Open Two-level System Research Articles

Modulated two-level system: Exact work statistics

We consider an open two-level system driven by a piecewise constant periodic field and described by a rate equation with Fermi, Bose, and Arrhenius rates, respectively. We derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds.

Non-Markovian dynamics for an open two-level system without rotating wave approximation: indivisibility versus backflow of information

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.

Ultranarrow resonance due to coherent population oscillations in a Λ-type atomic system

It is well known that ultranarrow electromagnetically induced transparency (EIT) resonances can be observed in atomic gases at room temperature. We report here the experimental observation of another type of ultranarrow resonance, as narrow as the EIT ones, in a $\ensuremath{\Lambda}$ system selected by light polarization in metastable ${}^{4}$He at room temperature. It is shown to be due to coherent population oscillations in an open two-level system (TLS). For perpendicular linearly polarized coupling and probe beams, this system can be considered as two coupled open TLSs, in which the ground-state populations exhibit antiphase oscillations. We also predict theoretically that in the case of two parallel polarizations, the system would behave like a closed TLS, and the narrow resonance associated with these oscillations would disappear.

Equivalence of the measures of non-Markovianity for open two-level systems

In order to depict the deviation of quantum time evolution in open systems from Markovian processes, different measures have been presented. We demonstrate that the measure proposed by Breuer, Laine and Piilo [Phys. Rev. Lett. 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga and Plenio [Phys. Rev. Lett. 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent each other when they apply to open two-level systems coupled to environments via Jaynes-Cummings or dephasing models. This equivalence implies that the three measures in different ways capture the intrinsical characters of non-Markovianty of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianty.

Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy

We study the influence of optical pumping on Doppler-broadened alkali-metal-atom $D$ line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.

Mode-locked pulses from mid-infrared Quantum Cascade Lasers

In this study, we report the unequivocal demonstration of midinfrared mode-locked pulses from quantum cascade lasers. The train of short pulses was generated by actively modulating the current and hence the gain of an edge-emitting quantum cascade laser (QCL). Pulses with duration of about 3 ps at full-width-at-half-maxima and energy of 0.5 pJ were characterized using a second-order interferometric autocorrelation technique based on a nonlinear quantum well infrared photodetector. The mode-locking dynamics in the QCLs was modeled based on the Maxwell-Bloch equations in an open two-level system. Our model reproduces the overall shape of the measured autocorrelation traces and predicts that the short pulses are accompanied by substantial wings as a result of strong spatial hole burning. The range of parameters where short mode-locked pulses can be formed is found.

Analytic solution to N vs. M photon phase control in an open two-level system

Decoherence effects on the traditional N vs. M photon coherent control of a two-level system are investigated, with 1 vs. 3 used as a specific example. The problem reduces to that of a two-level system interacting with a single mode field, but with an effective Rabi frequency that depends upon the fundamental and third harmonic fields. The resultant analytic control solution is explored for a variety of parameters, with emphasis on the dependence of control on the relative phase of the lasers. The generalization to off-resonant cases is noted.

Bellman equations for optimal feedback control of qubit states

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.

Electromagnetically induced gratings in a degenerate open two-level system

We have experimentally investigated laser diffraction on electromagnetically induced gratings in a degenerate open two-level system. The experiment employs the standard backward four-wave mixing configuration and the open ${6S}_{1/2}(F=4)\ensuremath{\rightarrow}{6P}_{3/2}{(F}^{\ensuremath{'}}=4)$ transition of cold cesium atoms. Population and coherence gratings are accessed for different relative polarizations of the incident laser beams. Natural and subnatural linewidths are observed depending on which frequency of the incident beams is scanned and reveal the effect of the atomic motion on the diffraction spectra. A simple theoretical model using a three-level $\ensuremath{\Lambda}$ system is in reasonable agreement with the observed results and allowed us to make a close connection with the phenomenon of electromagnetically induced transparency.

Narrow resonances observed with nearly degenerate light in an open two-level system

We report the observation of narrow resonances in the optical region by using the method of separated oscillatory fields in an atomic beam. Because of optical pumping, two nearly degenerate optical fields create a time-dependent modulation of the ground-state population, which interferes with the optical fields in a second region, resulting in a fringe pattern. The width and shape of the observed fringes are the same as those observed with the usual Ramsey method, although no coherence between the two levels under investigation is needed.

Ultranarrow extraresonant holes and antiholes in pump–probe and four-wave mixing spectroscopy of a two-level system interacting with two fields of arbitrary intensity

We study pump–probe and four-wave mixing spectroscopy for moderately intense copropagating pump and probe beams (Rabi frequencies 2|V1,2|) interacting with an open two-level system where the lower state of an optical transition relaxes faster to reservoir states than the upper state does. The probe absorption spectrum displays an ultranarrow extraresonant antihole (ERA) when |V1| ≥ |V2| and a ultranarrow dip when |V1| < |V2|. The pump and probe absorption profiles display opposite tendencies except for the case of |V1| = |V2| when identical ERA’s are produced. The four-wave mixing spectrum shows an extraresonant dip for |V1| ≥ |V2| and an ERA when |V1| < |V2| The subnatural features are not power broadened.

Ultranarrow extraresonant antiholes in pump–probe spectroscopy induced by inelastic collisions

Pump-probe spectroscopy with copropagating pump and probe beams of an open two-level system where, as a result of inelastic collisions, the lower state of an optical transition relaxes faster to reservoir states than the upper state does, may yield an antihole in the probe spectral profile whose linewidth is subnatural and unaffected by Doppler broadening.