Partial suppression of nonadiabatic transitions

The adiabatic following of eigenstates of time-varying Hamiltonians can serve as a useful tool in preparing or manipulating quantum states. If the time variation is not sufficiently slow, however, nonadiabatic transitions to unwanted states occur. Recently, it has been shown that the adiabatic following can be perfectly restored if the original Hamiltonian is complemented with an additional term. Although there is an explicit formula for this compensating term, typically one may not always be able to construct it in an experiment. Here we present a straightforward approach for a partial suppression of the nonadiabatic transitions applicable for any set of available Hamilton operators. We illustrate the method on several examples including interacting spin systems, interacting bosons in a double-well potential, a particle in an expanding box and a system of atoms interacting via a Rydberg-blockade. Whenever suitable compensating operators are available, the system may be evolved faster or with higher fidelity along an eigenstate of the original time-dependent Hamiltonian.

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