In this paper, we propose a protocol to realize the conversions between Greenberger-Horne-Zeilinger (GHZ) states and $W$ states of spin qubits. By analyzing and simplifying the dynamics of the system, the control fields are designed via the inverse Hamiltonian engineering based on the Lie transforms. Moreover, the states' conversions between multitype GHZ states and $W$ states can be executed deterministically and reversibly, which makes the protocol resource saving and flexible. We show in numerical simulations that the state conversions are robust against the systematic errors, random noise, and frequency mismatching of the control fields. Therefore, the protocol may provide some useful prospectives to the research of quantum mechanics and applications of quantum information processing based on GHZ states and $W$ states.

We derive the effective Hamiltonian of nonrelativistic quantum electrodynamics up to order $m{\alpha }^8$ by using a procedure of scattering matching. Our results are in agreement at order $m{\alpha }^6$ with those achieved by applying the Foldy-Wouthuysen transformation [K. Pachucki, Phys. Rev. A 71, 012503 (2005)]. Based on the obtained Hamiltonian, we further derive the photon-exchange interactions in the nonretardation approximation, as well as the retardation corrections up to order $m{\alpha }^8$. The energy shift due to the photon-exchange interactions is determined by studying the pole structure of the Green's function.

Low-energy (0–15 eV) resonance electron attachment to a series of five-membered heterocyclic rings (isoxazole, imidazole, pyrazole, pyrrole, 1-methyl-, and 2-methylimidazole) is studied under gas-phase conditions by means of electron transmission spectroscopy and dissociative electron attachment spectroscopy (DEAS). Experimental spectral features are assigned on the basis of Hartree-Fock and density functional theory calculations. Sharp features, with a width of less than 0.1 eV, observed in the electron transmission spectra of imidazole, pyrazole, and pyrrole close to 0.45 eV, i.e., well below the energy of their lowest-lying ${\pi }^{*}$ shape resonances detected at 1.90, 1.87, and 2.33 eV, respectively, are associated with formation of negative ion states bound by long-range electron-molecule interactions. Effective range theory calculations which include both dipolar and polarization interactions support this interpretation. In addition to the general observation of cleavage of the N–H bond at incident electron energies close to 2 eV, elimination of as many as three hydrogen atoms from the molecular negative ions is detected at higher energies by DEAS with the only exception of methylated imidazoles. This complex process is associated with ring opening and formation of diatomic hydrogen as one of the neutral fragments, as indicated by the calculations to satisfy the energetic requirements. The present results are of importance for understanding the basic mechanisms of damages caused in living tissues by high-energy radiations.

In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunneling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behavior in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond-mean-field dynamics.

We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component, and spinor Bose-Einstein condensates. The formation of solitonic entities of the dark-bright type is based on the so-called matter-wave interference of spatially separated condensates. In all three cases, a systematic numerical study is carried out upon considering different variations of each system's parameters both in the absence and in the presence of a harmonic trap. It is found that manipulating the initial separation or the chemical potential of the participating components allows us to tailor the number of nucleated dark-bright states. Particularly, the number of solitons generated increases upon increasing either the initial separation or the chemical potential of the participating components. Similarities and differences of the distinct models considered herein are showcased, while the robustness of the emerging states is illustrated via direct numerical integration, demonstrating their long time propagation. Importantly, for the spinorial system, we unravel the existence of beating dark soliton arrays that are formed due to the spin-mixing dynamics. These states persist in the presence of a parabolic trap, often relevant for associated experimental realizations.

Transfer and scattering matrix theories are derived for studying single-photon (SP) transport in optical waveguide ladders (OWLs). The OWLs consist of two one-dimensional waveguides connected by Jaynes-Cummings emitters (JCEs) and have two input and two output channels. The von Neumann entropy is introduced to describe the entanglement between the transmitted states from the two output channels. Two types of the OWLs are studied, i.e., the OWLs with two identical waveguides (i-OWLs) and those with two different waveguides (d-OWLs). When the OWLs contain only one JCE, the SP transport behavior in the i-OWLs is the same as that in the d-OWLs. When two JCEs are introduced, the quantum interference among the JCE-scattered waves can lead to the SP jumping with a 100% chance between the waveguides for the i-OWLs, while this is hard for the d-OWLs. As a result, the i-OWLs can serve as a SP router with respect to the d-OWLs. When the number of JCEs increases to a large value (e.g., 16), the transmission probabilities of the two output channels both tend to be 0.25 for the i-OWLs, but zero for d-OWLs. Correspondingly, the entanglements approximate a constant of 1 for the i-OWLs, but of zero for the d-OWLs. It shows that a large number of JCEs can suppress the influence of other system parameters including the SP frequency and JCE loss. Therefore, the i-OWLs with a large number of the JCEs show potential for a SP splitter and entanglement generator.

