Superconducting qubits arrays have become one of the most promising architectures for the practical implementation of universal quantum computing with quantum error correction codes. Here we propose a defect-tolerant surface code topology which is resistant to sparse fabrication defects. The topology is equivalent to a disk folded into $N$ layers. A physically defective qubit can be replaced with a working physical qubit within the same unit cell from a different layer. Thereby sparse fabrication errors can be collected into one sacrificial layer and isolated from the working layers by turning off their controllable couplers. We propose two schemes to realize this robust topology. One is to use flux qubits, and the other is based on Xmon qubits. A modified quantum circuit for the stabilization cycle of the Xmon qubits scheme is developed. We calculate and compare the per-operation error thresholds for these two schemes and find that the error threshold for the modified quantum circuit is close to that for the original stabilization cycle. A possible way to implement the intersecting connections between different Xmon qubits on the circuit level is also provided.

Expectation values of the Breit operators are calculated for the ${{\mathrm{D}}_2}^{+}$ molecular ion with the vibrational number $\left(v=0\text{–}4\right)$ and angular momentum $\left(L=0\text{–}4\right)$. Hyperfine splittings of energy levels of the states $(v=0\text{–}4,L=3,4)$ are also determined in the framework of the spin-dependent Breit-Pauli Hamiltonian, which can be considered as an extension of our previous work [Phys. Rev. A 88, 032519 (2013)]. These theoretical calculations may be used to improve spectroscopic precision of ${{\mathrm{D}}_2}^{+}$ and determine the dissociation or the ionization energy of ${\mathrm{D}}_2$.

The development of advanced quantum technologies and the quest for a deeper understanding of many-particle quantum mechanics requires control over the quantum state of interacting particles to a high degree of fidelity. However, the quickly increasing density of the spectrum, together with the appearance of crossings in time-dependent processes, makes any effort to control the system hard and resource intensive. Here we show that in trapped systems regimes can exist in which isolated energy bands appear that allow one to easily generalize known single-particle techniques. We demonstrate this for the well-known spatial adiabatic passage effect, which can control the center-of-mass state of atoms with high fidelity.

We investigate the multiple stable macroscopic quantum states of a Bose-Einstein condensate in an optomechanical cavity with pump-cavity field detuning and atom-photon interaction following the experimental realization of the quantum phase transition [Nature (London) 464, 1301 (2010)]. The spin-coherent-state variational method is useful in exploring the multistability since it has the advantage of including both normal and inverted pseudospin states. In the blue detuning regime the usual transition from normal to superradiant phases still exists, however, when the atom-field coupling increases to a certain value, called the turning point, the superradiant phase collapses due to the resonant damping of the mechanical oscillator. As a consequence, the system undergoes at this point an additional phase transition to the normal phase of the atomic population inversion state. In particular, the superradiant phase disappears completely at strong photon-phonon interaction, resulting in the direct atomic population transfer between two atomic levels. Moreover, the coupling-induced collapse and revival of the superradiant state are also found in the red detuning region.

Purely azimuthal entanglement is analyzed for noncollinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter $K$ on the order of the ratio of the pump waist to its wavelength. A scheme is suggested for partial realization of this high entanglement resource in the form of a multichannel Schmidt-type decomposition.

We report on the direct measurement in real space of the effect of the van der Waals forces between individual Rydberg atoms on their external degrees of freedom. Clusters of Rydberg atoms with interparticle distances of around $5\mu \mathrm{m}$ are created by first generating a small number of seed excitations in a magneto-optical trap, followed by off-resonant excitation that leads to a chain of facilitated excitation events. After a variable expansion time the Rydberg atoms are field ionized, and from the arrival time distributions the size of the Rydberg cluster after expansion is calculated. Our experimental results agree well with a numerical simulation of the van der Waals explosion.

Superconducting systems such as those modeled by the Kitaev Hamiltonian are found to exhibit Zitterbewegung (ZB) oscillations. Remarkably, the dispersion relation in one-dimensional Kitaev systems allows for wave packets of arbitrary size to undergo nondecaying ZB oscillations without any distortion, with the typical ZB amplitude being one lattice site. To motivate possible experimental interest in this dynamical aspect of superconducting systems, we further show that a certain on-resonance modulation of the Hamiltonian parameter can be exploited to convert ZB oscillations to net drifting of the particle's and hole's wave packet along opposite directions, leading to long-distance particle-hole separation.

We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian $\mathcal{L}\left(t\right)$. We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of $\mathcal{L}\left(t\right)$ will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time $T$. In the case of a finite number of level crossings, the scaling becomes $T^{-\eta }$ with an exponent $\eta$ that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time $T$ should be long compared to the corresponding minimum inverse gap squared of $\mathcal{L}\left(t\right)$. Our results are illustrated with several examples.

