Anita Dąbrowska

The excitation of atomic and molecular systems by propagating light in a two-photon state within the Wigner–Weisskopf approximation has been described using stochastic tools. The problem of a stochastic evolution of the quantum system, depending on the results of the measurement of the output field, was formulated and solved making use of the model of repeated interactions and measurement. We defined the discrete in-time interaction between the quantum system and its environment being the electromagnetic field approximated by a chain or chains of harmonic oscillators. We determined analytical formulae for quantum trajectories associated with one-dimensional and two-dimensional counting processes, corresponding respectively to unidirectional or bidirectional input field prepared in the two-photon states. We derived the formulae for the exclusive probability densities of photon counts that allow us to completely characterize the photon statistics of the output field. Finally, we showed how to apply the quantum trajectories to obtain the formula for the probability of the two-photon absorption for a three-level atom in a ladder configuration. The paper also includes a discussion on the optimal two-photon state that maximizes the two-photon absorption probability.

Quantum optical coherence tomography (Q-OCT) presents many advantages over its classical counterpart, optical coherence tomography (OCT), provides an increased axial resolution, and is immune to even orders of dispersion. The core of Q-OCT is the quantum interference of negatively correlated entangled photon pairs which, in the Fourier domain, are observed by means of a joint spectrum measurement. In this work, we explore the use of a spectral approach in a novel configuration where classical light pulses are employed instead of entangled photons. The intensity of these light pulses is reduced to a single photon level. We report theoretical analysis along with its experimental validation to show that although such a classical light is much easier to launch into an experimental system, it offers limited benefits compared to Q-OCT based on the entangled light. We analyze the differences in the characteristics of the joint spectrum obtained with entangled photons and with classical optical pulses and point out to the differences’ source: the lack of the advantage-bringing term in the signal.

We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of repeated interactions and measurements. In this approach, the quantum system undergoes a sequence of interactions with an environment defined by a chain of harmonic oscillators. We assume that the environment is prepared in an entangled state being a discrete analogue of a continuous-mode squeezed number state. We present a derivation of a discrete stochastic dynamics that depends on the results of measurement performed on the field after its interaction with the system. In this paper, we consider a photon counting measurement scheme. By taking a continuous time limit, we finally obtain differential stochastic equations for the system. Analytical formulae for quantum trajectories and exclusive probability densities that allow to fully characterize the statistics of photons in the output field are given.

In this paper, photon-counting statistics for an output field of a single-photon wave packet interacting with a quantum system was derived. The problem was formulated using a collision model with a bidirectional field approximated by two sequences of qubits. It was shown that the collision model formulated for the light with the temporal correlations allows deriving formulae for quantum trajectories in an effective and intuitive way. Starting from the discrete in-time evolution of the composed system, we determined the conditional and unconditional evolution of the quantum system, provided a physical interpretation of quantum trajectories, and determined the analytical formulae for the exclusive probability densities for the reflected and transmitted fields. Finally, our results were applied to a two-level atom, and we also determined analytical expressions for probability densities of arrival times of the successive counts.

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.

We present the analytical formulas for the conditional and unconditional states of a two-level atom interacting with a single-photon wavepacket. We express the a priori state of the system by means of the quantum trajectories related to the process of detection of photons in the output field. We give the formulas for the mean number of photons detected up to the given time and we derive the expressions for the mean time of detection of the photons.

We present the analytical formulas for the conditional and unconditional states of a two-level atom interacting with a single-photon wavepacket. We express thea prioristate of the system by means of the quantum trajectories related to the process of detection of photons in the output field. We give the formulas for the mean number of photons detected up to the given time, and we derive the expressions for the mean time of detection of the photons.

We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode N -photon state. To determine the conditional evolution of the quantum system depending on continuous in time measurements of the output field the model of repeated interactions and measurements is applied. The environment is defined as an infinite chain of harmonic oscillators which do not interact between themselves and they are prepared initially in an entangled state being a discrete analogue of a continuous-mode N -photon state. We provide not only the quantum trajectories but also the analytical formulae for the whole statistics of the output photons and the solution to the master equation. The solution in the continuous case is represented by a simple diagrammatic technique with very transparent ‘Feynmann rules’. This technique considerably simplifies the structure of the solution and enables one to find physical interpretation for the solution in terms of a few elementary processes.