In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser, and a strong classical coupling laser, which form a three-level $\Lambda$-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and interatomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.

Atomic Bose-Einstein condensate is heated by atomic losses. The losses act as a heat reservoir for the condensate. The condensate is approaching a state of thermal equilibrium with a thermal depletion ranging from 1% for a uniform three-dimensional (3D) condensate to around 13% for a quasi-1D condensate in a harmonic trap.

We investigate the spontaneous radiation from a two-level atom embedded in a three-dimensional anisotropic photonic crystal with two bands. The properties of the spontaneous emission are dependent strongly on the position of the upper level. The faster and slower decay components can occur in the emitted field, but it does not mean the existence of both accelerated and inhibited components for the atomic population decay. The radiation spectrum is dependent on the location of the observer. We also study the influence of the existence of the two bands on spontaneous emission, Lamb shift, the emitted field, and the radiation spectrum.

We propose and implement a method to produce a spatial antibunched field with free-propagating twin beams from spontaneous parametric down-conversion. The method consists in changing the spatial propagation by manipulating the transverse degrees of freedom through reflections of one of the twin beams. Our method uses reflective elements, eliminating losses from absorption by the objects inserted in the beams.

We analyze the quantum-mechanical limits to the plasmon-assisted entanglement transfer observed by Altewischer, van Exter, and Woerdman [Nature 418, 304 (2002)]. The maximal violation S of Bell’s inequality at the photodetectors behind two linear media (such as the perforated metal films in the experiment) can be described by two ratio’s ${\tau }_1,$ ${\tau }_2$ of polarization-dependent transmission probabilities. A fully entangled incident state is transferred without degradation for ${\tau }_1={\tau }_2,$ but a relatively large mismatch of ${\tau }_1$ and ${\tau }_2$ can be tolerated with a small reduction of S. We predict that fully entangled Bell pairs can be distilled out of partially entangled radiation if ${\tau }_1$ and ${\tau }_2$ satisfy a pair of inequalities.

We propose a generalized radiation-field quantization formalism, where quantization does not have to be referenced to a set of power-orthogonal eigenmodes as conventionally required. This formalism can be used to directly quantize the true system eigenmodes, which can be non-power-orthogonal due to the open nature of the system or the gain/loss medium involved in the system. We apply this generalized field quantization to the laser linewidth problem, in particular, lasers with non-power-orthogonal oscillation modes, and derive the excess-noise factor in a fully quantum-mechanical framework. We also show that, despite the excess-noise factor for oscillating modes, the total spatially averaged decay rate for the laser atoms remains unchanged.

Spin squeezing via atom-field interactions is considered within the context of the Tavis-Cummings model. An ensemble of N two-level atoms interacts with a quantized cavity field. For all the atoms initially in their ground states, it is shown that spin squeezing of both the atoms and the field can be achieved provided the initial state of the cavity field has coherence between number states differing by 2. Most of the discussion is restricted to the case of a cavity field initially in a coherent state, but initial squeezed states for the field are also discussed. Optimal conditions for obtaining squeezing are obtained. An analytic solution is found that is valid in the limit that the number of atoms is much greater than unity and is also much larger than the average number of photons, ${\alpha }^2,$ initially in the coherent state of the cavity field. In this limit, the degree of spin squeezing increases with increasing $\alpha ,$ even though the field more closely resembles a classical field for which no spin squeezing could be achieved.

The generation of tunable, nanosecond-pulsed extreme-ultraviolet (EUV) light $(84.92\mathrm{}\mathrm{nm}$ to $84.97\mathrm{nm}$ $\sim 14.6\mathrm{eV})$ using four-wave mixing in optically deep krypton gas was investigated experimentally and theoretically. The sum-frequency mixing scheme generated light from two overlapping autoionizing resonances, ${17s}^{\prime }$ and ${15d}^{\prime }$. We investigated whether the laser-induced atomic coherence effect of electromagnetically induced transparency (EIT) could enhance the intensity of the EUV light generated. The maximum EUV output was seen from the region where the ${15d}^{\prime }$ autoionizing resonance has a transparency window due to Fano-type quantum interference. An analytical model using appropriate atomic parameters explains how background absorption can prevent EIT enhancement of EUV generation; and shows how a background Raman-like coupling term in the nonlinear susceptibility can well describe the measured EUV generation spectrum.

