We study dressed-atom two-photon resonant nondegenerate four-wave mixing (NFWM) in a Doppler-broadened system. It is found that there exists interference between the macroscopic field polarizations from different ensembles of atoms within the atomic velocity distribution. This polarization interference can cause significant modification of the NFWM spectra. We also show that two-photon resonant NFWM in dressed atoms can be employed as a new type of Doppler-free high-resolution Autler-Townes spectroscopy for measuring transition dipole moments between two highly excited atomic states.

We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.

We have made a systematic study of rubidium optical pumping in a simple cylindrical cell geometry with a high-power $10\mathrm{W}$ diode laser array, low magnetic fields, and buffer-gas pressures of less than $50\text{torr}$. We have determined rubidium polarizations experimentally for ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, He, and Ar buffer gases, with Rb number densities from ${10}^{12}\text{to}{10}^{13}{\mathrm{cm}}^{-3}$. Comparison to a relatively simple optical pumping model allows us to extract useful information about radiation trapping and quenching effects.

We investigate the coupling between motional resonances of translationally cold ($10\mathrm{mK}$ range) atomic and molecular ions in multispecies Coulomb crystals, stored in a linear Paul trap. The atomic and molecular ions were sympathetically cooled by laser-cooled ${\mathrm{Be}}^{+}$ ions. The motional resonances of the different ion species were determined nondestructively with high mass-to-charge resolution upon excitation with an oscillating electric field. The experimental results show good agreement with results from molecular dynamics simulations and allow for a precise identification of sympathetically cooled particles in multispecies ion crystals.

We study the area-dependent entropy and two-site entanglement for two-state Bose-Einstein condensates in a two-dimensional optical lattice. We consider the case where the array of two-component condensates behaves like an ensemble of spin-half particles with the interaction to its nearest neighbors and next-nearest neighbors. We show how the Hamiltonian of their Bose-Einstein condensate lattice with nearest-neighbor and next-nearest-neighbor interactions can be mapped onto a harmonic lattice. We use this to determine the entropy and entanglement content of the lattice.

Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control theory (OCT). We derive from the Gross-Pitaevskii equation the optimality system for the OCT fields that allow efficient channeling of the condensate between given initial and desired states. For a variety of magnetic confinement potentials we study transport and wave-function splitting of the condensate, and demonstrate that OCT drastically outperforms simpler schemes for the time variation of the microtrap control parameters.

Coherent control of regions with spatial excitation of populations and coherence between two lower states in three-level $\Lambda$-type quantum systems mediated by the self-induced transparency (SIT) phenomenon is theoretically investigated with one- and two-color ultrashort pulses and with pulse sequences beyond the slowly varying envelope (SVEA) and rotating wave (RWA) approximations. The effects of different parameters characterizing the pulses and the medium on the location as well as the width of such excited regions have been studied numerically by means of the finite-difference time-domain (FDTD) method. It has been determined that with a scheme of two-pulse excitation one can effectively control the position at which the region is written and its width. In particular, the position of the excited region can be controlled by the area of the pulses. We find that the maximum value of the population transferred to the lower excited state depends on the detuning of the pulses with respect to the one-photon resonances, and that both position and width of the region also depend on the temporal duration of the pulses. We show how after the excited region is written, its position can be shifted by additional pulses. On the basis of numerical results, scaling laws are formulated for the reported phenomena. With such control, the width of the region excited inside the medium can be reduced to the order of the wavelength of the light.

A method to quantitatively evaluate the propagation of parametric fluorescence is proposed. The probability distribution of photon pairs, including the influence of the optical setup in accordance with the wave vector and frequency, is numerically calculated. From this probability distribution, the coincidence counting probability can be simply evaluated. Comparing with experimental data of the iris size dependences of single and coincidence counting rates, the calculated results reproduce the experimental data well without the use of fitting parameters.

