We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\mid 3s⟩$ ground state to the $\mid 4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\Omega$ to exceed the radial harmonic frequency ${\omega }_{\perp }$. In the regime $\Omega \gtrsim {\omega }_{\perp }$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity ${\Omega }_h$, a central hole appears in the condensate. Numerical studies confirm the predicted value of ${\Omega }_h$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).

A simple analytical solution for the propagation of a weak Gaussian pulse in a dense absorptive medium with electromagnetically induced transparency is found. This solution is applied to the analysis of three regimes: (1) and (2) the pulse spectrum is narrower than the transparency window [which is narrow (1) or wide (2) with respect to the width of the absorption line] and (3) the pulse spectrum is broader than the transparency window. It is shown that the pulse maintains its area in all three regimes and maintains its Gaussian shape but narrows in spectrum in regime 1. In regime 2, the pulse begins to distort after a certain distance. In regime 3, the pulse is split into two parts. One part is an adiabatic part with a spectrum defined by the effective width of the transparency window for a thick medium and the other is an oscillating nonadiabatic part of short duration. The adiabatic part propagates slowly and the nonadiabatic part propagates with a velocity close to the speed of light. Thus in regime 3, the medium acts as a time-frequency filter, separating the narrow and wide spectrum components of the pulse in time at the output of the absorber.

We demonstrate quantum algorithms to implement pseudorandom operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the algorithms are introduced for the less experimentally challenging quantum cellular automata. For implementing pseudorandom symplectic operators we provide gate sequences for the unitary part of the time-reversal operator.

In this Comment we question the security of the recently proposed scheme of a quantum dense key distribution by Degiovanni et al. [Phys. Rev. A 69, 032310 (2004)].

In this Reply we propose a modified security proof of the quantum dense key distribution protocol, detecting also the eavesdropping attack proposed by Wójcik in his Comment [Wójcik, Phys. Rev. A 71, 016301 (2005)].

We describe a method for the complete temporal characterization of attosecond extreme ultraviolet (xuv) fields. An electron wave packet is generated in the continuum by photoionizing atoms with the attosecond field, and a low-frequency dressing laser pulse is used as a phase gate for frequency-resolved-optical-gating-like measurements on this wave packet. This method is valid for xuv fields of an arbitrary temporal structure, e.g., trains of nonidentical attosecond pulses. It establishes a direct connection between the main attosecond characterization techniques demonstrated experimentally so far, and considerably extends their scope, thus providing a general perspective on attosecond metrology.

We present an optical scheme to implement the Deutsch-Jozsa algorithm using ac Stark shifts. The scheme uses an atomic ensemble consisting of four-level atoms interacting dispersively with a field. This leads to a Hamiltonian in the atom-field basis which is quite suitable for quantum computation. We show how one can implement the algorithm by performing proper one- and two-qubit operations. We emphasize that in our model the decoherence is expected to be minimal due to our usage of atomic ground states and freely propagating photon.

A geometrical description of three-qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric $\mathcal{Q}$, a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of $\mathcal{Q}$ with interesting geometric properties. An invariant characterizing the Greenberger-Horne-Zeilinger class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.

We show that radio-frequency spectroscopy on weakly bound molecules is a powerful and sensitive tool to probe molecular energy structure as well as atomic scattering properties. An analytic expression of the excitation line shape is derived, which in general contains a bound-free component and a bound-bound component. In particular, we show that the bound-free process strongly depends on the sign of the scattering length in the outgoing channel and acquires a Fano-type profile near a Feshbach resonance. The derived line shapes provide an excellent fit to both numerical calculations and recent experimental measurements based on ${}^6\mathrm{Li}_2$.

Using laser optical pumping, widths and frequency shifts are determined for microwave transitions between ground-state hyperfine components of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms contained in vapor cells with alkane antirelaxation coatings. The results are compared with data on Zeeman relaxation obtained in nonlinear magneto-optical rotation experiments, a comparison important for quantitative understanding of spin-relaxation mechanisms in coated cells. By comparing cells manufactured over a $40\text{‐}\text{year}$ period we demonstrate the long-term stability of coated cells, an important property for atomic clocks and magnetometers.

