In recent studies [Liew et al., Phys. Rev. Lett. 104, 183601 (2010); Bamba et al., Phys. Rev. A 83, 021802(R) (2011)], due to destructive interference between different paths for two-photon excitation, strong photon antibunching can be obtained in a photonic molecule consisting of two coupled cavity modes with weak Kerr nonlinearity when one of the cavity modes is driven resonantly. Here, we study the photon statistics in a nonlinear photonic molecule with both the two cavity modes being driven coherently. We show that the statistical properties of the photons can be controlled by regulating the strength ratio and the relative phase between the two driving fields. The photonic molecules with two driven modes can be used to generate tunable single-photon sources or controlled photonic quantum gates with weak Kerr nonlinearity.

The standard $\mathcal{PT}$-symmetric dimer is a linearly coupled two-site discrete nonlinear Schrödinger equation with one site losing and the other one gaining energy at the same rate. We show that despite gain and loss, the standard $\mathcal{PT}$ dimer is a Hamiltonian system. We also produce a Lagrangian formulation for the dimer.

Although interference is a classical-wave phenomenon, the superposition principle, which underlies interference of individual particles, is at the heart of quantum physics. An interaction-free measurement (IFM) harnesses the wave-particle duality of single photons to sense the presence of an object via the modification of the interference pattern, which can be accomplished even if the photon and the object have not interacted with each other. By using the quantum Zeno effect, the efficiency of an IFM can be made arbitrarily close to unity. Here we report an on-chip realization of the IFM based on silicon photonics. We exploit the inherent advantages of the lithographically written waveguides (excellent interferometric phase stability and mode matching) and obtain multipath interference with visibility above $98\%$. We achieved a normalized IFM efficiency up to $68.2\%$, which exceeds the $50\%$ limit of the original IFM proposal.

The surface code is a promising alternative for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attractive features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.

We report on experimental and theoretical investigations of dynamic evolution of individual $R$-branch laser lines from tunnel-ionized nitrogen molecules based on a pump-probe scheme. Our observation shows that the intensities of the $R$-branch laser lines exhibit rapid oscillations which can be decomposed into periodic oscillations at different frequencies. The oscillations can be attributed to the coupling between the rotational quantum states mediated either by the probe pulses or by the $P$-branch laser emission from the molecular ions.

A modified empirical ionization formula is proposed to extend Tong and Lin's ionization formula [X. M. Tong and C. D. Lin, J. Phys. B 38, 2593 (2005)] to a laser field up to 4.5 times barrier-suppression strength $\left(E_b\right)$ in the over-barrier regime. The validity of the formula is checked by solving the Schrödinger equation within the single-active-electron approximation with an excellent agreement. This modified empirical formula still keeps its simplicity and can calculate ionization rates in the deep over-barrier regime.

We study steady-state evaporation in an atom guide via Monte Carlo simulations. The evaporation surface follows a specific profile as a function of longitudinal guide location. We demonstrate that the choice of evaporation profile significantly impacts the performance of the evaporation. Our simulations also demonstrate a significant performance boost in the evaporation when using a longitudinally compressed guide. We show that for a purely pressure-driven atom beam, it should be possible to reach degeneracy within a 0.5 m guide for experimentally feasible, albeit challenging, loading conditions.

We study the stroboscopic and nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables, which commute with the operator to which the driving protocol couples. On the contrary, nonstroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a $2\times 2$ plaquette, as well as the chiral current operator flowing along the legs of a $2\times 20$ ladder. The exact evolution is compared with its stroboscopic and nonstroboscopic counterparts, including finite-frequency corrections.

Optical analogies of macroscopic quantum effects (Schrödinger cat states, squeezing, collapse, and revival) for light beams propagating in an inhomogeneous linear medium are demonstrated theoretically using exact analytical solutions of the wave equation. It is shown that the coherent superposition of macroscopically distinguishable states is generated via mode interference from an initial off-axis single wave packet. Squeezed cat states with a fidelity >99% arise periodically and disappear rapidly within limited intervals of a propagation distance. Collapse and revival of wave packets at long-term nonparaxial evolution due to mode interference is demonstrated. Oscillations of the beam trajectory occur with extremely small amplitude, of the order of $10{}^{-19}$ m, which is typical of the estimated displacement caused by cosmic gravitational waves in gravity-wave detectors.

We show the emergence of light localization in arrays of coupled optical waveguides with randomness only in the imaginary part of their refractive index and develop a one-parameter scaling theory for the normalized participation number of Floquet-Bloch modes. This localization introduces a different length scale in the decay of the autocorrelation function of a paraxial beam propagation. Our results are relevant to a vast family of systems with randomness in the dissipative part of their impedance spatial profile.

We describe and analyze a quasi-phase-matching scheme for nonlinear optical frequency conversion where the spatial modulation of mode intensity in coupled parallel waveguides provides the required modulation in the generation of the frequency conversion signal, instead of a variation of any material parameter or propagation constant. We analyze this coupling-length phase-matching (CLPM) scheme both for second-order frequency conversion, such as second harmonic generation or difference-frequency generation, as well as for third-order four-wave mixing processes, for which we consider the example of generating a longer wavelength by third-order nonlinear mixing of two shorter wavelength waves. Numerous phase-matching conditions are identified in each case. We show that the maximum photon conversion efficiencies reached after an optimum propagation length are always higher than half those obtained for perfect phase matching in a single waveguide, with nearly 100% photon conversion possible for several of the CLPM conditions we studied.

