We theoretically analyze atom interferometry based on trapped ultracold atoms and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows us to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom-number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms and the multiconfigurational time-dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.

We study spontaneous emission of an atom near a nanofiber with two fiber-Bragg-grating (FBG) mirrors. We show that the coupling between the atom and the guided modes of the nanofiber can be significantly enhanced by the FBG cavity even when the cavity finesse is moderate. We find that, when the fiber radius is 200 nm and the cavity finesse is about 30, up to 94% of spontaneous emission from the atom can be channeled into the guided modes in the overdamped-cavity regime. We show numerically and analytically that vacuum Rabi oscillations and strong coupling can occur in the FBG cavity even when the cavity finesse is moderate (about 30) and the cavity length is large (on the order of 10 cm to 1 m), unlike the case of planar and curved Fabry-Perot cavities.

We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as those obtained from maximally path-entangled $\left(\right|N,0⟩+|0,N⟩)/\sqrt{2}$ (“NOON”) states, have commensurately high information yield (as quantified by the Fisher information). However, this information is also highly ambiguous because it does not distinguish between phases at the same point on different fringes. We provide schemes to eliminate this phase ambiguity in a highly efficient way, providing phase estimates with uncertainty that is within a small constant factor of the Heisenberg limit, the minimum allowed by the laws of quantum mechanics. These techniques apply to NOON state and multipass interferometry, as well as phase measurements in quantum computing. We have reported the experimental implementation of some of these schemes with multipass interferometry elsewhere. Here, we present the theoretical foundation and also present some additional experimental results. There are three key innovations to the theory in this paper. First, we examine the intrinsic phase properties of the sequence of states (in multiple time modes) via the equivalent two-mode state. Second, we identify the key feature of the equivalent state that enables the optimal scaling of the intrinsic phase uncertainty to be obtained. This enables us to identify appropriate combinations of states to use. The remaining difficulty is that the ideal phase measurements to achieve this intrinsic phase uncertainty are often not physically realizable. The third innovation is to solve this problem by using realizable measurements that closely approximate the optimal measurements, enabling the optimal scaling to be preserved. We consider both adaptive and nonadaptive measurement schemes.

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitrary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times.

Two-electron reduced density matrices (2-RDMs) and their energies have recently been computed accurately for singlet molecular states through the solution of the anti-Hermitian part of the contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. In this work we directly solve the ACSE for the 2-RDMs of open-shell molecular systems in arbitrary spin states. This generalization is achieved by spin coupling the open-shell molecule to one or more hydrogen atoms to form a singlet composite system, which can be solved by existing ACSE algorithms. Advantages of the spin-coupled approach include: (i) applicability of the singlet ACSE algorithm to high-spin open-shell molecules, (ii) consistent treatment of arbitrary spin states that avoids spin-free or other approximations to the cumulant reconstruction of higher RDMs, and (iii) computational reduction in floating-point operations and storage from exploiting the singlet spin symmetry of the composite system. The ACSE energy of the composite system we showed is the sum of the open-shell energy and the energies of the hydrogens, and the open-shell 2-RDM can be readily extracted from the composite 2-RDM. With the open-shell ACSE method we calculate energies and natural-orbital occupation numbers for a variety of doublet and triplet open-shell molecules including potential-energy curves for CH, ${\text{B}}_2$, ${\text{N}}_2^{+}$, and ${\text{H}}_2{\text{O}}^{+}$. The ACSE produces energies that are consistently more accurate than those from either multireference second-order perturbation theory or coupled cluster singles-doubles, and as with singlet states, it provides a balanced description of single-reference and multireference correlation, which is exemplified in its dissociation of open-shell ${\text{N}}_2^{+}$. Computed 2-RDMs nearly satisfy necessary $N$-representability constraints.

We study effects of the dipole-dipole interaction on fermionic cold atomic gases in two-dimensional optical lattice. We calculate spin and density correlation functions within the random-phase approximation. It is shown that the spin-correlation functions of spin components perpendicular to the lattice plane show a characteristic peak structure different from that of the parallel component. We study $s$-wave and $d$-wave superfluidity induced by the spin and density correlations and show that the dipole-dipole interaction assists the $d$-wave superfluidity.

The azimuthal asymmetry of the polarized backscattering cone and the intimately related polarization opposition effect (POE) are corollaries of the theory of coherent backscattering (CB) valid in the asymptotic limit of very small particle packing density. In this paper we use numerically exact solutions of the Maxwell equations to study the evolution of these and other manifestations of CB as the packing density in a multiparticle group increases from zero to values typical of actual particle suspensions and particulate surfaces. Our results reveal a remarkable robustness of virtually all effects predicted by the low-density concept of CB and allow us to conclude that the azimuthal asymmetry and POE observed in the laboratory for densely packed discrete random media are indeed caused by CB.

We present an efficient method to generate a ultrashort attosecond (as) pulse when a model ${\text{He}}^{+}$ ion is exposed to the combination of an intense few-cycle chirped laser pulse and its 27th harmonics. By solving the time-dependent Schrödinger equation, we found that high-order harmonic generation (HHG) from ${\text{He}}^{+}$ ion is enhanced by seven orders of magnitude due to the presence of the harmonic pulse. After optimizing the chirp of the fundamental pulse, we show that the cut-off energy of the generated harmonics is extended effectively to $I_p+25.5U_p$. As a result, an isolated 26-as pulse with a bandwidth of 170.5 eV can be obtained directly from the supercontinuum around the cut-off of HHG. To better understand the physical origin of HHG enhancement and attosecond pulse emission, we perform semiclassical simulations and analyze the time-frequency characteristics of attosecond pulse.

