Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

Abstract

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

Photon counting probabilities of the output field for a single-photon input

“…One can recognise in these formulae the processes of emission, absorption and reemission of the photon. About the physical interpretation of the quantum trajectories for the system interacting with the singlephoton field and N -photon field one can read more in [31,41]. Similar discussion one can find also in [35].…”

“…where σ z = |e e| − |g g|, and ∆ 0 = ω c − ω 0 , where ω 0 is the transition frequency of the atom and ω c represents the carrier frequency of the input wave packet. The formula for the reduced state of the atom at time t for an arbitrary initial state of the atom and any photon profile was given in [41]. We will not discuss it here but it is clear that the single-photon input drives the atom and that asymptomatically the atom relaxes to the ground state.…”

“…The initial correlation present in the bath make the reduced evolution of the system non-Markovian. This problem was carefully discussed in [41]. We gain the information about the system indirectly -by performing the measurements on the bath elements just after their interactions with the system.…”