The photoabsorption cross section and ion-yield spectra of He have been measured in the region of the double-excitation resonances below the $N=2\mathrm{}$ threshold. For resonances decaying predominantly by autoionization [the ${2,0}_n$ series, low values of $n;$ notation of Herrick and Sinanoǧlu, Phys. Rev. A 11, 97 (1975)], the two kinds of spectra yield the same information. For resonances where substantial decay by fluorescence occurs ${(2,1\mathrm{}}_n$ and $2,-1_n$ series), the ion-yield spectrum differs significantly from the cross section. The ratios of peak intensity of one series to the other are clearly different and the Fano line shape parameter $\mathrm{}\left(q\right)\mathrm{}$ of the ${2,1}_n$ series also changes as a function of $n,$ in qualitative agreement with the trends expected when the fluorescence channel is taken into account. These direct measurements confirm the influence of fluorescence on the cross section and agree with previous indirect measurements.

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.

Effects caused by the electron electric dipole moment (EDM) in gadolinium garnets are considered. Experimental studies of these effects could improve the current upper limit on the electron EDM by several orders of magnitude. We suggest a consistent theoretical model and perform calculations of observable effects in gadolinium gallium garnet and gadolinium iron garnet. Our calculation accounts for both direct and exchange diagrams.

We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and non-negative in the basis of the eigenstates of the symmetry operator.

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. $88,$ 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

We propose a scheme to produce the maximally two-photon polarization entangled state with single-photon sources and the passive linear optics devices. In particular, our scheme only requires the normal photon detectors which distinguish the vacuum and non-vacuum Fock number states. A sophisticated photon detector distinguishing between one-photon state and two-photon state is unnecessary in the scheme.

Experimental data are presented from three different heavy-ion storage rings (ASTRID in Aarhus, CRYRING in Stockholm, and TSR in Heidelberg) to assess the reliability of this experimental tool for the extraction of absolute rate coefficients and cross sections for dissociative recombination (DR). The DR reaction between ${\mathrm{HD}}^{+}$ and electrons has been studied between 0 and 30 eV on a dense energy grid. ${\mathrm{HD}}^{+}$ displays two characteristic local maxima in the DR rate around 9 and 16 eV. These maxima influence the data analysis at smaller collision energies. We conclude that resonant structures in the DR cross sections are reproduced among the experiments within the collision energy resolution. The absolute cross sections agree within the systematic experimental errors of 20% related to the measurement of the ion currents. Absolute thermal rate coefficients for ${\mathrm{HD}}^{+}$ ions are given for an electron temperature range of 50–300 K. Results for the DR cross section and the thermal rate coefficients are compared to recent theoretical calculations including rotational effects, finding satisfactory agreement.

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.

We investigate a radial spin hedgehog, analogous to the Dirac monopole, in an optically trapped atomic spin-1 Bose-Einstein condensate. By joining together a monopole-antimonopole pair, we may form a vortex line with free ends. We numerically simulate the three-dimensional dynamics and imaginary time relaxation of these structures to nonsingular textures and show that they can be observable for realistic experimental parameters.

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.

We experimentally observe the formation of high-order transverse patterns in a laser resonator with a high degree of frequency degeneracy. It is found that the transverse patterns are well localized on the Lissajous orbits. The connection between the wave functions and the classical periodic orbits is analytically constructed by using the representation of SU(2) coherent states. With this connection, the observed transverse patterns are reconstructed very well. The nice reconstruction suggests that the laser resonators can be deliberately designed to attain a more thorough understanding of the quantum-classical connection.

We generate high-order harmonics by using an 800-nm fundamental pulse whose polarization evolves with time. Controlling the ellipticity modulation of the fundamental field allows us to continuously confine the harmonic emission from an estimated minimum value of 7 fs $\left(1\mathrm{}\mathrm{fs}{=10\mathrm{}}^{-15}\mathrm{s}\right)$ up to more than the 35 fs input pulse duration. Depending on the observed harmonic, the harmonic spectrum can show either a narrowing or a broadening when the ellipticity is changed in good agreement with an effective confinement of the high-order harmonic generation.