We study the dynamics of multimode semiconductor lasers with optical feedback. Our model takes into account explicitly spatial effects, which are included by considering spatial profiles for $N$ longitudinal modes coupled to the space-dependent gain. We also consider the effect of carrier diffusion. We find that in the weak feedback regime the longitudinal modes display antiphase oscillations that lead to a nearly constant output intensity. This result is largely independent of the value of the diffusion coefficient. For larger feedback we observe in-phase fast oscillations at a frequency close to the relaxation oscillation frequency of the solitary laser. In these two regimes, the total output of the laser has the properties of a single-mode laser for nondispersive applications. We assess the validity of an existing approximation scheme that has dealt with spatial inhomogeneities by expanding the carrier density into a truncated hierarchy of moments. We demonstrate that this approximation is very good when the underlying carrier diffusion is fast, thus leading to a weakly developed carrier grating.

Criteria for the nonclassicality of a quantum state of the harmonic oscillator are formulated in terms of normally ordered moments of quadratures. Inequalities are obtained that are equivalent to the failure of the Glauber-Sudarshan $P$ function to be a probability density. A possibility to measure the required moments is proposed.

We suggest using insulating garnets doped by rare-earth ions for measurements of nuclear anapole moments. A parity violating shift of the NMR frequency arises due to the combined effect of the lattice crystal field and the anapole moment of the rare-earth nucleus. We show that there are two different observable effects related to frequency: (1) a shift of the NMR frequency in an external electric field applied to the solid; the value of the shift is about $\Delta {\nu }_1\sim {10}^{-5}\mathrm{Hz}$ with $E=10\mathrm{kV}∕\mathrm{cm}$; (2) a splitting of the NMR line into two lines. The second effect is independent of the external electric field. The value of the splitting is about $\Delta {\nu }_2\sim 0.5\mathrm{Hz}$ and it depends on the orientation of the crystal with respect to magnetic field. Both estimates are presented for a magnetic field of about $10\mathrm{T}$. We also discuss a radio frequency electric field and a static macroscopic magnetization caused by the nuclear anapole moment.

We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analyzed.

The ability to measure and reduce systematic errors in single-qubit logic gates is crucial when evaluating quantum computing implementations. We describe pulsed electron paramagnetic resonance (EPR) sequences that can be used to measure precisely even small systematic errors in rotations of electron-spin-based qubits. Using these sequences we obtain values for errors in the rotation angle and axis for single-qubit rotations using a commercial EPR spectrometer. We conclude that errors in qubit operations by pulsed EPR are not limiting factors in the implementation of electron-spin-based quantum computers.

We show an rf-induced Sisyphus cooling process for magnetic traps that may easily be applied to many of the current Bose-Einstein condensation experiments. Through Monte Carlo simulations of magnetically trapped ${}^{87}\mathrm{Rb}$ we have shown a cooling rate of $\sim 15\mu \mathrm{K}∕\mathrm{s}$. We have also shown a greater efficiency than evaporative cooling from $250\to \sim 7\mu \mathrm{K}$ with an efficiency $\alpha =d\ln T∕d\ln N>3$ over the majority of this range.

We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of the modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high-quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength $g$, critical atom number $N_0$, and critical photon number $n_0$ for cesium are calculated and shown to exceed values currently possible using Fabry-Perot cavities. Modeling predicts coupling rates $g∕2\pi$ exceeding $700\mathrm{MHz}$ and critical atom numbers approaching ${10}^{-7}$ in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of $852\mathrm{nm}$ indicate that quality factors in excess of ${10}^8$ can be obtained in a $50\text{‐}\mu \mathrm{m}$ principal diameter cavity, which would result in strong-coupling values of $\mathbf{(}g∕\left(2\pi \right),n_0,N_0\mathbf{)}=(86\mathrm{MHz},4.6\times {10}^{-4},1.0\times {10}^{-3})$.

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. 92, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases $\mathrm{S}\mathrm{O}\left(n\right)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of Phys. Rev. Lett. 92, 060406 (2004) to the complex Hamiltonian case does not provide any new information.