The description of a non-Markovian process is presented and the asymptotic solution of the generalized master equation is obtained for a two-level atom pumped externally by a monochromatic time-dependent electric field. We give the explicit expression for the absorption line-shape function and discuss its features as a function of the temperature and the memory parameter. We verified the following interesting results: (a) At a critical temperature the line shape undergoes a phase transition, the single-bump profile splits into two bumps; (b) for small values of the memory parameter k the linewidths broaden, becoming larger than the ones calculated under the Markovian approximation, and after reaching some maximum value they narrow monotonically with increasing values of k, this behavior being standard for any finite temperature.
The description of a non-Markovian process is presented and the asymptotic solution of the generalized master equation is obtained for a two-level atom pumped externally by a monochromatic time-dependent electric field. We give the explicit expression for the absorption line-shape function and discuss its features as a function of the temperature and the memory parameter. We verified the following interesting results: (a) At a critical temperature the line shape undergoes a phase transition, the single-bump profile splits into two bumps; (b) for small values of the memory parameter k the linewidths broaden, becoming larger than the ones calculated under the Markovian approximation, and after reaching some maximum value they narrow monotonically with increasing values of k, this behavior being standard for any finite temperature.
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 \ensuremath{\eta} 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.
The absorptive part of the susceptibility of a system constituted by a strongly driven two-level atom (interacting with a reservoir) is analyzed when probed by a weak field. Memory effects are taken into account (the correlation time of the reservoir variables is finite) and we verify that they lead to several distinct features for the absorption and stimulated emission of radiation, when compared with those obtained in the Markovian approximation. Moreover, we verify that memory effects lead to a signature, namely, the sensitive dependence of the maxima of the absorption lines on the Rabi frequency at off-resonance pumping. Other characteristics of the spectrum are enhanced, even in the presence of a small but non-null correlation time of the reservoir, for instance, the maxima of the dispersionlike absorption curves at on-resonance pumping. In this work several situations are analyzed for different values of the parameters of the problem: the off-resonance frequencies of the driving field, the Rabi frequency, the memory time, and temperature of the reservoir.
Based on the standard system-heat-bath model, we have formulated a theory of the non-Markovian master equation for linear and nonlinear systems for a correlation time that is short but finite. We have applied the theory to linear systems, such as harmonic oscillators and two-level atoms and calculated the band-shape functions for transient optical absorption in the pump-probe experiments. The significant interplay of nonlinearity and non-Markovian decay has been illustrated by another application of the theory to a Morse oscillator. The theory is valid for arbitrary nonlinearity and finite temperatures but within the weak-coupling limit and has been derived without ad hoc implementation of a phenomenological memory function.
We derive the stochastic equations and consider the non-Markovian dynamics of a system of multiple two-level atoms in a common quantum field. We make only the dipole approximation for the atoms and assume weak atom–field interactions. From these assumptions, we use a combination of non-secular open- and closed-system perturbation theory, and we abstain from any additional approximation schemes. These more accurate solutions are necessary to explore several regimes: in particular, near-resonance dynamics and low-temperature behavior. In detuned atomic systems, small variations in the system energy levels engender timescales which, in general, cannot be safely ignored, as would be the case in the rotating-wave approximation (RWA). More problematic are the second-order solutions, which, as has been recently pointed out (Fleming and Cummings 2011 Phys. Rev. E 83 031117), cannot be accurately calculated using any second-order perturbative master equation, such as RWA, Born–Markov, Redfield, etc. The latter problem, which applies to all perturbative open-system master equations, has a profound effect upon calculation of entanglement at low temperatures. We find that even at zero temperature all initial states will undergo finite-time disentanglement (sometimes termed ‘sudden death’), in contrast to the previous work. We also use our solution, without invoking the RWA, to characterize the necessary conditions for Dicke subradiance at finite temperature. We find that the sub-radiant states fall into two categories at finite temperature: one that is temperature independent and one that acquires temperature dependence. With the RWA, there is no temperature dependence in any case.
A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.
The effect of a driving or pump field on the emission and absorption line-shape functions for an atom is discussed. The pump field is assumed to oscillate at a frequency near the resonance frequency for transitions between a single pair of atomic states, and transitions between one of these states and any other state of the atom are analyzed. The pump field is treated classically, and atomic relaxation is treated in general terms. The emission and absorption line-shape function (the latter is defined as the rate of absorption of energy from a weak signal field, applied in addition to the pump field, as a function of the signal-field frequency) are found by evaluating the relevant two-time atomic correlation functions in the Markoff approximation. In the limit of high pump-field intensity, both the absorption and the emission spectra are doubly peaked at frequencies which differ from the usual resonance frequency by $\ifmmode\pm\else\textpm\fi{}\frac{1}{2} \ensuremath{\Omega}$, where $\ensuremath{\Omega}$ is the frequency of the pump-field-induced oscillations in the populations of the two strongly coupled states. The absorption and the emission spectra are represented by essentially the same function in the limit of high pump-field intensity, as they are also in the limit of vanishing pump-field intensity. For intermediate pump-field intensities, however, the two functions are quite different in form, and no simple proportionality exists between them.