Coherent control of collective spontaneous emission in an extended atomic ensemble resonantly interacting with single-photon wave packets is analyzed. A scheme for coherent manipulation of collective atomic states is developed such that superradiant states of the atomic system can be converted into subradiant ones and vice versa. Possible applications of such a scheme for optical quantum-state storage and single-photon wave packet shaping are discussed. It is shown that also in the absence of inhomogeneous broadening of the resonant line, single-photon wave packets with arbitrary pulse shape may be recorded as a subradiant state and reconstructed even although the duration of the wave packets is larger than the superradiant lifetime. Specifically the applicability for storing time-bin qubits, which are used in quantum cryptography, is analyzed.

The presence of an additive-conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, perfect repeatability and distinguishability of the apparatus cannot be attained simultaneously. Instead of repeatability, in this paper, the distinguishability in both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. An inequality shows that perfect distinguishability of both systems cannot be attained simultaneously.

The bound-state properties and hyperfine-structure splitting in the ground $S(L=0)$ states in the ${}^9\mathrm{Be}^{4+}{\mu }^{-}{e}^{-}$ and ${}^{10}\mathrm{Be}^{4+}{\mu }^{-}{e}^{-}$ beryllium-muonic ions are determined numerically with the use of highly accurate variational-wave three-body functions. Analogous hyperfine splittings are computed for the triplet (electronic) $2{}^{3}S(L=0)$ states in the four-body beryllium-muonic ions ${}^9\mathrm{Be}^{4+}{\mu }^{-}{e}_2^{-}$ and ${}^{10}\mathrm{Be}^{4+}{\mu }^{-}{e}_2^{-}$ and for the ground states in the five-body beryllium-muonic atoms ${}^9\mathrm{Be}^{4+}{\mu }^{-}{e}_3^{-}$ and ${}^{10}\mathrm{Be}^{4+}{\mu }^{-}{e}_3^{-}$.

We develop a time-dependent Hartree-Fock approximation that is appropriate for Bose-condensed systems. Defining a depletion Green’s function allows the construction of condensate and depletion particle densities from eigenstates of a single time-dependent (oscillating) Hamiltonian, guaranteeing that our approach is a number-conserving approximation. The poles of this Green’s function yield the energies of number-changing excitations for which the condensate particle number is held fixed, which we show has a gapped spectrum in the superfluid state. The linearized time-dependent version of this has poles at the collective frequencies of the system, yielding the expected zero sound mode for a uniform infinite system. We show how the approximations may be expressed in a general linear response formalism.

We study defect modes of a Bose-Einstein condensate in an optical lattice with a localized defect within the framework of the one-dimensional Gross-Pitaevskii equation. It is shown that for a significant range of parameters the defect modes can be accurately described by an expansion over Wannier functions, whose envelope is governed by the coupled nonlinear Schrödinger equations with a $\delta$ impurity. The stability of the defect modes is verified by direct numerical simulations of the underlying Gross-Pitaevskii equation with a periodic and defect potentials. We also discuss possibilities of driving defect modes through the lattice and suggest ideas for their experimental generation.

In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all components of the acceleration and rotation frequency projection on the plane perpendicular to gravity acceleration. Atom interference on the Raman transition driving by noncounterpropagating optical fields is proposed to exclude stimulated echo processes which can affect the accuracy of the atomic gyroscopes. Using noncounterpropagating optical fields allows one to get a new type of the Ramsey fringes arising in the unidirectional Raman pulses and therefore centered at the two-quantum line center. Density matrix in the Wigner representation is used to perform calculations. It is shown that in the time between pulses, in the noninertial frame, for atoms with fully quantized spatial degrees of freedom, this density matrix obeys classical Liouville equations.

Bose-Einstein condensates of ${}^{87}\mathrm{Rb}$ atoms are transferred into radio-frequency induced adiabatic potentials and the properties of the corresponding dressed states are explored. We report on measurements of the spin composition of dressed condensates. We also show that adiabatic potentials can be used to trap atom gases in novel geometries, including suspending a cigar-shaped cloud above a curved sheet of atoms.

High fidelity transmission of quantum polarization states is essential for realizing quantum networks. The degenerate ${\Psi }^{-}$ state is an eigenstate of a transmission fiber. In this paper we propose a method for preparing the degenerate ${\Psi }^{-}$ state using spontaneous four wave mixing (SFWM) in a fiber Sagnac loop excited by two orthogonally polarized pump waves. This configuration includes a 45° Faraday rotator, which creates a relative phase of $\pi$ between the two counterpropagating entangled photon pairs with indistinguishability both in frequencies and generation paths. We confirm that only the amplitude is degraded in the output wave form of nonlinear sum frequency generation in the Bell state analyzer after propagation through the fiber due to the polarization mode dispersion.

We show that contrarily to what it is claimed in Phys. Rev. A 72, 064306 (2005) entanglement is not necessary for explaining experimental results associated with the “single particle-vacuum” state $\mid \psi ⟩\sim \mid 0{⟩}_A\mid 1{⟩}_B+\mid 1{⟩}_A\mid 0{⟩}_B$.

I try to rebut Drezet's arguments [Phys. Rev. A. 74, 026301 (2006)]) against the state $\mid 0⟩\mid 1⟩+\mid 1⟩\mid 0⟩$ being entangled by agreeing with them. I also address some old arguments repeated by Drezet.

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.

