M. Radonjić

Statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems

General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.

Efficient parametric non-degenerate four-wave mixing in hot potassium vapor

We have observed high gains of the probe and the conjugate beams in non-degenerate four-wave mixing in hot potassium vapor, using a double-Λ configuration at the D1 line of the 39 K isotope. Gains of up to 82 for the conjugate beam and 63 for the probe beam have been achieved. Higher gains were obtained than with other alkali atoms under comparable experimental conditions due to lower ground state hyperfine splitting in the potassium atom. Experimental parameters for maximal gain have been determined. Notable gains are achieved at low pump intensities (~10 W cm−2) that are attainable even by conventional laser diodes. Due to their high gains, the probe and the conjugate beams may be suitable for utilization in quantum correlation and relative intensity squeezing experiments.

Dissipative two-mode Tavis-Cummings model with time-delayed feedback control

We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we analytically calculate up to four possible non-equilibrium steady states (fixed points) and determine the corresponding complex phase diagram. Various possible phases are distinguished by the actual number of fixed points and their stability. In addition, we apply three time-delayed Pyragas feedback control schemes. Depending on the time delay and the strength of the control term this can lead to the stabilization of unstable fixed points or to the selection of a particular cavity mode that is macroscopically occupied.

Emergence of classical behavior from the quantum spin

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system.

Transient development of Zeeman electromagnetically induced transparency during propagation of Raman–Ramsey pulses through Rb buffer gas cell

We investigate, experimentally and theoretically, time development of Zeeman electromagnetically induced transparency (EIT) during propagation of two time separated polarization laser pulses, preparatory and probe, through Rb vapour. The pulses were produced by modifying laser intensity and degree of elliptical polarization. The frequency of the single laser beam is locked to the hyperfine transition of the D1 line in 87Rb. Transients in the intensity of component of the transmitted light are measured or calculated at different values of the external magnetic field, during both preparatory and probe pulse. Zeeman EIT resonances at particular time instants of the pulse propagation are reconstructed by appropriate sampling of the transients. We observe how laser intensity, Ramsey sequence and the Rb cell temperature affect the time dependence of EIT line shapes, amplitudes and linewidths. We show that at early times of the probe pulse propagation, several Ramsey fringes are present in EIT resonances, while at later moments a single narrow peak prevails. Time development of EIT amplitudes are determined by the transmitted intensity of the component during the pulse propagation.

Ehrenfest principle and unitary dynamics of quantum-classical systems with general potential interaction

Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between classical and quantum ones. We solved the problem of unitary description of two interpolating systems with general potential interaction. The general solution is used to show that with arbitrary potential interaction between the two interpolating systems the evolution of the so called unobservable variables is decoupled from that of the observable ones if and only if the interpolation parameters in the two interpolating systems are equal.

Influence of a laser beam radial intensity distribution on Zeeman electromagnetically induced transparency line-shapes in the vacuum Rb cell

Experimental and theoretical analyses show the effect of laser beam radial intensity distribution on line-shapes and line-widths of the electromagnetically induced transparency (EIT). We used Gaussian and Π (flat top) laser beam profiles, coupling the D1 transition of 87Rb atoms in the vacuum cell in the Hanle experimental configuration. We obtained non-Lorentzian EIT line-shapes for a Gaussian laser beam, while line-shapes for a Π laser beam profile are very well approximated with Lorentzian. EIT line-widths, lower for Gaussian than for Π, show nonlinear dependence on laser intensity for both laser beam profiles. EIT amplitudes have similar values and dependence on laser intensity for both laser beams, showing the maximum at around 0.8 mW cm−2. Differences between the EIT line-shapes for the two profiles are mainly due to distinct physical processes governing atomic evolution in the rim of the laser beam, as suggested from the EIT obtained from the various segments of the laser beam cross-section.

Effects of a laser beam profile on Zeeman electromagnetically induced transparency in the Rb buffer gas cell

Electromagnetically induced transparency (EIT) due to Zeeman coherences in the Rb buffer gas cell is studied for different laser beam profiles, laser beam radii and intensities from 0.1 to 10 mW cm?2. EIT line shapes can be approximated by the Lorentzian for wide Gaussian laser beam (6.5?mm in diameter) if laser intensity is weak and for a ? laser beam profile of the same diameter. Line shapes of EIT become non-Lorentzian for the Gaussian laser beam if it is narrow (1.3?mm in diameter) or if it has a higher intensity. EIT amplitudes and linewidths, for both laser beam profiles of the same diameter, have very similar behaviour regarding laser intensity and Rb cell temperature. EIT amplitudes are maximal at a certain laser beam intensity and this intensity is higher for narrower laser beams. The EIT linewidth estimated at zero laser intensity is about 50 nT or 0.7?kHz, which refers to 1.5?ms relaxation times of Zeeman coherences in 87Rb atoms in our buffer gas cell. Blocking of the centre of the wide Gaussian laser beam in front of the photo detector yields Lorentzian profiles with a much better contrast to the linewidth ratio for EIT at higher intensities, above ?2 mW cm?2.

Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics

Abstract A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

The connection between electromagnetically induced transparency in the Zeeman configuration and slow light in hot rubidium vapor

We experimentally studied Zeeman electromagnetically induced transparency (EIT) resonances and slow light propagation in hot Rb vapor. Propagation of weak σ− polarized light pulses in the presence of stronger σ+ polarized background through Rb vapor was realized using a single laser beam and the Pockels cell. The dependences of slow light group velocity and fractional pulse delay on the overall laser beam intensity and temporal pulse length showed that lower optical power and longer light pulses lead to improved EIT and slow light features. The connection between EIT and slow light was also investigated showing that narrower and more contrasted EIT resonances are necessary for further decreasing a group velocity.