We develop a semianalytical approach beyond the Born-Markov approximation to study the quench dynamics of the spin-boson model in the strong-coupling regime ($\alpha \le 1/2$) for the Ohmic bath. The basic idea in our approach is to write an effective time-dependent model for the dynamics of the system coupled to the bosonic bath after integrating out high-frequency bath modes. By applying this procedure to the Heisenberg equations of motion, we derive a set of flow equations for the system parameters as a function of time. The final flow equations look similar to those of the equilibrium renormalization-group theory; however, in our derivation the scaling parameter is set by the real time. We solve the equations of motion with time-dependent renormalized parameters and show that the resulting dynamics is in decent agreement with the exact NRG calculations as well as the noninteracting blip approximation that is a well-known good solution in this limit.

Quantum key distribution (QKD) guarantees unconditional communication security based on the laws of quantum physics. However, practical QKD suffers from a number of quantum hackings due to the device imperfections. From the security standpoint, measurement-device-independent quantum key distribution (MDI-QKD) is in the limelight since it eliminates all the possible loopholes in detection. Due to active control units for mode matching between the photons from remote parties, however, the implementation of MDI-QKD is highly impractical. In this paper, we propose a method to resolve the mode matching problem while minimizing the use of active control units. By introducing the plug-and-play (P&P) concept into MDI-QKD, the indistinguishability in spectral and polarization modes between photons can naturally be guaranteed. We show the feasibility of P&P MDI-QKD with a proof-of-principle experiment.

In this work we investigate the decay of the $|2p^{5}3s{}^{3}P_0\rangle$ state in neon-like ions along the isoelectronic sequence ranging from $Z=10$ to $Z=35$. In the absence of a nuclear spin, the magnetic dipole transition to $|2p^{5}3s{}^{3}P_1\rangle$ is the dominating decay channel. However, for isotopes with a nuclear spin, the interaction between the nuclear magnetic dipole moment and the electronic field introduces a mixing of $|2p^{5}3s{}^{3}P_1\rangle$ and $|{}^{1}P_1\rangle$ into the $|{}^{3}P_0\rangle$ state, which in turn opens up a competing hyperfine-induced electric dipole decay channel to the ground state. This hyperfine-induced transition channel clearly dominates over the magnetic dipole channel for the neutral end of the isoelectronic sequence, when present. We give values for the rates of both these competing channels and discuss how the introduction of the hyperfine-induced transition channel could have a dramatic influence on the spectrum, not only because it introduces a new line, but also since it can substantially decrease the intensity of the magnetic dipole $2p^{5}3s{}^{3}P_0\to 2p^{5}3s{}^{3}P_1$ line and affect the predicted ionization balance in different plasmas.

In this paper, we present experimental and theoretical studies on the interference between resonant and nonresonant photorecombinations for the main resonances of ground-state He-, Be-, B-, C-, N-, and O-like W ions. Experiments were done using a fast electron energy scanning technique at the upgraded Shanghai electron-beam ion trap. Asymmetric resonances were observed, and their Fano factors, which measure the interference degree, were determined. The calculations were done under the framework of Fano's theory by using the flexible atomic code, in which the relativistic configuration interaction method was employed. Among the nine resonances studied in this work, eight experimental results agree with the calculation within experimental uncertainties. But the experimental result for the resonance of Be-like W ions, through the intermediate state of ${\left[{\left(1s2s^{2}2p_{1/2}\right)}_{1}2p_{3/2}\right]}_{5/2}$, deviates from its corresponding theoretical result by 1.3 times experimental uncertainty.

We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a nonclassical path. The Gouy phase differs for classical and nonclassical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter $\kappa$ used to estimate the nonclassical path contribution in a nontrivial way, shedding some light on the implementation of experiments to detect nonclassical path contributions.

We investigate strongly correlated spin-1 ultracold bosons with antiferromagnetic interactions in a cubic optical lattice, based on bosonic dynamical mean-field theory. Rich phase diagrams of the system are mapped out at both zero and finite temperature, and in particular the existence of a spin-singlet condensate is established. Interestingly, at finite temperature, we find that the superfluid can be heated into a Mott insulator with even (odd) filling via a first- (second-) order phase transition, analogous to the Pomeranchuk effect in ${}^3\mathrm{He}$. Moreover, for typical experimental setups, we estimate the critical temperature (entropy) for different ordered phases and our results suggest that direct experimental observation of these phases is promising.