We propose a scheme for quantum cryptography that uses the squeezing phase of a two-mode squeezed state to transmit information securely between two parties. The basic principle behind this scheme is the fact that each mode of the squeezed field by itself does not contain any information regarding the squeezing phase. The squeezing phase can only be obtained through a joint measurement of the two modes. This, combined with the fact that it is possible to perform remote squeezing measurements, makes it possible to implement a secure quantum communication scheme in which a deterministic signal can be transmitted directly between two parties while the encryption is done automatically by the quantum correlations present in the two-mode squeezed state.

It has long been known that reduced density matrices (RDM) can be used to obtain the exact ground state energy of many-particle Hamiltonians by performing a constrained minimization over the set of all $N$-representable reduced density matrices. In this paper, we present a set of $N$-representability constraints for both bosons and fermions based on expectation values. These expectation value constraints are derived from a simple yet nontrivial recursive formula, and can easily be included in RDM-based variational schemes. The expectation value constraints are shown to provide additional $N$-representability information when compared to existing $N$-representability constraints.

In a large variety of spectroscopical applications Bloch-Boltzmann equations (BBE) play an essential role. They describe the evolution of the reduced-density operator of an active atom, which is coupled to radiation (Bloch part) and which interacts collisionally with the perturber gas (Boltzmann part). The standard approach to the collisional part is well known from the literature. It preserves hermiticity and normalization, but the question of whether it preserves positivity seems to remain open. The completely positive BBE were recently derived via the general master-equation techniques. These two approaches are applied for a model of $n$-level nondegenerate atom. We show that within this model both approaches to the collisional part of BBE are equivalent (give the same physical predictions). The approach based upon master-equation techniques guarantees the preservation of hermiticity, normalization, and positivity. The proven equivalence ascertains that the standard approach also preserves positivity. Moreover, some aspects of the standard derivation (which atomic states do contribute to the evolution) are clarified by the established equivalence.

We discuss the implementation and characterization of the source of a slow, intense, and collimated beam of rubidium atoms. The cold atomic beam is produced by two-dimensional magneto-optical trapping in directions transverse to the atomic beam axis and unbalanced Doppler cooling in the axial direction. The vacuum design allows use of relatively low laser power and a considerably simplified assembly. The atomic beam has a high flux of about $2\times {10}^{10}\mathrm{atoms}∕\mathrm{s}$ at a total cooling laser power of $55\mathrm{mW}$. It has a narrow longitudinal velocity distribution with mean velocity $15\mathrm{m}∕\mathrm{s}$ with full width at half maximum $3.5\mathrm{m}∕\mathrm{s}$ and has a low divergence of $26\mathrm{mrad}$. The high flux enables ultrafast loading of about ${10}^{10}$ atoms into a three-dimensional (3D) magneto-optical trap within 500 ms. The variation of the atomic beam flux was studied as a function of the rubidium vapor pressure, cooling laser power, transverse cooling laser beam length, detuning of the cooling laser, and relative intensities of the cooling beams along the atomic beam axis. We also discuss a detailed comparison of our measurements of the cold atomic beam with a 3D numerical simulation.

We derive an analytical formula for the ionization rate of neutral atoms and molecules in a strong monochromatic field. Our model is based on the strong-field approximation with transition amplitudes calculated by an extended saddle-point method. We show that the present two-term saddle-point method reproduces even complicated structures in angular resolved photoelectron spectra.

Additional variables (also often called “hidden variables”) are sometimes added to standard quantum mechanics in order to remove its indeterminism or “incompleteness” and to make the measurement process look more classical. Here we discuss a case in which an additional variable arises almost spontaneously from the quantum formalism: the emergence of a relative phase between two highly populated Fock-state Bose-Einstein condensates. The model simulated here involves the interference of two Bose condensates, one with all up spins and the other with down spins, along a $z$ axis. With the clouds overlapping, we consider the results of measuring spins in a transverse plane (the general direction is studied in an appendix). The determination of the previously “hidden” phase becomes progressively more definite as additional measurements are made. We also provide an analysis of a recent and closely related experiment.

We study the effect of thermal fluctuations on homogeneous infinite Bose-Einstein condensate with spin $F=2$ in the cyclic state, when atoms occupy three hyperfine states with $m_F=0,\pm 2$. We use both the approach of small-amplitude oscillations and mapping of our model on the sine-Gordon model. We show that thermal fluctuations lead to the existence of the rough phase in one- and two-dimensional systems, when the presence of kinks is favorable. The structure and energy of a single kink are found. We also discuss the effect of thermal fluctuations on spin degrees of freedom in $F=1$ condensate.

We consider the evolution of a single-atom wave function in a time-dependent double-well interferometer in the presence of a spatially asymmetric potential. We examine a case where a single trapping potential is split into an asymmetric double well and then recombined again. The interferometer involves a measurement of the first excited state population as a sensitive measure of the asymmetric potential. Based on a two-mode approximation a Bloch vector model provides a simple and satisfactory description of the dynamical evolution. We discuss the roles of adiabaticity and asymmetry in the double-well interferometer. The Bloch model allows us to account for the effects of asymmetry on the excited state population throughout the interferometric process and to choose the appropriate splitting, holding, and recombination periods in order to maximize the output signal. We also compare the outcomes of the Bloch vector model with the results of numerical simulations of the multistate time-dependent Schrödinger equation.

We present for the first time a detailed experimental study of the oscillation frequency, linewidth, RF spectrum and the phase noise of a radiation-pressure-driven micromechanical oscillator in a microtoroid geometry. Through this study we identify the critical parameters for optimal operation of this device and derive key expressions for tailoring the desired characteristics. The outcome of this study paves the ground for exploiting this unique phenomenon in photonic systems as well as fundamental studies in macroscopic quantum mechanics.