We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimizing the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order $h\times 1\mathrm{MHz}$.

A spin-1 ferromagnetic Bose-Einstein condensate subject to a certain magnetic field exhibits a broken-axisymmetry phase in which the magnetization tilts against the applied magnetic field due to the competition between ferromagnetism and linear and quadratic Zeeman effects. The Bogoliubov analysis shows that in this phase two Goldstone modes associated with U(1) and SO(2) symmetry breakings exist, in which phonons and magnons are coupled to restore the two broken symmetries.

Stimulated cross-cavity photon emission and carrier depletion in closely packed microlaser arrays supports the propagation of long-range intercavity oscillations in the coupled populations of coherent photons and carriers. The related periodic variations in the cavity radiation envelopes propagate as slow optical waves over the array at sonic group velocity. Externally driven excitation of such waves is investigated by numerical simulations and compared with theoretically obtained dispersion relation. While the theoretical minimum group velocity tends to zero at the lattice dispersion band edges, the requirement that the spatial decay constant be much smaller than the inverse lattice period limits the useful parameter regime. The lowest observed propagation velocities are of the order of the sound speed (km/s), a five order of magnitude reduction.

A quantum mechanical model is formulated to describe the coupling between pump intensity noise and laser frequency noise in a solid-state laser. The model allows us to investigate the limiting effects of closed-loop stabilization schemes that utilize this coupling. Two schemes are considered: active control of the quadrature phase noise of the laser and active control of the amplitude noise of the laser. We show that the noise of the laser in the actively stabilized quadrature is ultimately limited by the vacuum noise introduced by the feedback beamsplitter in both schemes. In the case of active control of the quadrature phase noise, the noise is also limited by the intensity noise floor of the detection scheme. We also show that some sources of noise in the passively stabilized quadrature can be suppressed and that it is possible to achieve simultaneous quadrature amplitude and phase stabilization of a solid-state laser. However, the quantum mechanically driven noise in the passively stabilized quadrature cannot be suppressed. While this poses the ultimate limit to the noise in the passively stabilized quadrature, we show that it is experimentally feasible to observe squeezing directly generated by a solid-state laser using this technique.

We analyze a class of entangled states for bipartite $d\otimes d$ systems, with $d$ nonprime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such a simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition. Moreover, for a restricted set of such states, we prove that there exists an interval of the mixing parameter such that both partial transposition and realignment (i.e., all permutational criteria in the bipartite setting) fail to detect them as entangled. In the range in which the states are positive under partial transposition (PPT), they are not distillable; on the other hand, the states in the considered class are provably distillable as soon as they are nonpositive under partial transposition. The states are associated to any set of more than two pure states. The analysis is extended to the multipartite setting. By an opportune selection of the set of multipartite pure states, it is possible to construct mixed states which are PPT with respect to any choice of bipartite cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we show that every $k$-positive but not completely positive map is associated to a family of nondecomposable maps.

We show how to quantify the optimal tradeoff between the amount of information retrieved by a quantum measurement in estimating an unknown spin coherent state and the disturbance on the state itself, and how to derive the corresponding minimum-disturbing measurement.

We demonstrate a method to make mixtures of ultracold atoms that does not make use of a two-species magneto-optical trap. We prepare two clouds of ${}^{87}\mathrm{Rb}$ atoms in distinct magnetic quadrupole traps and mix the two clouds by merging the traps. For correctly chosen parameters the mixing can be done essentially without loss of atoms and with only minor heating. The basic features of the process can be accounted for by a classical simulation of particle trajectories. Such calculations indicate that mixing of different mass species is also feasible, opening the way for using the method as a starting point for making quantum gas mixtures.

We study the acoustic attenuation rate in the Fermi-Bose model describing mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic change of the acoustic attenuation rate as the fermionic component is evolved through the BEC to BCS crossover, in the context of a mean-field model applied to a finite-range fermion-fermion interaction at zero temperature, such as discussed previously by Parish et al. [Phys. Rev. B 71, 064513 (2005)] and Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the acoustic attenuation rate as a function of the boson energy represents a signature for superfluidity in the fermionic component.

We calculate the critical rotation frequency at which a vortex state becomes energetically favorable over the vortex-free ground state in a harmonically trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as well as the usual $s$-wave contact interactions. In the Thomas-Fermi (hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with the dipoles aligned along the axis of symmetry of the trap) tend to have lower critical rotation frequencies than their purely $s$-wave contact interaction counterparts. The converse is true for dipolar condensates in prolate traps. Quadrupole excitations and center of mass motion are also briefly discussed as possible competing mechanisms to a vortex as means by which superfluids with partially attractive interactions might carry angular momentum.

An interferometer using fermions with transverse momentum is analyzed. It is shown that the phase uncertainty $\Delta \theta$ of such a fermion interferometer with either two-dimensional (2D) or one-dimensional (1D) transverse momentum states can be lower than that of an interferometer using fermions with the longitudinal momentum state. The improvement is due to the fact that the transit time for the transverse momentum states is a constant and thus the phase evolution factor is a quadratic function of the dispersive momentum compared to the linear dependence of phase evolution on the dispersive momentum for the longitudinal momentum state. Furthermore, 2D transverse momentum state may have lower phase uncertainty than 1D transverse momentum state because of dimensional effects.

Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopants in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rare-earth-ion-doped crystals.

We present an investigation of the resonances of a doubly excited helium atom in a strong magnetic field covering the regime $B=0–100\mathrm{a.u.}$ A full-interaction approach which is based on an anisotropic Gaussian basis set of one-particle functions being nonlinearly optimized for each field strength is employed. Accurate results for a total of 17 resonances below the threshold consisting of ${\mathrm{He}}^{+}$ in the $N=2$ state are reported in this work. This includes states with total magnetic quantum numbers $M=0,-1,-2$ and even $z$ parity. The corresponding binding energies are compared to approximate energies of two-particle configurations consisting of two hydrogenlike electrons in the strong-field regime, thereby providing an understanding of the behavior of the energies of the resonances with varying field strength.

We derive a general framework, in terms of elastic theory, for describing the distortion of the vortex lattice in a rotating Bose-Einstein condensate at arbitrary rotation speed and determining the dependence of the distortion on the density inhomogeneity of the system. In the rapidly rotating limit, we derive the energetics in terms of Landau levels, including excitation to higher levels; the distortion depends on the excitation of higher levels as well as on the density gradient. As we show, the dominant effect of higher Landau levels in a distorted lattice in equilibrium is simply to renormalize the frequency entering the lowest Landau level condensate wave function—from the transverse trap frequency, $\omega$, to the rotational frequency, $\Omega$, of the system. Finally, we show how the equilibrium lattice distortion emerges from elastohydrodynamic theory for inhomogeneous systems.

It is shown that by switching a specific time-dependent interaction between a harmonic oscillator and a transmission line (a waveguide, an optical fiber, etc.) the quantum state of the oscillator can be transferred into that of another oscillator coupled to the distant other end of the line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time $T$, the fidelity approaches 1 exponentially in $\gamma T$ where $\gamma$ is a characteristic damping rate. Hence, a good fidelity is achieved even for a transfer time of a few damping times. Some implementations are discussed.

Qubit loss and gate failure are significant problems for the development of scalable quantum computing. Recently, various schemes have been proposed for tolerating qubit loss and gate failure. These include schemes based on cluster and parity states. We show that by designing such schemes specifically to tolerate these error types we cause an exponential blowout in depolarizing noise. We discuss several examples and propose techniques for minimizing this problem. In general, this introduces a tradeoff with other undesirable effects. In some cases this is physical resource requirements, while in others it is noise rates.

We propose the dynamical creation of twin Fock states, which exhibit Heisenberg-limited interferometric phase sensitivities, in an optical lattice. In our scheme a two-component Mott insulator with two bosonic atoms per lattice site is melted into a superfluid. This process transforms local correlations between hyperfine states of atom pairs into multiparticle correlations extending over the whole system. The melting time does not scale with the system size which makes our scheme experimentally feasible.

We examine the entanglement creation between two mutually independent two-level atoms immersed in a thermal bath of quantum scalar fields in the presence of a perfectly reflecting plane boundary. With the help of the master equation that describes the evolution in time of the atom subsystem obtained, in the weak-coupling limit, by tracing over environment (scalar fields) degrees of freedom, we find that the presence of the boundary may play a significant role in the entanglement creation in some circumstances and the new parameter, the distance of the atoms from the boundary, besides the bath temperature and the separation between the atoms, gives us more freedom in manipulating entanglement generation. Remarkably, the final remaining entanglement in the equilibrium state is independent of the presence of the boundary.

We propose the efficient combinations of laser pulses for constructing a multiqubit gate with cold trapped ions in order to implement maximally entangled states with quantum logic. Within the ion-trap quantum computation using the center of mass as the data bus, we can minimize the number of laser pulses as well as their operation time, which can improve the fidelity. We also present some numerical results of the operation time for different numbers of qubits and values of the Lamb-Dicke parameter.

In two and three coupled Josephson charge qubits, we exemplify how to take pulses for realizing quantum gates from fidelity-limited pioneering stages to the decoherence limit of near time optimal high-fidelity controls. Thus, a CNOT gate can be obtained with a fidelity $>1$–${10}^{-9}$ for the two qubits. Even when including higher charge states, the leakage is below $1\%$, although the pulses are nonadiabatic. The controls are five times faster than the pioneering experiment [Nature (London) 425, 941 (2003)] for otherwise identical parameters—i.e., a progress towards the error-correction threshold by a factor of 100. We outline schemes to generate these shaped pulses by Cauer synthesis, or more generally by few LCR circuits. The approach generalizes to larger systems: e.g., directly realizing a TOFFOLI gate in three linearly coupled charge qubits is shown to be 13 times faster than decomposing it into a circuit of nine CNOT gates of the above experimental work. In view of the next generation of fast pulse shapers, the combination of methods is designed to find wide application in quantum control of pseudospin and macroscopic quantum systems.