We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function indicates that this transition is first order, and the precursors of the phase transition are already displayed in systems of a few dozen bosons. Systems of this size do not exhibit new phases as more vortices are added to the system.

We present a quantum theory of light scattering for the analysis of the quantum statistical and fluctuation properties of light scattered or emitted by micrometric and nanometric three-dimensional structures of arbitrary shape. We obtain general three-dimensional quantum-optical input-output relations providing the output photon operators in terms of the input photon operators and of the noise currents of the scattering system. These relations hold also for photon operators associated with evanescent fields, for anisotropic scattering systems and/or for media with a nonlocal susceptibility. We find that the commutation relations of the output photon operators, carrying all the information on the scattering and/or the emission process, result to be fixed by energy conservation and reciprocity. We prove that this quantization scheme is consistent with QED commutation rules by using a novel relationship between vacuum and thermal fluctuations. This theoretical framework has been applied to analyze the spectral density of light close to a point scatterer under different nonequilibrium conditions.

We demonstrate that radiation field in mixed thermal or phase-randomized coherent state can be entangled in such a way that Bell inequalities are violated. A counterintuitive result is obtained: a specific test reveals that maximal violation can be achieved with mixed states exhibiting large entropy.

We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both nonadaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be $\dot{\phi }=\sqrt{\kappa }\xi \mathrm{}\left(t\right),$ where $\xi \mathrm{}\left(t\right)\mathrm{}$ is δ-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is $N=P/ħ\omega \kappa ,$ the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance $\simeq N^{-1/2}/2.\mathrm{}$ This is $\sqrt{2}$ times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as $N^{-2/3},$ compared to $N^{-1/2}$ for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as $N^{-1/2}.$ It offers a significant improvement over nonadaptive interferometry only for N of order unity.

We show that the effect of coherent population trapping may result in resonant enhancement of ${\chi }^{\mathrm{}\left(5\right)\mathrm{}}$ or higher-order nonlinearities. The enhancement is accompanied by suppression of the other linear and nonlinear susceptibility terms. This effect has promise for a realistic scheme of photon phase gates necessary for practical implementation of quantum processing protocols.

Doppler-free resonances have been observed in Rb atomic vapor coherently driven by two strong-coupling fields in an intrinsically non-Doppler-free geometry. A four-level theoretical model explains the experimental results. The explanation of the physics is based on the interplay between coherences generated in a four-level system.

The pulse width of $\mathrm{Xe}\mathrm{}\left(M\right)\mathrm{}$ emission, whose photon energy is $\sim 1\mathrm{keV},$ from Xe clusters excited by a subpicosecond intense laser pulse was estimated to be shorter than 100 ps. While that of $\mathrm{Xe}\mathrm{}\left(N\right)\mathrm{}$ emission, whose photon energy is $\sim 100\mathrm{eV},$ was longer than 1 ns. The theoretical estimation of radiative recombination rates suggests that the observed keV x ray is a prompt x ray.

The energy straggling of protons penetrating thin foils is theoretically and experimentally investigated for intermediate and high impact velocities. We calculate separately the contributions due to the interaction of the projectile with valence and core electrons. The energy straggling originated in the valence band is evaluated within the dielectric formalism, using the Mermin-Lindhard dielectric response function. The contribution coming from the core ionization is calculated with the continuum-distorted-wave–eikonal-initial-state (CDW-EIS) approximation. The predictions of the model are compared with recent measurements for Al, Zn, and Au targets. In addition, experimental results of straggling for Si are presented. The transmission method is used to measure the straggling, and experimental data are corrected to consider roughness effects. Theoretical values are in good agreement with the experiments in the whole range of energies considered. At low energies the binary interaction with valence electrons is the dominant mechanism, while the inner-shell contribution becomes the most important one as the energy increases.

We derive two different sets of rate equations for sympathetic cooling of harmonically trapped bosons or fermions. The rate equations are obtained from a master equation derived earlier by Lewenstein et al. [Phys. Rev. A 51, 4617 (1995)] by means of decoherence and ergodicity arguments. We show analytically that the thermal equilibrium state is a stationary solution of our rate equation. We present analytical results for the rate coefficients which are needed to solve the rate equations, and we give approximate formulas that permit their computation in practice. We solve the two sets of rate equations numerically and compare the results. The cooling times obtained in both approaches agree very well. The equilibration rates show fair agreement.

We present a set of exploratory experimental studies of velocity-selective coherent population trapping (VSCPT) on the $2{}^3{S}_1\to 2{}^3{P}_1$ transition of Helium, including the effect of an external magnetic field along the propagation direction of the light. We also investigate in detail the effects of the laser detuning and the atom-laser interaction time in determining the shape and width of the VSCPT velocity distribution. Our data corroborates some previous theory and calculations. We demonstrate that the only observable effect of a magnetic field applied along the direction of light propagation is to shift the center of the VSCPT peaks in the atomic velocity distribution by an amount proportional to the magnitude of the applied field. We present a semiclassical picture that describes the atomic motion of VSCPT in such a B field.