The $\pi$-phase shift between $|F=1,m_F=0⟩$ and $|F=2,m_F=0⟩$ states for an adiabatic rotation of a magnetic field observed in Ramsey atom interferometry arises from the negative sign of the transition amplitude between the $|1,0⟩$ and $|2,0⟩$ states when the wave functions are rotated to the opposite direction. Using a two-photon Raman atom interferometer with a cold ensemble of sodium atoms, the phase shift for a half-rotation of the magnetic field was confirmed to be $\pi \text{rad}$ with an uncertainty of 4%, and the phase shift for a noncyclic adiabatic rotation of the magnetic field was investigated.

We show the existence of a permanent molecular planar alignment in field-free conditions. We present different control strategies using shaped laser pulses to reach this state. The strategies are robust with respect to the temperature and can be implemented with the state of the art technology. They can be applied not only to linear molecules but also to symmetric or asymmetric top molecules along the most polarizable molecular axis. We propose potential applications of this planar alignment such as the increase of the adsorption on a surface.

The dynamics of a system, consisting of a particle initially in a Gaussian state interacting with a field mode, under the action of repeated measurements performed on the particle, is examined. It is shown that regardless of its initial state the field is distilled into a squeezed state. The dependence on the physical parameters of the dynamics is investigated.

We study a natural construction of a general class of inhomogeneous quantum walks (namely, walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on the period, such walks can be bounded or unbounded in time; in the latter case we analyze the asymptotic speed. We compare the construction to others in the existing literature. As an example we give a quantum version of a nonirreducible classical walk: the Pólya Urn.

We present a theory of vibrationally enhanced positron annihilation on molecules based on the Feshbach projection operator formalism. A key aspect of the present approach is the fact that no direct vibrational excitation is assumed, i.e., the attachment mechanism is electronic in nature, arising from positron-electron correlation-polarization forces, and energy transfer to the nuclei essentially follows from the difference between the potential-energy surfaces of the isolated target and the positron-molecule compound; moreover, no a priori assumption is made on the character of the transient (bound or virtual state). An approximate relation between the annihilation parameter $Z_{\text{eff}}$ and the vibrationally summed cross section is presented, as well as a hierarchy of approximations that may allow for elaborate model calculations. We also discuss how important aspects of the annihilation process are taken into account in the present theory, such as isotope effects, vibrational energy redistribution and relative strengths among vibrational resonances. For completeness, semiempirical model calculations for acetylene and ethylene are presented. Despite the stringent approximations employed in this simplest version of the theory, fair agreement with experimental data was obtained in the vicinity of $0\to 1$ thresholds.

In an intense laser field, an electron may decay by emitting a pair of photons. The two photons emitted during the process, which can be interpreted as a laser-dressed double Compton scattering, remain entangled in a quantifiable way: namely, the so-called concurrence of the photon polarizations gives a gauge-invariant measure of the correlation of the hard gamma rays. We calculate the differential rate and concurrence for a backscattering setup of the electron and photon beam, employing Volkov states and propagators for the electron lines, thus accounting nonperturbatively for the electron-laser interaction. The nonperturbative results are shown to differ significantly compared to those obtained from the usual double Compton scattering.

Disorder modifies the sound-wave excitation spectrum of Bose-Einstein condensates. We consider the classical hydrodynamic limit, where the disorder correlation length is much longer than the condensate healing length. By perturbation theory, we compute the phonon lifetime and the correction to the speed of sound. This correction is found to be negative in all dimensions, with universal asymptotics for smooth correlations. Considering in detail optical speckle potentials, we find a quite rich intermediate structure. This has consequences for the average density of states, particularly in one dimension, where we find a “boson dip” next to a sharp “boson peak” as function of frequency. In one dimension, our prediction is verified in detail by a numerical integration of the Gross-Pitaevskii equation.

We have observed the photodetachment spectrum near the lowest detachment threshold from ${\text{S}}^{-}$ in a 1 T field. The spectroscopy shows a small degree of magnetic field structure of the type observed in similar experiments at the higher-energy threshold of the electron affinity. Furthermore, our results yield a measurement of the lowest detachment threshold energy.

Perfect state transfer (PST) is discussed in the context of passive quantum networks with logical bus topology, where many logical nodes communicate using the same shared media without any external control. The conditions under which a number of point-to-point PST links may serve as building blocks for the design of such multinode networks are investigated. The implications of our results are discussed in the context of various Hamiltonians that act on the entire network and are capable of providing PST between the logical nodes of a prescribed set in a deterministic manner.

Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.

Recent absorption measurements of the self-broadening of Rb principal series lines [C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006)] verified the existence of minima in highly excited long-range potentials of ${\text{Rb}}_2$ which were predicted theoretically as bound Rydberg molecule [C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour, Phys. Rev. Lett. 85, 2458 (2000)]. The present paper reports on the extension of these experimental studies to principal series lines of K broadened by K as well as Cs broadened by Cs. In addition, the broadening of some lower members of the K, Rb, and Cs principal line series due to heteroatomic interactions was investigated. The analysis of the measured satellite structures in the quasistatic line wings and their comparison to the previously published analogous data for ${\text{Rb}}^{\ast }+\text{Rb}$ system lead to the conclusion that one can expect existence of potential minima in homo- and heteroatomic alkali-metal $A^{\ast }+B$ systems in a wide range of principal quantum numbers, starting with K, Rb, and Cs excited to the third resonance states. The positions and strengths of the satellite structures indicate that the potential minima are due to scattering of the valence electron by ground-state perturbers.