We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the nonretarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation.

We develop a field integral formalism to study spin-orbit-coupled (SOC) Bose gases with arbitrary interspecies interaction. We identify various features arising from the interplay of SOC and interspecies interaction, including a roton minimum in the excitation spectrum and dual effects of SOC on ground-state energies depending on interspecies interactions. Counterintuitively, we find that at low interspecies interaction the SOC stabilizes the system by suppressing the quantum depletion. We show that the static structure factor is immune to the SOC in the phase space where time-reversal symmetry is preserved. Furthermore, we present an alternate way of studying phase fluctuations of the system.

We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold-atomic gases with various desired properties such as low excess energies. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling amplitude, we show that the optimal protocol, for maximizing any figure of merit in a given time, is bang-bang, i.e., the coupling alternates between only two values through a sequence of sudden quenches. Minimizing the energy of one of the quasicondensates with such a nonadiabatic protocol, and then decoupling it at the end of the process, can result in effective cooling beyond the current state of the art. Our cooling method can be potentially applied to arbitrary systems through an integration of the experiment with simulated annealing computations.

We propose an optical trapping technique in which a fundamental soliton traps an ultrashort small amplitude radiation in a symmetric hollow-core photonic crystal fiber filled with a noble gas, preventing its dispersion. The system is Raman- and plasma-free. Trapping is due to the cross phase modulation effect between the two pulses. The trapped radiation inside the soliton-induced potential will oscillate periodically due to the shock effect, similar to the motion of a mechanical pendulum.

We describe the design of a temporal imaging system that simultaneously reshapes the temporal profile and converts the frequency of a photonic wave packet, while preserving its quantum state. A field lens, which imparts a temporal quadratic phase modulation, is used to correct for the residual phase caused by field curvature in the image, thus enabling temporal imaging for phase-sensitive quantum applications. We show how this system can be used for temporal imaging of time-bin entangled photonic wave packets and compare the field lens correction technique to systems based on a temporal telescope and far-field imaging. The field-lens approach removes the residual phase using four dispersive elements. The group delay dispersion $D$ is constrained by the available bandwidth $\Delta \nu$ by $D>t/\Delta \nu$, where $t$ is the temporal width of the wave form associated with the dispersion $D$. This is compared to the much larger dispersion $D\gg \pi t^2/8$ required to satisfy the Fraunhofer condition in the far-field approach.

We present an exact analytical solution of the two-photon scattering in a cavity optomechanical system. This is achieved by solving the quantum dynamics of the total system, including the optomechanical cavity and the cavity-field environment, with the Laplace transform method. The long-time solution reveals detailed physical processes involved as well as the corresponding resonant photon frequencies. We characterize the photon correlation induced in the scattering process by calculating the two-photon joint spectrum of the long-time state. Clear evidence for photon frequency anticorrelation can be observed in the joint spectrum. In addition, we calculate the equal-time second-order correlation function of the cavity photons. The results show that the radiation pressure coupling can induce photon blockade effect, which is strongly modulated by the phonon sideband resonance. In particular, we obtain an explicit expression of optomechanical coupling strength determining these sideband modulation peaks based on the two-photon resonance condition.

The Gaussian quantum adaptation deterministically protecting a negativity of a Wigner function of a non-Gaussian quantum state transmitted through a lossy channel is proposed. For the pure non-Gaussian states, an optimized Gaussian presqueezing of the non-Gaussian state keeps the negativity pronouncedly visible. For the mixed states, the optimized Gaussian presqueezing makes the negativity of the Wigner function more robust against the loss. The Gaussian quantum adaptation increasing a fidelity of the transmitted state can be directly applied to a broad class of the non-Gaussian states of light and matter.

A detailed theoretical formalism for the calculation of energy levels and eigenfunctions of molecules with a large amplitude coordinate in the presence of a strong laser pulse is developed based on a discrete variable representation to setup the Hamiltonian matrix. This approach is applied to nonrigid biphenyl-like molecules displaying a large amplitude motion corresponding to respective rotations of their two groups. The eigenvalues and eigenvectors obtained in several limiting cases of the hindering potential can be symmetry labeled and provide us with useful insights into the feasibility of torsional alignment. The present results support the rotation-induced breakdown of torsional alignment, under adiabatic following, previously described by Coudert, Pacios, and Ortigoso [Phys. Rev. Lett. 107, 113004 (2011)].

The interference minimum in the high-order harmonic spectrum of H${}_2{}^{+}$ is studied by solving the full three-dimensional time-dependent Schrödinger equation for the electronic motion keeping the nuclei fixed. The two-center interference model works well when the internuclear distance is around its equilibrium value where also recombination to the ${}^2{\Sigma }_{\mathrm{g}}^{+}$ (1$s$${\sigma }_{\mathrm{g}}$) ground state dominates. As the internuclear distance is increased, the minimum first shifts in position compared with the prediction of the two-center interference model and subsequently disappears. These effects are caused by the excited ${}^2{\Sigma }_{\mathrm{u}}^{+}$ (2$p$${\sigma }_{\mathrm{u}}$) state, partly due to the interference between the amplitudes of recombination to the ground and excited states, but also partly due to the signal associated with recombination to the excited state alone. We find that at internuclear distances beyond $R\simeq 3$ a.u. the signal close to the harmonic cutoff may be completely dominated by recombination into the excited ${}^2{\Sigma }_{\mathrm{u}}^{+}$ (2$p$${\sigma }_{\mathrm{u}}$) state.