We encode the many-body wave function of a Bose-Einstein condensate (BEC) in the $N$-particle sector of an extended catalytic state. This catalytic state is a coherent state for the condensate mode and an arbitrary state for the modes orthogonal to the condensate mode. Going to a time-dependent interaction picture where the state of the condensate mode is displaced to the vacuum, we can organize the effective Hamiltonian by powers of $N^{-1/2}$. Requiring the terms of order $N^{1/2}$ to vanish gives the Gross-Pitaevskii equation. Going to the next order, $N^0$, we derive equations for the number-conserving Bogoliubov approximation, first given by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. In contrast to other approaches, ours is well suited to calculating the state evolution in the Schrödinger picture; moreover, it is straightforward to generalize our method to multicomponent BECs and to higher-order corrections.

We calculate the energy fluctuation of a truly finite number of interacting bosons and study the role of interaction. Although the ideal Bose gas in thermodynamic limit is an exactly solvable problem and analytic expression of various fluctuation measures exists, the experimental Bose-Einstein condensation (BEC) is a nontrivial many-body problem. We employ a two-body correlated basis function and utilize the realistic van der Waals interaction. We calculate the energy fluctuation $(△E^2)$ of the interacting trapped bosons and plot $\frac{△E^2}{k_B^2{T}^2}$ as a function of $\frac{T}{T_c}$. In the classical limit $△E^2$ is related to the specific heat per particle $c_v$ through the relation $△E^2=k_B{T}^2{c}_v$. We have obtained a distinct hump in $\frac{△E^2}{k_B^2{T}^2}$ around the condensation point for three-dimesional harmonically trapped Bose gas when the particle number $N\simeq 5000$ and above which corresponds to the second-order phase transition. However for finite-size interacting bosons ($N\simeq$ a few hundred) the hump is not sharp, and the maximum in $\frac{△E^2}{k_B^2{T}^2}$ can be interpreted as a smooth increase in the scaled fluctuation below $T_c$ and then a decrease above $T_c$. To illustrate the justification we also calculate $c_v$, which exhibits the same feature, which leads to the conjecture that for finite-sized interacting bosons phase transition is ruled out.

We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that the interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, interspecies scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a time-dependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diffraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.

We discuss the quantum phase transition between the Mott-insulator state and the density-wave state of cold Bose atoms in a two-dimensional (2D) square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave state, one obtains a disordered state. An intrinsic relation of the problem to Bloch oscillations of hard-core bosons in a 2D lattice is illuminated.

We use a density matrix formalism to study the equilibrium phases and nonequilibrium dynamics of a system of dissipative Rydberg atoms in an optical lattice within mean-field theory. We provide equations for the fixed points of the density matrix evolution for atoms with infinite on-site repulsion and analyze these equations to obtain their Mott-insulator–superfluid (MI-SF) phase boundary. A stability analysis around these fixed points provides us with the excitation spectrum of the atoms both in the MI and SF phases. We study the nature of the MI-SF critical point in the presence of finite dissipation of Rydberg excitations, discuss the fate of the superfluid order parameter of the atoms in the presence of such dissipation in the weak-coupling limit using a coherent state representation of the density matrix, and extend our analysis to Rydberg atoms with finite on-site interaction via numerical solution of the density matrix equations. Finally, we vary the boson (atom) hopping parameter $J$ and the dissipation parameter $\mathrm{\Gamma }$ according to a linear ramp protocol. We study the evolution of entropy of the system following such a ramp and show that the deviation of the entropy from its steady-state value for the latter protocol exhibits power-law behavior as a function of the ramp time. We discuss experiments that can test our theory.

We study the topological configurations of the two-component condensates of bosons with the three-dimensional $\left(3\mathrm{D}\right) \vec{\sigma }·\vec{p}$ Weyl-type spin-orbit coupling subject to a harmonic trapping potential. The topology of the condensate wave functions manifests in the quaternionic representation. In comparison to the $\text{U}\left(1\right)$ complex phase, the quaternionic phase manifold is $S^3$ and the spin orientations form the $S^2$ Bloch sphere through the first Hopf mapping. The spatial distributions of the quaternionic phases exhibit the 3D skyrmion configurations, and the spin distributions possess nontrivial Hopf invariants. Spin textures evolve from the concentric distributions at the weak spin-orbit coupling regime to the rotation symmetry-breaking patterns at the intermediate spin-orbit coupling regime. In the strong spin-orbit coupling regime, the single-particle spectra exhibit the Landau-level-type quantization. In this regime, the three-dimensional skyrmion lattice structures are formed when interactions are below the energy scale of Landau-level mixings. Sufficiently strong interactions can change condensates into spin-polarized plane-wave states or superpositions of two plane waves exhibiting helical spin spirals.