We numerically evaluate the density distribution of a spin-1 bosonic condensate in its ground state within a modified Gross-Pitaevskii theory, which is obtained by the combination of the exact solution of the corresponding integrable model with the local-density approximation. Our study reveals that atoms in the $m_F=0$ state are almost completely suppressed for the antiferromagnetic interactions in both weakly and strongly interacting regimes, whereas all three components remain nonvanishing for ferromagnetic interactions. In particular, when the system is in the Tonks-Girardeau regime, obvious Fermi-like distribution emerges for each component. We also discuss the possible deviation of the spatial distribution from the Fermi-like distribution when the spin-spin interaction is strong enough.

We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite-temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature, we find the possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite-temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while the higher one corresponds to the usual superfluid-normal transition. We discuss how these phase transitions could be observed in ultracold gases of fermionic atoms.

We study a gas of fermions undergoing a wide resonance $s$-wave BCS–Bose-Einstein-condensate (BEC) crossover, in the BEC regime at zero temperature. We calculate the chemical potential and the speed of sound of this Bose-Einstein-condensed gas, as well as the condensate depletion, in the low-density approximation. We discuss how higher-order terms in the low-density expansion can be constructed. We demonstrate that the standard BCS-BEC gap equation is invalid in the BEC regime and is inconsistent with the results obtained here. The low-density approximation we employ breaks down in the intermediate BCS-BEC crossover region. Hence our theory is unable to predict how the chemical potential and the speed of sound evolve once the interactions are tuned towards the BCS regime. As a part of our theory, we derive the well-known result for the bosonic scattering length diagrammatically and check that there are no bound states of two bosons.

Faraday rotation based on ac Stark shifts is a mechanism that can entangle the polarization states of photons and atoms. We study the entanglement dynamics inside an optical cavity, and characterize the photon-atom entanglement by using the Schmidt decomposition method. The time dependence of entanglement entropy and the effective Schmidt number are examined. We show that the entanglement can be enhanced by the cavity, and the entanglement entropy can be controlled by the initial fluctuations of atoms and photons.

An ensemble of multilevel atoms is a good candidate for a quantum information storage device. The information is encrypted in the collective ground state atomic coherence, which, in the absence of external excitation, is decoupled from the vacuum and therefore decoherence free. However, in the process of manipulation of atoms with light pulses (writing, reading), one inadvertently introduces a coupling to the environment, i.e., a source of decoherence. The dissipation process is often treated as an independent process for each atom in the ensemble, an approach which fails at large atomic optical depths where cooperative effects must be taken into account. In this paper, the cooperative behavior of spin decoherence and population transfer for a system of two, driven multilevel atoms is studied. Not surprisingly, an enhancement in the decoherence rate is found, when the atoms are separated by a distance that is small compared to an optical wavelength; however, it is found that this rate increases even further for somewhat larger separations for atoms aligned along the direction of the driving field’s propagation vector. A treatment of the cooperative modification of optical pumping rates and an effect of polarization swapping between atoms is also discussed, lending additional insight into the origin of the collective decay.

We study the effects of frequency-dependent squeeze-amplitude attenuation and squeeze-angle rotation by electromagnetically induced transparency (EIT) on gravitational-wave (GW) interferometers. We propose the use of low-pass, bandpass, and high-pass EIT filters, an S-shaped EIT filter, and an intracavity EIT filter to generate frequency-dependent squeezing for injection into the antisymmetric port of GW interferometers. We find that the EIT filters have several advantages over the previous filter designs with regard to optical losses, compactness, and the tunability of the filter linewidth.

We present a molecular dynamics model giving a classical description of valence and core electrons in Na clusters irradiated by intense laser pulses. Both core electrons and valence electrons are treated at the same level as classical Coulomb interacting particles. A minimum of quantum information is embodied by giving to each electron a finite width adjusted to the energies and radii of the related atomic shells. This model provides a surprisingly stable cluster ground state and a fair description of optical linear response. We focus on electron emission under laser irradiation in the intermediate and high-intensity regime. With increasing laser intensity, we observe a clear threshold for core ionization at a critical intensity of ${10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$. Excitation at the critical intensity produces a fragmentation of the cluster into single ions with an average charge state of $+2$ and a kinetic energy distribution, which clearly indicates a Coulomb explosion.

In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local noise other than photon loss noise. We obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible in the combined presence of both noise types, provided that the loss probability is less than $3\times {10}^{-3}$ and the depolarization probability is less than ${10}^{-4}$. Our fault-tolerant protocol involves a number of innovations, including a method for syndrome extraction known as telecorrection, whereby repeated syndrome measurements are guaranteed to agree. This paper is an extended version of Dawson et al. [Phys. Rev. Lett. 96, 020501 (2006)].

We propose an efficient approach to prepare Einstein-Podolsky-Rosen (EPR) pairs in currently existing Josephson nanocircuits with capacitive couplings. In these fixed coupling circuits, two-qubit logic gates could be easily implemented while, strictly speaking, single-qubit gates cannot be easily realized. For a known two-qubit state, conditional single-qubit operation could still be designed to evolve only the selected qubit and keep the other qubit unchanged; the rotation of the selected qubit depends on the state of the other one. These conditional single-qubit operations allow us to deterministically generate the well-known Einstein-Podolsky-Rosen pairs, represented by EPR-Bell (or Bell) states. Quantum-state tomography is further proposed to experimentally confirm the generation of these states. The decays of the prepared EPR pairs are analyzed using numerical simulations. Possible application of the generated EPR pairs to test Bell’s Inequality is also discussed.