The ultrastrong-coupling regime, where the atom-cavity coupling rate reaches a considerable fraction of the cavity or atom transition frequencies, has been reported in a flux qubit superconducting quantum circuit coupled to an on-chip coplanar resonator. In this regime situations may arise where the resonator field $\widehat{X}=\widehat{a}+{\widehat{a}}^{†}$ acquires a nonzero expectation value in the system ground state. We demonstrate that, in this case, the parity symmetry of an additional artificial atom with an even potential is broken by the interaction with the resonator. Such a mechanism is analogous to the Higgs mechanism where the gauge symmetry of the weak force's gauge bosons is broken by the nonzero vacuum expectation value of the Higgs field. The results presented here open the way to controllable experiments on symmetry-breaking mechanisms induced by nonzero vacuum expectation values. Moreover, the mechanism proposed here can be used as a probe of the ground-state macroscopic coherence emerging from quantum phase transitions with vacuum degeneracy.

Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses the ultimate limit on precision which can only be approached but never be violated. Depending on analytic techniques, these bounds may not be unique. Here, in view of prior information, we investigate systematically the precision bounds of the total mean-square error of vector parameter estimation which contains $d$ independent parameters. From quantum Ziv-Zakai error bounds, we derive two kinds of quantum metrological bounds for vector parameter estimation, both of which should be satisfied. By these bounds, we show that a constant advantage can be expected via a simultaneous estimation strategy over the optimal individual estimation strategy, which solves a long-standing problem. A general framework for obtaining the lower bounds in a noisy system is also proposed.

We investigate a type of matched infrared soliton pairs based on four-wave mixng (FWM) in Landau-quantized graphene by using density-matrix method and perturbation theory. The linear and nonlinear dynamical properties of the graphene system are first discussed, and, in particular, we focus on the signatures of nonlinear optical response. Then we present analytical solutions for the fundamental bright and dark solitons, as well as bright two-soliton, which are in good agreement with the results of numerical simulations. Moreover, due to the unusual dispersion relation and chiral character of electron states, we find that the matched spatial soliton pairs can propagate through a two-dimensional crystal of graphene and their carrier frequencies are adjustable within the infrared frequency regimes. Our proposed scheme may provide a route to explore the applications of matched infrared soliton pairs in telecommunication and optical information processing.

We investigate the effects of a time-periodic, non-Hermitian, $\mathcal{PT}\text{−}\mathrm{symmetric}$ perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We prove that when the perturbation frequency is close to one of the system resonances, even a vanishingly small gain-loss potential leads to $\mathcal{PT}$ symmetry breaking. We also find a restored $\mathcal{PT}\text{−}\mathrm{symmetric}$ phase at high frequencies, and at moderate perturbation strengths, we predict the existence of multiple frequency windows where $\mathcal{PT}$ symmetry is broken and restored. Our results imply that the $\mathcal{PT}\text{−}\mathrm{symmetric}$ Rabi problem shows exceptionally rich phenomena absent in its Hermitian or static counterparts.

Time-resolved photon detection can be used to generate entanglement between distinguishable photons. This technique can be extended to entangle quantum memories that emit photons with different frequencies and identical temporal profiles without the loss of entanglement rate or fidelity. We experimentally realize this process using remotely trapped ${}^{171}{\mathrm{Yb}}^{+}$ ions where heralded entanglement is generated by interfering distinguishable photons. This technique may be necessary for future modular quantum systems and networks that are composed of heterogeneous qubits.

Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of an infinite number of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.

The classical capacity of phase-invariant Gaussian channels has been recently determined under the assumption that such channels are memoryless. In this work we generalize this result by deriving the classical capacity of a model of quantum memory channel, in which the output states depend on the previous input states. In particular we extend the analysis of Lupo et al. [Phys. Rev. Lett. 104, 030501 (2010) and Phys. Rev. A 82, 032312 (2010)] from quantum limited channels to thermal attenuators and thermal amplifiers. Our result applies in many situations in which the physical communication channel is affected by nonzero memory and by thermal noise.

We study the robustness of quantum transport in four-site one-dimensional (1D) particle quantum networks irreversibly connected to a target site in the presence of environmental dephasing noise. Under conditions of Markovian decoherence we define a quantity—which we denote as geometrical robustness—to quantify the robustness of transport with regard to the geometrical arrangement of the spin network. We examine the behavior of this geometrical robustness for both nearest and non-nearest site interactions and show that for some values of dephasing noise and other network parameters the robustness undergoes revivals, i.e., the robustness periodically increases with dephasing. In addition, we find that for high amounts of dephasing noise, the pattern of optimal network configurations changes noticeably from central symmetric configurations to laterally gathered ones, and we show that this change of pattern seems to occur for any number of network sites in the 1D chain.