A method is developed to calculate all excitations of trapped gases using hydrodynamics at zero temperature for any equation of state $\mu =\mu \left(n\right)$ and for any trapping potential. It is shown that a natural scalar product can be defined for the mode functions, by which the wave operator is Hermitian and the mode functions are orthogonal. It is also shown that the Kohn modes are exact for harmonic trapping in the hydrodynamic theory. Excitations for fermions are calculated in the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation transition region using the equation of state of the mean-field Leggett model for isotropic harmonic trap potential.

Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of $M$ infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds $(M=1)$. Finally we discuss how these states can be experimentally engineered from $N$ copies of a three-mode building block and $N$ two-mode finitely squeezed states.

We investigate the problem of Bayesian updating of a probability distribution encoded in the quantum state of $n$ qubits. The updating procedure takes the form of a quantum algorithm that prepares the quantum register in the state representing the posterior distribution. Depending on how the prior distribution is given, we describe two implementations, one probabilistic and one deterministic, of such an algorithm in the standard model of a quantum computer.

We describe a method for precise estimation of the polarization of a mesoscopic spin ensemble by using its coupling to a single two-level system. Our approach requires a minimal number of measurements on the two-level system for a given measurement precision. We consider the application of this method to the case of nuclear-spin ensemble defined by a single electron-charged quantum dot: we show that decreasing the electron spin dephasing due to nuclei and increasing the fidelity of nuclear-spin-based quantum memory could be within the reach of present day experiments.

We propose and prove the protocol of remote implementations of partially unknown quantum operations of multiqubits belonging to the restricted sets. Moreover, we obtain the general and explicit forms of restricted sets and present evidence of their uniqueness and optimization. In addition, our protocol has universal recovery operations that can enhance the power of remote implementations of quantum operations.

We describe purification protocols for bicolorable graph states. The protocols scale efficiently for large graph states. We introduce a method of analysis that allows us to derive simple recursion relations characterizing their behavior as well as analytical expressions for their thresholds and fixed-point behavior. We introduce two purification protocols with high threshold. They can, for graph degree 4, tolerate 1% (3%) gate error or 20% (30%) local error.

We have performed a kinematically complete experiment on transfer excitation in intermediate-energy proton-helium collisions. The differential cross sections were compared to double excitation data and a nonperturbative time-dependent calculation. This comparison reveals the importance of dynamic couplings between the motion of the heavy nuclei and electronic transitions and/or electron-electron correlation effects.

We present ab initio calculations of the interaction of the hydrogen molecule with an intense few-cycle near-infrared laser pulse beyond the one-dimensional approximation. The results show that the two pathways to nonsequential double ionization of the molecule, namely, the emission of a correlated electron pair near the zeros of the field and the electron emission from the previously excited molecular ion near the maxima of the field, are linked to the return of the initially singly ionized electron wave packet to the residual ion. Patterns in the double ionization probability distributions arise due to interference effects between different quantum paths.

Three-photon excitation and associated wave mixing near the $6s$ and $6s^{\prime }$ resonances of xenon have been studied utilizing resonance-enhanced multiphoton ionization in angled beams with different polarizations. It has been shown that a complete cancellation of three-photon resonant atomic excitation caused by the well-known destructive wave-mixing interference occurs in $s$ and $p$ polarization of angled beams but distinct resonance ionization enhancement is observed when pump beams have orthogonal polarization planes. Pressure-induced evolution of the resonance ionization peak in cross-polarized beams is identical to that observed with counterpropagating beams. The reason for such resonance ionization enhancement is unknown and cannot be explained within the frame work of existing theory. The effect may result from some peculiarities of wave-mixing interference in a multilevel atomic system, where different degenerate magnetic sublevels of the upper atomic state and multiple interfering excitation processes are involved. Another possibility is that the resonance ionization enhancement results from a process where weak counterpropagating light is generated within the excitation region of cross-polarized angled beams.

Time-resolved photoelectron spectra are proposed for the measurement of classical information recorded in the quantum phases of a molecular rotational wave packet. Taking ${\mathrm{Li}}_2$ as a prototypical system, we show that an interference arises from the electron-nuclei entanglement induced by the molecular anisotropy. This phenomenon is used to transfer the information that was stored initially in the nuclear rotational degree of freedom into the electronic degree of freedom.

We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We show the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell’s inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.

