Creation of qutrit and one-qubit gates in atom–cavity–laser systems by adiabatic passage

We derive an adiabatic technique that implements arbitrary qutrit and one-qubit rotation gates in a quantum system composed of two tripod atoms each of which interacting with two laser pulses and a cavity field. In this method, the atomic ground states playing the role of the qutrit and qubit subspace and losses due to atomic spontaneous emissions and the cavity decay are efficiently suppressed by employing adiabatic passage technique. In order to create qutrit gates, we exploit generalized quantum Householder reflection in which each Householder reflection is implemented by two-step adiabatic passage technique in a seven-state system with two dark states. With a similar method, an arbitrary rotation gate is constructed in this system. We also implement the Fourier transform in a qutrit as an example.