We present a general quantum theory capable of describing photon statistics under the combined effects of four-wave mixing and Raman scattering inside optical fibers. Our theory is vectorial in nature and includes all polarization effects. Our analysis shows that spontaneous Raman scattering degrades the pair correlation in all cases but the extent of degradation depends on the pumping configuration employed. In a single-pump configuration, photon pairs can be created with polarization either parallel or orthogonal to the pump. Our results show that the orthogonal configuration can improve the extent of quantum correlation considerably over a broad bandwidth. In the case of a dual-pump configuration, we show that imbalance of two pump powers can be used to improve the quality of photon pairs. We show that orthogonally polarized pumps can generate photon pairs automatically in a polarization-entangled state. In particular, orthogonal pumping with circular polarizations produces such an entangled state with relatively high quality. We also quantify the quality of polarization entanglement as well as energy-time entanglement constructed using correlated photon pairs.

We report theoretically on a pure frequency-induced polarization bistability in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection, i.e., the master laser light polarization is orthogonal to that of the slave VCSEL. As the frequency detuning is scanned from negative to positive values and for a fixed injected power, the VCSEL exhibits two successive and possibly bistable polarization switchings. The first switching (from the slave laser polarization to the injected light polarization) exhibits a bistable region whose width is maximum for a given value of the injected power. Such a dependency of hysteresis width on the injected power is similar to that recently found experimentally by Hong et al.[Electron. Lett. 36, 2019 (2000)]. The bistability accompanying the second switching (from the injected light polarization back to the slave laser free-running polarization) exhibits, however, significantly different features related to the occurrence of optical chaos. Interestingly, the width of the bistable region can be tuned over a large range not only by modifying the injection parameters but also by modifying the device parameters, in particular the VCSEL linewidth enhancement factor.

The Shor-Preskill proof of the security of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the “dual-containing” property. A practical implementation of the BB84 protocol thus requires explicit and efficiently decodable constructions of such codes, which are not known. On the other hand, modern coding theory abounds with non-dual-containing codes with excellent performance and efficient decoding algorithms. We show that the dual-containing constraint can be lifted at a small price: instead of a key distribution protocol, an efficiently implementable key expansion protocol is obtained, capable of increasing the size of a preshared key by a constant factor.

We investigate for which resource states an efficient classical simulation of measurement-based quantum computation is possible. We show that the Schmidt-rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt-rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement-based quantum computation is possible for all states with logarithmically bounded Schmidt-rank width (with respect to the system size). For graph states where the Schmidt-rank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.

Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded in a coded subspace, and error recovery is performed via an operation designed to perfectly correct for a set of errors, presumably a large subset of the physical noise process. In this paper, we examine the choice of recovery operation. Rather than seeking perfect correction on a subset of errors, we seek a recovery operation to maximize the entanglement fidelity for a given input state and noise model. In this way, the recovery operation is optimal for the given encoding and noise process. This optimization is shown to be calculable via a semidefinite program, a well-established form of convex optimization with efficient algorithms for its solution. The error recovery operation may also be interpreted as a combining operation following a quantum spreading channel, thus providing a quantum analogy to the classical diversity combining operation.

Electric ring currents $I_{nlm}$ and corresponding magnetic fields ${\mathbf{B}}_{nlm}$ exist in atomic orbitals ${\psi }_{nlm}$ $(m\ne 0)$. Simple expressions are derived for $I_{nlm}$ and for ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ at the nucleus. The magnitude of $I_{nlm}$ depends only on $n$ and decreases with increasing quantum number $n$. In contrast, ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ decreases with increasing quantum numbers $n$ and $l$ but increases with $m$. The largest magnitudes of the electric ring currents and induced magnetic fields are thus obtained for $2p_{\pm 1}$ orbitals. Moreover, $I_{nlm}$ and ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ increase with the nuclear charge $Z$ as $Z^2$ and $Z^3$, respectively. Simple circularly polarized $\pi$ laser pulses are designed for complete population transfers from $1s$ to target $2p_{\pm 1}$ orbitals. The corresponding solutions of the time-dependent Schrödinger equation for the hydrogen atom H $(Z=1)$ imply equivalent solutions for arbitrary $Z$, by means of simple scaling laws for the time $(1∕Z^2)$, frequency $\left(Z^2\right)$, and field strength $\left(Z^3\right)$ or intensity $\left(Z^6\right)$. For example, the parameters of the $\pi$ pulse for H (pulse duration $\tau =115\mathrm{fs}$, maximum intensity ${\mathcal{I}}_{\max }=1.47\times {10}^{10}\mathrm{W}{\mathrm{cm}}^{-2}$) are scaled to values $\tau =679$ as and ${\mathcal{I}}_{\max }=7.09\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ for ${\mathrm{Al}}^{12+}$, inducing the giant magnetic field $\mid {\mathbf{B}}_{21\pm 1}(\mathbf{r}=\mathbf{0})\mid =1146\mathrm{T}$. The results for hydrogenlike atoms allow corresponding estimates of electric ring currents and magnetic fields in molecules, where molecular orbitals are expressed as linear combinations of atomic orbitals.