The high precision relativistic and radiative corrections to the energy of the excited $3{}^{1}S$ state of the beryllium atom are obtained. The nonrelativistic wave function, expanded in a basis of exponentially correlated Gaussian functions, yields the lowest upper bounds to the energy of $2{}^{1}S$ and $3{}^{1}S$ states. By means of the integral representation, a reference-quality Bethe logarithm has been obtained. The resulting theoretical $2{}^{1}S\text{−}3{}^{1}S$ transition energy amounts to $54677.78\left(45\right){\mathrm{cm}}^{-1}$ and differs from the known experimental value by about $0.5{\mathrm{cm}}^{-1}$.

The filamentation of powerful, ultrashort laser pulses in liquids is investigated. It is shown that the multiple filaments produced in ethanol can be modified into controllable, regular patterns by doping the medium with dyes at high concentrations. Experimental results are confirmed by three-dimensional numerical simulations. Pump-dump pulse experiments furthermore reveal that the stimulated emission from excited dye molecules in the bundle can be locked in phase and leads to bright interference patterns.

We assess the effect of the heat radiation emitted by mesoscopic particles on their ability to show interference in a double-slit arrangement. The analysis is based on a stationary, phase-space-based description of matter-wave interference in the presence of momentum-exchange-mediated decoherence.

We derive analytical formulas for the forward emission and side emission spectra of cavity-modified single-photon sources, as well as the corresponding normal-mode oscillations in the cavity quantum electrodynamics strong-coupling regime. We investigate the effects of pure dephasing, treated in the phase-diffusion model based on a Wiener-Levy process, on the emission spectra and normal-mode oscillations. We also extend our previous calculation of quantum efficiency to include the pure dephasing process. All results are obtained in the Weisskopf-Wigner approximation for an impulse-excited emitter. We find that the spectra are broadened, the depths of the normal-mode oscillations are reduced and the quantum efficiency is decreased in the presence of pure dephasing.

The mean king’s problem with mutually unbiased bases is reconsidered for arbitrary $d$-level systems. Hayashi et al. [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of $d-1$ mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when, e.g., $d=6$ or $d=10$. In contrast to their result, we show that the king’s problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.

We propose a double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation, and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similar to the six-state protocol, under individual attacks. Our scheme allows a robust implementation under the current technology.

We describe experiments on the trapping of atoms in microscopic magneto-optical traps on an optically transparent permanent-magnet atom chip. The chip is made of magnetically hard ferrite-garnet material deposited on a dielectric substrate. The confining magnetic fields are produced by miniature magnetized patterns recorded in the film by magneto-optical techniques. We trap Rb atoms on these structures by applying three crossed pairs of counterpropagating laser beams in the conventional magneto-optical trapping geometry. We demonstrate the flexibility of the concept in creation and in situ modification of the trapping geometries through several experiments.

We analyze the performance of holonomic quantum gates in semiconductor quantum dots, driven by ultrafast lasers, under the effect of a dissipative environment. The environment is modeled as a thermal bath of oscillators linearly coupled with the electron states of the quantum dot. Standard techniques make the problem amenable to a numerical treatment and allow one to determine the fidelity as a function of all the relevant physical parameters. As a consequence of our analysis, we show that the disturbance of the environment can be (approximately) suppressed and the performance of the gate optimized—provided that the thermal bath is purely super-Ohmic. We conclude by showing that such an optimization is impossible for Ohmic environments.

We study decoherence induced by stochastic squeezing control errors considering the particular implementation of a Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for the Hadamard gate when the control noise is modeled by the Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.

Nonperturbative quantum control schemes in the intermediate field strength (nonionizing) regime are investigated. We restrict the matter-field interaction to the nonresonant dynamic Stark effect (NRDSE) as induced by infrared laser fields, which we argue is a new and general tool for quantum control of atomic and molecular dynamics. For the case of Raman coupled matter states, an effective Hamiltionian may be constructed, and quantum control via NRDSE may be thought of as reversibly modifying the effective Hamiltonian during system propagation, thus leading to control over dynamic processes. As an illustration, the creation of field-free “switched” wave packets through the adiabatic turn on and sudden turn off of the NRDSE is considered and experimentally demonstrated. Wave packets generated through the switched NRDSE interaction may be very different in form and content than wave packets generated via resonant transitions with Gaussian optical pulses. In order to provide an example, we discuss the specific case of rotational wave packet dynamics where the NRDSE manifests itself as molecular axis alignment. This technique is applied to the creation of field-free molecular axis alignment using an intense switched $1.064\mu \mathrm{m}$ laser pulse. This switched laser pulse was generated via a plasma shuttering technique, giving a pulse with a rise time of $150\mathrm{ps}$ and a fall time of $170\mathrm{fs}$. The temporal evolution of the molecular axis alignment is probed via the optical Kerr effect. Field-free alignment via the switched NRDSE is demonstrated for both linear ($\mathrm{C}{\mathrm{O}}_2$, $\mathrm{C}{\mathrm{S}}_2$) and symmetric top (1,2-propadiene) polyatomic molecules.