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.
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 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.
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 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.
When attempting to split a coherent noninteracting atomic cloud by bifurcating the initial trap into two well-separated wells, slow adiabatic following is unstable with respect to any slight trap asymmetry, and the matter wave ``collapses'' to the well with the lowest energy. A generic fast chopping splits the wave but it also excites it. Shortcuts to adiabaticity engineered to speed up the unperturbed adiabatic process through nonadiabatic transients provide, instead, quiet and robust balanced splitting. For a Bose-Einstein condensate in the mean-field limit, the interatomic interaction makes the splitting, adiabatic or via shortcuts, more stable with respect to trap asymmetry. Simple formulas are provided to distinguish different regimes.
We design fast protocols to separate or recombine two ions in a segmented Paul trap. By inverse engineering the time evolution of the trapping potential composed of a harmonic and a quartic term, it is possible to perform these processes in a few microseconds without final excitation. These times are much shorter than the ones reported so far experimentally. The design is based on dynamical invariants and dynamical normal modes. Anharmonicities beyond the harmonic approximation at potential minima are taken into account perturbatively. The stability versus an unknown potential bias is also studied.
We study the shuttling of an atom in a trap with controllable position and frequency. Using invariant-based inverse engineering, protocols in which the trap is simultaneously displaced and expanded are proposed to speed up transport between stationary trap locations as well as launching processes with narrow final-velocity distributions. Depending on the physical constraints imposed, either simultaneous or sequential approaches may be faster. We consider first a perfectly harmonic trap, and then extend the treatment to generic traps. Finally, we apply this general framework to a double-well potential to separate different motional states with different launching velocities.