In this paper we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound states and cause scattering resonances. This represents the dipole-induced resonance in low dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using the asymptotic Bethe ansatz. Despite the long-range nature of dipolar interaction, we find that the behavior is similar to a short-range Lieb-Liniger gas emerging at the resonance region.

Fault-tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction (QEC) can be applied significantly less often with only a minimal loss of fidelity. This is done by simulating the implementation of 50 encoded, single-qubit, quantum gates within the [[7,1,3]] QEC code in a noisy, nonequiprobable Pauli error environment with QEC being applied at different intervals. We find that applying QEC after every gate is rarely optimal and even applying QEC only once after all 50 gates sacrifices only a slight amount of fidelity with the benefit of 50-fold saving of resources. In addition, we find that in cases where bit-flip errors are dominant, it is best not to apply QEC at all.

Toward complete coupling between propagating light (PL) and a single localized-surface-plasmon (LSP) nanostructure, we propose a tapered-fiber-coupled microspherical cavity system combining an Au-coated probe tip. This system possesses the unique characteristic of precise adjustability for the fiber-cavity coupling rate and the cavity-plasmon coupling rate, which is indispensable for achieving the critical coupling conditions. We successfully demonstrate the 93% PL coupling into the LSP antenna with an effective area of a 58 nm circle, exceeding the diffraction limit.

We prove that several known upper bounds on the classical capacity of thermal and additive noise bosonic channels are actually strong converse rates. Our results strengthen the interpretation of these upper bounds, in the sense that we now know that the probability of correctly decoding a classical message rapidly converges to 0 in the limit of many channel uses if the communication rate exceeds these upper bounds. In order for these theorems to hold, we need to impose a maximum photon number constraint on the states input to the channel (the strong converse property need not hold if there is only a mean photon number constraint). Our first theorem demonstrates that Koenig and Smith's upper bound on the classical capacity of the thermal bosonic channel is a strong converse rate, and we prove this result by utilizing the structural decomposition of a thermal channel into a pure-loss channel followed by an amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s upper bound on the classical capacity of a thermal bosonic channel corresponds to a strong converse rate, and we prove this result by relating the success probability to the rate, the effective dimension of the output space, and the purity of the channel as measured by the Rényi collision entropy. Finally, we use similar techniques to prove that similar previously known upper bounds on the classical capacity of an additive noise bosonic channel correspond to strong converse rates.

We consider a many-body system consisting of a harmonic oscillator linearly coupled to $N$ others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the $N$ others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the $N$ others and these are found entangled.

Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-squares fitting procedure provided by the cowan codes. This allows us to predict nine unobserved odd-parity energy levels of total angular momentum $J=5$, 6, and 7, in the range 25 000–31 000 cm${}^{-1}$ above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient $C_6^{\mathrm{iso}}=1760$ a.u. To the contrary, the photon-scattering rate shows a pronounced anisotropy since it strongly depends on the polarization of the trapping light.

Analytic expressions for the differential cross sections of ultracold atoms and molecules that scatter primarily due to dipolar interactions are derived within the first-order Born approximation and are shown to agree with the partial wave expansion. These cross sections are applied to the problem of cross-dimensional rethermalization. Strikingly, the rate of rethermalization can vary by as much as a factor of 2, depending on the orientation of the dipoles. Thus the anisotropic dipole-dipole interaction can have a significant effect even on the behavior of a nondegenerate ultracold gas.

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present the systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\Lambda$-type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find an optimal control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented, showing the effectiveness of the SLC method.

The many-body Schrödinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to 10 000 bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubbard model. We thereby show that the extent to which many-body effects become important at later times depends crucially on the initial state. Even for arbitrarily large particle numbers and arbitrarily weak interaction strength the dynamics is many-body in nature and the fragmentation universal. There is no weakly interacting limit where the Gross-Pitaevskii mean field is valid for long times.

We propose methods to create and observe Laughlin-like states of photons in a strongly nonlinear optical cavity. Such states of strongly interacting photons can be prepared by pumping the cavity with a Laguerre-Gauss beam, which has a well-defined orbital angular momentum per photon. The Laughlin-like states appear as sharp resonances in the particle-number-resolved transmission spectrum. Power spectrum and second-order correlation function measurements yield unambiguous signatures of these few-particle strongly correlated states.

We investigate beam diffraction and spatial modulation instability of coherent light beams propagating in the nonparaxial regime in a nonlinear Kerr medium. We study the instability of plane-wave solutions in terms of the degree of nonparaxiality, beyond the regime of validity of the nonlinear Schroedinger equation. We also numerically analyze the way nonparaxial terms break the integrability and affect the periodical evolution of higher-order soliton solutions. We discuss nonlocality and effective dissipation introduced by the nonlinear coupling with evanescent waves.

