We present a dissipative protocol to engineer two ${}^{87}\mathrm{Rb}$ atoms into a form of three-dimensional entangled state via spontaneous emission. The combination of coupling between ground states via microwave fields and dissipation induced by spontaneous emission makes the current scheme deterministic and a stationary entangled state is always achievable without state initialization. Moreover, this scheme can be straightforwardly generalized to preparation of an $N$-dimensional entangled state in principle.

We theoretically investigate the interference effect of high-order harmonics generated from molecules at different alignment angles. It is shown that the interference of the harmonic emissions from molecules aligned at different angles can significantly modulate the spectra and result in the anomalous harmonic cutoffs observed in a recent experiment [Nat. Phys. 7, 822 (2011)]. The shift of the spectral minimum position with decreasing the degree of alignment is also explained by the interference effect of the harmonic emissions.

Multielectron coincidence spectroscopy has been used to study core $4f$ valence $5d$, $6s$ double photoionization of atomic mercury. Multiconfiguration Dirac–Fock calculations were performed to calculate the energies and to estimate the single-photon intensities of the $4f^{13}(5d^{9}6s^2+5d^{10}6s^1)$ double-ionized states of atomic mercury. Reasonable agreement between the measured and simulated spectra is found if the relaxation effects of the bound-state density is taken into account in the computation of the photoionization amplitudes.

The spectral function of a spin-balanced two-dimensional Fermi gas with short-range interactions is calculated by means of a quantum cluster expansion. Good qualitative agreement is found with a recent experiment by Feld et al. [Nature (London) 480, 75 (2011)]. The effects of pairing are clearly visible in the density of states, which displays a suppression of spectral weight due to the formation of a two-body bound state. In addition, the momentum distribution and the radio-frequency spectrum are derived, which are in excellent agreement with exact universal results. It is demonstrated that in the limit of high temperature, the quasiparticle excitations are well defined, allowing for a kinetic description of the gas.

Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a vacuum squeezed state of arbitrary squeezing strength, thereby constituting a mechanism allowing perfect squeezing. Given the recent experimental realizations in circuit QED of a microwave resonator with a tunable damping rate [Yin et al., Phys. Rev. Lett. 110, 107001 (2013)], superconducting circuits are an ideal playground to implement this technique. By dispersively coupling a qubit to the microwave resonator, it is possible to obtain qubit-state-dependent squeezing.

We investigate the possibility of guiding stable ultraslow weak-light bullets by using Airy beams in a cold, lifetime-broadened four-level atomic system via electromagnetically induced transparency (EIT). We show that under EIT condition the light bullet with ultraslow propagating velocity and extremely low generation power formed by the balance between diffraction and nonlinearity in the probe field can be not only stabilized but also steered by the assisted field. In particular, when the assisted field is taken to be an Airy beam, the light bullet can be trapped into the main lobe of the Airy beam, propagate ultraslowly in longitudinal direction, accelerate in transverse directions, and move along a parabolic trajectory. We further show that the light bullet can bypass an obstacle when guided by two sequential Airy beams. A technique for generating ultraslow helical weak-light bullets is also proposed.

We propose a hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $>0.99$ are possible on submicrosecond time scales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.

In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and may therefore not be able to implement a known optimal scheme. We introduce a simple procedure for minimizing the uncertainty in the reconstructed quantum state for an arbitrary tomographic scheme. We do this by defining a figure of merit based on the equally weighted variance of the measurement statistics. This figure of merit is straightforwardly based on the singular value decomposition of the measurement matrix, making it well suited for optimization.

We address the non-Markovian character of quantum maps describing the interaction of a qubit with a random classical field. In particular, we evaluate trace- and capacity-based non-Markovianity measures for two relevant classes of environments showing non-Gaussian fluctuations, described respectively by random telegraph noise and colored noise with spectra of the the form $1/f^{\alpha }$. We analyze the dynamics of both the trace distance and the quantum capacity, and show that the behavior of non-Markovianity based on both measures is qualitatively similar. Our results show that environments with a spectrum that contains a relevant low-frequency contribution are generally non-Markovian. We also find that the non-Markovianity of colored environments decreases when the number of fluctuators realizing the environment increases.

We propose a general strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately $8.7\%$. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.

We present measurements of trapped-ion motional-state heating rates in niobium and gold surface-electrode ion traps over a range of trap-electrode temperatures from approximately 4 K to room temperature (295 K) in a single apparatus.Using the sideband-ratio technique after resolved-sideband cooling of single ions to the motional ground state, we find low-temperature heating rates more than two orders of magnitude below the room-temperature values and approximately equal to the lowest measured heating rates in similarly sized cryogenic traps. We find similar behavior in the two very different electrode materials, suggesting that the anomalous heating process is dominated by non-material-specific surface contaminants. Through precise control of the temperature of cryopumping surfaces, we also identify conditions under which elastic collisions with the background gas can lead to an apparent steady heating rate, despite rare collisions.