Low-energy, polarized-electron scattering from ground state zinc atoms has explored the influence of open and closed $3d$-shell effects in the ionization-with-excitation scattering process. Observations of nonzero values of the Stokes $P_2$ parameter of the $589.4\mathrm{nm}$ photons from the open-shell $3d^{9}4s^2{}^{2}D_{3∕2}$ ionic state reveals spin-orbit interaction effects. In contrast, negligible spin-orbit interaction was deduced from the vanishing Stokes $P_2$ parameter of the $602.2\mathrm{nm}$ photons from the closed-shell $3d^{10}5d{}^{2}D_{3∕2}$ ionic state, for which the core-valence correlation is less important. A strong resonance in the closed-shell transition was observed in the $P_3$ parameter, about $0.8\mathrm{eV}$ above the excitation threshold with positive orientation. There are indications of a resonance in the open-shell transition.

We explore theoretically the consequence of the presence of structured multiple continua on the electromagnetically induced transparency (EIT) effect with pulsed lasers. The theory is developed in a rigorous manner using the overlapping resonances perspective. As one consequence of the theory we show that due to the structure in the continuum (which can also be induced optically) the EIT line shapes become asymmetric for a strong coupling piulse.

We use a simplified essential state model to compare two quantum field theoretical approaches to study the creation of electron-positron pairs from the vacuum. In the unitary approach the system is characterized by a state with different numbers of particles that is described by occupation numbers and evolves with conserved norm. The nonunitary approach can predict the evolution of wave functions and density operators with a fixed number of particles but time-dependent norms. As an example to illustrate the differences between both approaches, we examine the degree of entanglement for the Klein paradox, which describes the creation of an electron-positron pair from vacuum in the presence of an initial electron. We demonstrate how the Pauli blocking by the initial electron comes at the expense of a gain in entanglement of this electron with the created electron as well as with the created positron.

We study the groundstates of weakly interacting atomic Bose gases under conditions of rapid rotation. We present the results of large-scale exact diagonalization studies on a periodic geometry (a torus) which allows studies of compressible states with broken translational symmetry. Focusing on filling factor $\nu =2$, we show a competition between the triangular vortex lattice, a quantum smectic state, and the incompressible $k=4$ Read-Rezayi state. We discuss the corrections arising from finite size effects, and the likely behavior for large system sizes. The Read-Rezayi state is stabilized by a moderate amount of additional dipolar interactions.

We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov–de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.

We present a largely analytical theory for two-photon correlations $G^{\left(2\right)}$ between Stokes $\left(s\right)$ and anti-Stokes $\left(a\right)$ photon pairs from an extended medium (amplifier) composed of double-$\Lambda$ atoms in counterpropagating geometry. We generalize the parametric coupled equations with quantum Langevin noise given in a beautiful experimental paper of Balic et al. [Phys. Rev. Lett. 94, 183601 (2005)] beyond adiabatic approximation and valid for arbitrary strength and detuning of laser fields. We derive an analytical formula for cross correlation $G_{as}^{\left(2\right)}=⟨{\widehat{E}}_s^{†}\left(L\right){\widehat{E}}_a^{†}(0,\tau ){\widehat{E}}_a(0,\tau ){\widehat{E}}_s\left(L\right)⟩$ and use it to obtain results that are in good quantitative agreement with the experimental data. Results for $G_{as}^{\left(2\right)}$ obtained using our coupled equations are in good quantitative agreement with the results using the equations of Balic et al., while perfect agreement is obtained for sufficiently large detuning. We also compute the reverse correlation $G_{sa}^{\left(2\right)}$ which turns out to be negligibly small and remains classical while the cross correlation violates the Cauchy-Schwartz inequality by a factor of more than a hundred.