The time of flight for a laser beam through the atmosphere will fluctuate as the path-averaged index of refraction varies with atmospheric turbulence, air temperature, and pressure. We measure these fluctuations by transmitting optical pulses from a frequency comb across a 2-km horizontal path and detecting variations in their time of flight through linear optical sampling. This technique is capable of continuous measurements, with femtosecond resolution, over time scales of many hours despite turbulence-induced signal fading. The power spectral density for the time of flight, or equivalently for the optical phase, follows a simple power-law response of $\propto$$f^{-2.3}$ measured down to Fourier frequencies, $f$, of 100 μHz. There is no evidence of a roll-off at low frequencies associated with an outer scale for turbulence. Both of these results depart from the predictions of turbulence theory, but are consistent with some other results in the literature. We discuss the implications for the stability and accuracy of one-way optical time-frequency transfer.

We propose a scheme of the interaction-free all-optical switching in a multiatom cavity-QED system consisting of three-level atoms confined in a cavity and coupled by a free-space control laser. A signal laser field is coupled into the cavity and its transmission through and reflection from the cavity form two output channels. We show that the free-space control laser induces destructive quantum interference in the excitation of the atom-cavity normal mode, which can be used to switch on or off the output signal light of the reflection and the transmission channels. When the control light is coupled to the atoms, the input signal light is nearly totally reflected and this means that there is no direct coupling of the control light and the signal light through the cavity-confined atoms. We present analytical and numerical calculations that show that this type of the interaction-free all-optical switching in the coupled cavity-atom system can be realized with high switching efficiencies and at low light intensities.

We study the interplay between coherence trapping, information backflow and the form of the reservoir spectral density for dephasing qubits. We show that stationary coherence is maximized when the qubit undergoes non-Markovian dynamics, and we elucidate the different roles played by the low- and high-frequency parts of the environmental spectrum. We show that the low frequencies fully determine the presence or absence of information backflow while the high frequencies dictate the maximal amount of coherence trapping.

We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path-integral formulation, we are able to study memory effects on the dynamics of the coherent-state qubits due to strong environment coupling. We apply this formulation to examine the time evolution of a noisy quantum channel formed by two coherent-state qubits that are subject to uncorrelated local environment noises. In particular, we examine the time evolution of entanglement and maximal teleportation fidelity of the noisy quantum channel and show that at strong coupling, due to large feedback effects from the environment noise, it is possible to maintain a robust quantum channel in the long-time limit if an appropriate error-correcting code is applied.

We consider the two-photon exchange contribution to the $2P-2S$ Lamb shift in muonic deuterium in the framework of forward dispersion relations. The dispersion integrals are evaluated using experimental data on elastic deuteron form factors and inelastic electron-deuteron scattering, both in the quasielastic and hadronic range. The subtraction constant that is required to ensure convergence of the dispersion relation for the forward Compton amplitude $T_1(\nu ,Q^2)$ is related to the deuteron magnetic polarizability $\beta \left(Q^2\right)$. Based on phenomenological information, we obtain for the Lamb shift $\Delta E_{2P-2S}=2.01\pm 0.74$ meV. The main source of the uncertainty of the dispersion analysis is due to lack of quasielastic data at low energies and forward angles. We show that a targeted measurement of the deuteron electrodesintegration in the kinematics of upcoming experiments A1 and MESA at Mainz can help in quenching this uncertainty significantly.

The evolution dynamics of temporal Airy pulses in optical fibers with periodic dispersion modulation are numerically studied. We show that in a quasilinear regime with a low pump power, the finite-energy Airy waves may endlessly retain their shapes and follow preengineered temporal trajectories, forming accelerating or decelerating light bullets. We also demonstrate that Airy wave packets are more capable of adapting to the dispersion variation than the temporal sech-shaped pulses below a moderate pump power. However, the Airy nature of the pulse will eventually vanish due to the detrimental role of optical nonlinearities in the regime of high pump power, and the boundary between the linear and nonlinear dynamics is also analyzed. Numerical results are consistent with the theoretical predictions. Our approach gives insights into exploring the Airy light bullets in nonlinear and biological optics.

We study the dynamics of a zero-temperature Bose condensate following a sudden quench of the scattering length from noninteracting to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rate. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be understood within a simple, analytic two-body model. We make a quantitative prediction for the evolution of Tan's contact and find features in the momentum distribution that are absent in equilibrium. Third, we study three-body loss at finite density under the same dynamic scenario. We find lifetimes that are long compared to the saturation times of large-momentum modes, and we relate this result to the three-body inelasticity parameter.