, selectivity, and reversibility.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven nonadiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies, and accelerations involved are analyzed along with the relation to previous approaches based on classical trajectories or ``fast-forward'' and ``bang-bang'' methods, which can be integrated in the invariant-based framework.