Recent femtosecond processes [Phys. Rev. Lett. 66, 2464 (1991)] confirm the importance of non-Markovian effects since the dynamical characteristic times of the system become of the same time scale as the reservoir. We analyze here the memory effects in the density-matrix coherence for a driven two-level atom in the stationary regime. The coherence parameter η is written in terms of the detuning, the strength of the external driving force, and the temperature as the reservoir. We verify that the memory effects, present in the density matrix, are enhanced by the external driving force. We introduce the Shanon information entropy and we verify that, while in the Markovian approximation the entropy decreases monotonically as function of the detuning, in the non-Markovian approach it is characterized by a minimum, which enables us to differentiate between the two processes.

We propose a measurement scheme that allows determination of even moments of a Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuous photodetection of an off-resonant quantized optical field. A fast cavity photocounting process limits the heating of atomic samples with a relatively small number of atoms, being convenient for BECs on microchip scale applications. The measurement back-action introduces a counting-conditioned phase damping, suppressing the condensate typical collapse and revival dynamics.

A system of N spin-1/2 particles interacting with a thermal reservoir is used as a pedagogical example for advanced undergraduate and graduate students. We introduce and illustrate some methods, approximations, and phenomena related to dissipation and nonlinearity in many-particle physics. We start our analysis from the dynamical Sudarshan-Lindblad quantum master equation for the density operator of a system S interacting with a thermal reservoir R. We derive the quantum version of the so-called Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations such that the master equation can be decomposed in a hierarchical set of N - 1 equations (N > 1). The hierarchy is broken by introducing the mean-field approximation and reducing the problem to a nonlinear single particle system. In this scenario, the Hamiltonian is nonlinear (i.e., it depends on the state of <S), although the superoperator responsible for the dissipation and decoherence of S remains unaffected. To provide a useful tool to students: (1) we discuss the physical approximations involved, (2) we derive the analytical solution to the mean values equations of motion resulting from the Hamiltonian, (3) we solve analytically the master equation in the stationary regime, (4) we obtain and discuss the solution of the nonlinear master equation, numerically, and finally, (5) we discuss the master equation beyond the mean-field approximation and show how to introduce higher order quantum correlations that have been previously neglected.

We consider $N$ two-level atoms in a ring cavity interacting with a broadband squeezed vacuum centered at frequency ${\omega }_s$ and an input monochromatic driving field at frequency $\omega$. We show that, besides the central mode (at $\omega$), an infinity of sideband modes are produced at the output, with frequencies shifted from $\omega$ by multiples of $2\left(\omega -{\omega }_s\right)$. We analyze the optical bistability of the two nearest sideband modes, red shifted and blue shifted.

We propose a scheme to measure the cross correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.

We present a technique for direct measurement of the Wigner distribution function of a traveling field, based on a Mach-Zehnder interferometer with a phase-sensitive element. In our scheme, the problem arising from the non-unity efficiency of the photodetectors is circumvented by the optical intensity of the input field for interferometry.