We show that unconventional spin order arises naturally in two-component dipolar Fermi gases of atoms or molecules, which recently became accessible experimentally, in optical lattices. Using an unbiased functional renormalization-group analysis, we find that dipolar interactions lead to an instability of the gas toward an $\ell =1$ spin-density wave state. This phase is the particle-hole analog of spin-triplet, $p$-wave Cooper pairs. The order parameter for such spin-density waves of $p$-wave orbital symmetry is a vector in spin space and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half filling on the square lattice as a function of the dipolar orientation and discuss how these exotic spin-density waves emerge amidst competition with superfluid and charge-density wave phases.

We examine the local behavior of the regularized stress tensor commonly used in calculations of the Casimir force for a dielectric medium inhomogeneous in one direction. It is shown that the usual expression for the stress tensor is not finite anywhere within the medium, whatever the temporal dispersion or index profile, and that this divergence is unlikely to be removed through a simple modification to the regularization procedure. Our analytic argument is illustrated numerically for a medium approximated as a series of homogeneous strips, as the width of these strips is taken to zero. The findings hold for all magnetodielectric media.

We propose a quantum computer architecture that is robust against decoherence and scalable. As a qubit we adopt rotational states of a nonpolar ionic molecule trapped in an ion trap. It is revealed that the rotational-state qubits are much more immune to decoherence than the conventional electronic-state qubits of atomic ions. A complete method set that includes state preparation, a single-qubit gate, a controlled-not gate, and qubit readout suitable for the rotational-state qubits is provided. Since the ionic molecules can be transported in an array of ion traps, the rotational-state qubits are expected to be a promising candidate to build a large-scale quantum computer.

We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that possess a transversal Hadamard operation, enabling each of these codes to distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify other high-fidelity magic states to even higher fidelity, which we call multilevel distillation. When distilling in the asymptotic regime of infidelity $\epsilon \to 0$ for each input magic state, the number of input magic states consumed on average to yield an output state with infidelity $O\left({\epsilon }^{2^r}\right)$ approaches $2^r+1$, which comes close to saturating the conjectured bound in another investigation [Bravyi and Haah, Phys. Rev. A 86, 052329 (2012)]. We show numerically that there exist multilevel protocols such that the average number of magic states consumed to distill from error rate ${\epsilon }_{\mathrm{in}}=0.01$ to ${\epsilon }_{\mathrm{out}}$ in the range ${10}^{-5}$–${10}^{-40}$ is about $14{\log }_{10}(1/{\epsilon }_{\mathrm{out}})-40$; the efficiency of multilevel distillation dominates all other reported protocols when distilling Hadamard magic states from initial infidelity 0.01 to any final infidelity below ${10}^{-7}$. These methods are an important advance for magic-state distillation circuits in high-performance quantum computing and provide insight into the limitations of nearly resource-optimal quantum error correction.

We explore the entanglement generation between two dipole emitters via a hybrid photonic-plasmonic resonant structure which consists of two metal nanoparticles (MNPs) and a high-$Q$ whispering-gallery-mode (WGM) microcavity. Because the coupling strength between the dipole emitter and the cavity can be substantially enhanced with the help of MNPs and maintained by the WGM cavity, the maximum entanglement plateau between two dipole emitters can be deterministically created even in the presence of the spontaneous emission of the dipole emitters and the decay induced by the microcavity and MNPs. The width of the plateau depends on the coupling strengths (or the radii of the MNPs) and the initial state, but is insensitive to the dipole-cavity detuning. These results are useful in real experiments.

We prove that a beam splitter, one of the most common optical components, fulfills several classes of majorization relations, which govern the amount of quantum entanglement that it can generate. First, we show that the state resulting from $k$ photons impinging on a beam splitter majorizes the corresponding state with any larger photon number $k^{\prime }>k$, implying that the entanglement monotonically grows with $k$. Then we examine parametric infinitesimal majorization relations as a function of the beam-splitter transmittance and find that there exists a parameter region where majorization is again fulfilled, implying a monotonic increase of entanglement by moving towards a balanced beam splitter. We also identify regions with a majorization default, where the output states become incomparable. In this latter situation, we find examples where catalysis may nevertheless be used in order to recover majorization. The catalyst states can be as simple as a path-entangled single-photon state or a two-mode squeezed vacuum state.

The optical forces on neutral two-level atoms by the subcycle pulsed focused vector field are investigated by numerically solving the density-matrix equations without the rotating-wave approximation. The phenomena of focusing or defocusing of the neutral atom are analyzed. For the transverse optical force, an acceleration of an atom that is 10 orders of magnitude higher than the Earth's gravitational acceleration $g$ can be obtained. The optical force can change from a focusing force to a defocusing force depending on the initial state of the atom. The optical potential may be used to trap the neutral two-level atoms in the experiment of cold atoms.

Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular, and optical physics, such as transport, cooling and expansion, wave-packet splitting, or internal state control. Here we examine the limitations and capabilities of superadiabatic iterations to produce a sequence of shortcuts to adiabaticity. The general formalism is worked out as well as examples for population inversion in a two-level system.