We propose a method for preparing maximal path entanglement with a definite photon-number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form $|4,0〉+|0,4〉,$ using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.

We present quantum path distributions of high-order harmonics produced by rare gas atoms interacting with an intense 810 nm laser field, obtained by numerical integration of the time-dependent Schrödinger equation within the single active electron approximation. We find that the distributions are sensitive to the atomic potentials, and differ from the distributions predicted by the strong field approximation. We demonstrate that these differences can lead to significant differences in the time-frequency behavior of the harmonics produced in a macroscopic nonlinear medium.

It is shown that the detection loophole that arises when trying to rule out local realistic theories as alternatives for quantum mechanics can be closed if the detection efficiency $\eta >~{\mathrm{Cd}}^{3/4}{2}^{-0.0035d}$ where d is the dimension of the bipartite entangled system and C is a positive constant. Furthermore it is argued that such an exponential decrease of the detector efficiency required to close the detection loophole is almost optimal. This optimality argument is based on a close connection that exists between closing the detection loophole and the amount of classical communication required to simulate quantum correlations when the detectors are perfect.

We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the Hamilton trajectories of the particle in complex phase space and time. In a magnetic field, the tunneling particle comes from beneath the barrier with a nonzero velocity. The exit location in the classically allowed region is obtained by matching the decaying and outgoing branches of the WKB wave function on a caustic of the set of the complex trajectories. The slope of the logarithm of the wave function sharply changes on the anti-Stokes surface where there occurs switching between different WKB branches. For potential wells that are parabolic near the minimum, we also provide a bounce-type formulation. The theory is applied to the models that are relevant to tunneling from correlated two-dimensional electron systems in a magnetic field parallel to the electron layer.

We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].

The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (“independent decoherence”) and qubits interacting collectively with the same reservoir (“collective decoherence”). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: We show that this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A nontrivial behavior (“recoherence”) is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system’s Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of “noiseless” quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the dynamical results obtained for the register density matrix.

It is shown how to exactly simulate many-body interactions and multiqubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a geometric phase, depending on a product of commuting operators. The latter allows one to simulate many-body Hamiltonians and nonlinear Hamiltonians, and to implement a big variety of multiqubit quantum gates on both qubits and encoded qubits. An application to the quantum amplitude amplification algorithm will be discussed.

The robustness of entanglement for the set of eight total spin states of three qubits is characterized and related to their permutation symmetries. These states fall into four sets of two entangled states, differing in their patterns of robustness to entanglement when one of the states is lost. Their entanglement measures are shown to contain certain permutation symmetries of the spin states and their corresponding marginal two-particle states. The eight entangled states are also found to be eigenstates of the Heisenberg Hamiltonian, ${\overrightarrow{\sigma }}_A\cdot {\overrightarrow{\sigma }}_B+{\overrightarrow{\sigma }}_A\cdot {\overrightarrow{\sigma }}_C+{\overrightarrow{\sigma }}_B\cdot {\overrightarrow{\sigma }}_C/2.\mathrm{}$ This allows the entanglement to be tuned in a systematic way by adjusting the symmetries of a general three-qubit Hamiltonian. The necessary and sufficient conditions for separability of a general three-particle state in terms of (a) three one-particle states and (b) one one-particle and one two-particle state are also given.

The analytic origin behavior of Hartree-Fock and Dirac-Fock-Coulomb electron-electron interaction potentials is derived. This yields explicit expressions, which depend on $〈{1/r}^n〉$ matrix elements. The direct part of the electron-electron interaction including the self-interaction is equal for all shells. If the self-interaction is subtracted the Coulomb part will become shell dependent. Additional shell dependence of the origin behavior originates from the true exchange-interaction terms. For the Dirac-Fock-Coulomb operator we find singular behavior for non s shells, if a Coulomb-type electron-nucleus potential is used, while it is nonsingular for s shells. For all shells in case of finite nuclear models, the electron-electron interaction potentials are nonsingular at the origin. A comparison of potentials for the small and large component of the relativistic radial spinor shows that they are equal in the long-range limit, while this is not true, in general, at the origin. The analytic results presented are tested by comparing them to numerical results obtained for the zinc atom.

Four basic theorems involving the correlation matrices are demonstrated here. One of these theorems establishes, as a necessary and sufficient condition, that the solutions of the fourth-order modified contracted Schrödinger equation correspond uniquely to those of the Schrödinger equation. The complete equivalence between these two equations is demonstrated. Another equation equivalent to the Schrödinger equation but involving only the correlation matrices is also obtained as a consequence of the second theorem.