The Casimir force between two inhomogeneous metal-dielectric composite slabs with spatial dispersion is investigated theoretically. The equivalent permittivity and permeability of the nonlocal metallic nanosphere is originally derived based on full-wave nonlocal Mie theory. We then adopt two nonlocal effective medium models to study the effective permittivity and permeability of the composite slabs and calculate the Casimir force with Casimir-Lifshitz theory. Due to the excitation of the longitudinal modes, the attractive Casimir force between nonlocal composite materials is much weaker than that of the local composites, and numerical results show that the relative errors between local and nonlocal calculations of Casimir force can be on the order of $25\%$. Moreover, the nonlocal effects on the Casimir force are strongly dependent on the microstructures, and they become significant near the percolation threshold of the composite media. The study may be of great interest for making a precise comparison between theoretical and experimental results on the Casimir force between inhomogeneous composite materials.

The van der Waals force between objects of nontrivial geometries is considered. A technique based on a perturbation series approach is formulated in the dilute limit. We show that the dielectric response and object size can be decoupled and dominant contributions in terms of object separations can be obtained. This is a powerful method, which enables straightforward calculations of the interaction for different geometries. Our results for planar structures, such as thin sheets, infinitely long ribbons, and ribbons with finite dimensions, may be applicable for nanostructured devices where the van der Waals interaction plays an important role.

The unperturbed Hamiltonian for the Bose-Einstein condensate, which includes not only the first and second powers of the zero mode operators but also the higher ones, is proposed to determine a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of $-1/3$, which is universal for both homogeneous and inhomogeneous systems.

We examine the spatiotemporal compression of energetic femtosecond laser pules within short gas-filled fibers. The study is undertaken using an advanced nonlinear pulse propagation model based on a multimode generalized nonlinear Schrödinger equation that has been modified to include plasma effects. Plasma defocusing and linear propagation effects are shown to be the dominant processes within a highly dynamical mechanism that enables $\text{100-fs}$ pulses to be compressed into the few-cycle regime after $<\text{50}\text{mm}$ of propagation. Once the mechanism has been introduced, parameter spaces are explored and compressor designs suitable for performing high-field experiments in situ are presented. We finish by showing how these designs may be extended to novel wavelengths and driving pulses delivered by state-of-the-art high-repetition-rate lasers.

We present a quantum open-system approach to analyze the nonunitary dynamics of a superconducting qubit when it evolves under the influence of external noise. We consider the presence of longitudinal and transverse environmental fluctuations affecting the system's dynamics and model these fluctuations by defining their correlation function in time. By using a Gaussian-like noise correlation, we can study low- and high-frequency noise contribution to decoherence and implement our results in the computation of geometric phases in open quantum systems. We numerically study when the accumulated phase of a solid-state qubit can still be found close to the unitary (Berry) one. Our results can be used to explain experimental measurements of the Berry phase under high-frequency fluctuations and design experimental future setups when manipulating superconducting qubits.

We introduce an action principle for a class of integer-valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth-limited harmonic oscillators, which encode the Schrödinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.

A method for deriving accurate analytic approximations for Markovian open quantum systems was recently introduced by Lucas and Hornberger [Phys. Rev. Lett. 110, 240401 (2013)]. Here, we present a detailed derivation of the underlying nonperturbative jump expansion, which involves an adaptive resummation to ensure optimal convergence. Applying this to a set of exemplary master equations, we find that the resummation typically leads to convergence within the lowest two to five orders. Besides facilitating analytic approximations, the optimal jump expansion thus provides a numerical scheme for the efficient simulation of open quantum systems.

We analyze three different post-processing methods applied to a single-shot qubit readout: the average-signal (boxcar filter), peak-signal, and maximum-likelihood methods. In contrast to previous work, we account for a stochastic turn-on time $t_i$ associated with the leading edge of a pulse signaling one of the qubit states. This model is relevant to spin-qubit readouts based on spin-to-charge conversion and would be generically reached in the limit of large signal-to-noise ratio $r$ for several other physical systems, including fluorescence-based readouts of ion-trap qubits and nitrogen-vacancy center spins. We derive analytical closed-form expressions for the conditional probability distributions associated with the peak-signal and boxcar filters. For the boxcar filter, we find an asymptotic scaling of the single-shot error rate $\varepsilon \sim lnr/\sqrt{r}$ when $t_i$ is stochastic, in contrast to the result $\varepsilon \sim lnr/r$ for deterministic $t_i$. Consequently, the peak-signal method outperforms the boxcar filter significantly when $t_i$ is stochastic, but is only marginally better for deterministic $t_i$ (a result that is consistent with the widespread use of the boxcar filter for fluorescence-based readouts and the peak signal for spin-to-charge conversion). We generalize the theoretically optimal maximum-likelihood method to stochastic $t_i$ and show numerically that a stochastic turn-on time $t_i$ will always result in a larger single-shot error rate. Based on this observation, we propose a general strategy to improve the quality of single-shot readouts by forcing $t_i$ to be deterministic.

We present a bound on the length of the path defined by the ground states of a continuous family of Hamiltonians in terms of the spectral gap $\Delta$. We use this bound to obtain a significant improvement over the cost of recently proposed methods for quantum adiabatic state transformations and eigenpath traversal. In particular, we prove that a method based on evolution randomization, which is a simple extension of adiabatic quantum computation, has an average cost of order $1/{\Delta }^2$, and a method based on fixed-point search has a maximum cost of order $1/{\Delta }^{3/2}$. Additionally, if the Hamiltonians satisfy a frustration-free property, such costs can be further improved to order $1/{\Delta }^{3/2}$ and $1/\Delta$, respectively. Our methods offer an important advantage over adiabatic quantum computation when the gap is small, where the cost is of order $1/{\Delta }^3$.