In order to be able to study dissipation, the interaction between a single system andtheir environment was introduced in quantum mechanics. Master and quantum Langevingequations was derived. Moreover, decoherence has been studied using this approach.One of the most commonly used model in this research field is a single harmonic oscillatorinteracting with a reservoir. In this work we analytically solve this model, in theresonance case, using the evolution operator method. Then, we use this result to study aquantum coupler, which is a particular case where there are a finite number of harmonicoscillators interacting with the single one. After that, we focuses in the analisis of theconditional quantum dynamics of the quantum coupler (using the computational basis oftwo qubits) by choosing a proper interaction time. This conditional dynamics providesa realization of a new quantum phase gate, which we call the relative phase gate. To thebest of our knowledge, this phase gate has not been previously defined or proposed.
['P. C. Garcia Quijas', 'L. M. Arevalo Aguilar']
A quantum coupler and the harmonic oscillator interacting with a reservoir: defining the relative phase gate