We analyze hybrid absorptive-dispersive optical bistability (OB) and multistability (OM) behavior in a generic $N$-type atomic system driven by a degenerate probe field and a coherent coupling field by means of a unidirectional ring cavity. We show that the OB can be controlled by adjusting the intensity and the detuning of the coupling field, and the OM can also be observed under the appropriate detuning. The influence of the atomic cooperation parameter on atomic OB behavior is also discussed.

The basic idea of spin-chain engineering for perfect quantum state transfer (QST) is to find a set of coupling constants in the Hamiltonian such that a particular state initially encoded on one site will evolve freely to the opposite site without any dynamical controls. The minimal possible evolution time represents a speed limit for QST. We prove that the optimal solution is the one simulating the precession of a spin in a static magnetic field. We also argue that, at least for solid-state systems where interactions are local, it is more realistic to characterize the computation power by the couplings than the initial energy.

Geometric phases are important in quantum physics and are now central to fault-tolerant quantum computation. For spin $1∕2$, the Bloch sphere $S^2$, together with a U(1) phase, provides a complete SU(2) description. We generalize to $N$-level systems and $\mathrm{SU}\left(N\right)$ in terms of a $2(N-1)$-dimensional base space and reduction to a $(N-1)$-level problem, paralleling closely the two-dimensional case. This iteratively solves the time evolution of an $N$-level system and gives $(N-1)$ geometric phases explicitly. A complete analytical construction of an $S^4$ Bloch-like sphere for two qubits is given for the Spin(5) or SO(5) subgroup of SU(4).

We study the phases of the amplitudes for transmission through and near-side quantum reflection by the nonclassical regions of singular attractive potential tails, as occur in the interaction of atoms and molecules with each other and with surfaces. The derivatives of these phases with respect to energy or momentum are interpreted as time and space shifts according to the prescription of Eisenbud and Wigner. The results for transmission through the nonclassical part of the potential follow a straightforward pattern: Near threshold, the time and space shifts are close to those of a free particle and only marginally resolve the influence of the attractive potential; with increasing energy they rapidly approach the expectations for a classical particle accelerated in the potential. The phase of the amplitude for near-side quantum reflection leads to a negative time shift. In a regularized potential obtained by smoothly continuing the attractive tail to a deep constant at negative distances, this can be understood as a small boost for a wave packet approaching the origin from the left—relative to a free wave totally reflected at the origin.

We analyze the tunneling-time problem via the presence time formalism. With this method we reproduce previous results for very long wave packets and we are able to calculate the tunneling time for general wave packets of arbitrary shape and length. The tunneling time for a general wave packet is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wave packet evolution.

One promising route towards the first experimental verification of parity violation (PV) in chiral molecular systems is the detection of line splittings between nuclear magnetic resonance (NMR) spectra of enantiomers. Those numerical methods which can be systematically refined and allow for an accurate and reliable prediction of molecular PV effects will play a crucial role for the preparation and interpretation of such experiments. In this work the ab initio calculation of isotropic parity-violating NMR-shielding constants $\left({\sigma }^{\mathrm{PV}}\right)$ within coupled cluster and multiconfiguration linear response approaches to electroweak quantum chemistry is reported and the results are compared to data obtained at the uncoupled density functional theory level. The ${\sigma }^{\mathrm{PV}}$ of the heavy nuclei in hydrogen peroxide, disulfane and diselane (${\mathrm{H}}_2{X}_2\mathrm{with}X={}^{17}\mathrm{O}$, ${}^{33}\mathrm{S}$, ${}^{77}\mathrm{Se}$) computed at the coupled cluster singles and doubles level are found to typically deviate from their electron-uncorrelated counterparts by approximately 20%, while in 2-fluorooxirane, electron correlation alters ${\sigma }^{\mathrm{PV}}$ of individual nuclei by almost a factor of 2. It is therefore imperative in the accurate prediction of parity-nonconserving phenomena in NMR experiments that systematically improvable electron-correlating electroweak quantum chemical approaches, such as those presented in this study, are employed.

We consider a pair of three-level atoms interacting with the vacuum. The process of disentanglement due to spontaneous emission and the role of quantum interference between principal transitions in this process, are analyzed. We show that the presence of interference can slow down disentanglement. In the limit of maximal interference, some part of initial entanglement can survive.

Dynamical formation of entanglement is studied for quantum chaotic biparticle systems. We find that statistical properties of the Schmidt eigenvalues for strong chaos are well described by the random matrix theory of the Laguerre unitary ensemble. This implies that entanglement formation for quantum chaos has universal properties, and does not depend on specific aspects of the systems.