The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched “on” and “off” nonadiabatically. We show that by using a superconducting circuit which allows one to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible to observe the dynamical Lamb effect. The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops. By solving the Schrödinger equation for a qubit coupled to a resonator, we calculate the time evolution of the number of excitations in the qubit and the resonator due to the dynamical Lamb effect. The number of excitations created in the system is maximum when the coupling is periodically switched between longitudinal and transverse using a square-wave or sinusoidal modulation of the magnetic flux with frequency equal to the sum of the average qubit and photon transition frequencies.

We study the robustness of single-mode squeezing nonclassicality against the action of single-mode Gaussian noise (Gaussian channels), first in its local single-mode form and second in its nonlocal distributed form as two-mode entanglement, with the channel acting locally on the single-mode. We find that the distributed single-mode nonclassicality is more robust than local single-mode nonclassicality against the local application of the canonical single-mode Gaussian channels i.e., for the canonical attenuator channel, the canonical amplifier channel, the canonical phase-conjugation channel, and the channel with a singular $X$ matrix, with the exception of the channel with a singular $Y$ matrix. This robustness persists even when the canonical channel is nonclassicality breaking. For the canonical channel with a singular $Y$ matrix, we find that the distributed as well as the local single-mode nonclassicality is equally robust against the local application of the channel. We illustrate examples where local single-mode squeezing is more robust than distributed squeezing against the local application of the channel, for channels not of the canonical form.

We discuss a class of interactions between self-confined optical beams breaking the action-reaction principle. The effective force intertwining the beams does not satisfy momentum conservation, paving the way to the potential existence of situations where both beams are pushed in the same direction, in turn leading to the so-called diametric drive. In our theoretical proposal the interaction between the two light beams is enabled by optical nonlinearity. The nonlinearity is assumed to change sign with the light polarization, in turn allowing the two light beams to be attracted or repelled by an inhomogeneous region according to the photon polarization. We demonstrate that this exotic type of nonlinear spin-orbit-like interaction can be achieved in nematic liquid crystals (NLCs). In fact, depending on the input polarization, in NLCs a change in temperature corresponds to a focusing or defocusing index change. For the polarization seeing a thermal defocusing response (corresponding to the extraordinary component), the self-confinement is ensured by the simultaneous action of reorientational nonlinearity.

Quantum low-density parity-check codes can be decoded using a syndrome based GF(4) belief propagation decoder (where GF denotes Galois field). However, the performance of this decoder is limited both by unavoidable 4-cycles in the code's factor graph and the degenerate nature of quantum errors. For the subclass of CSS codes, the number of 4-cycles can be reduced by breaking an error into an $X$ and $Z$ component and decoding each with an individual $\mathrm{GF}\left(2\right)$ based decoder. However, this comes at the expense of ignoring potential correlations between these two error components. We present a number of modified belief propagation decoders that address these issues. We propose a $\mathrm{GF}\left(2\right)$ based decoder for CSS codes that reintroduces error correlations by reattempting decoding with adjusted error probabilities. We also propose the use of an augmented decoder, which has previously been suggested for classical binary low-density parity-check codes. This decoder iteratively reattempts decoding on factor graphs that have a subset of their check nodes duplicated. The augmented decoder can be based on a $\mathrm{GF}\left(4\right)$ decoder for any code, a $\mathrm{GF}\left(2\right)$ decoder for CSS code, or even a supernode decoder for a dual-containing CSS code. For CSS codes, we further propose a $\mathrm{GF}\left(2\right)$ based decoder that combines the augmented decoder with error probability adjustment. We demonstrate the performance of these new decoders on a range of different codes, showing that they perform favorably compared to other decoders presented in literature.

We present a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of multiple independent executions of an algorithm. Denoting by $\rho$ an upper bound of this probability (wlog; assume $\rho \le \frac{1}{2}$), classical techniques require $O\left(\frac{\rho }{{[(1-\rho )-\rho ]}^2}\right)$ executions to reduce the error to a negligible constant. We investigate when and how quantum algorithmic techniques like amplitude amplification and estimation may reduce the number of executions. On one hand, the former idea does not directly benefit algorithms that can err on both yes and no answers and the number of executions in the latter approach is $O\left(\frac{1}{(1-\rho )-\rho }\right)$. We propose a quantum approach called amplitude separation that combines both these approaches and achieves $O\left(\frac{1}{\sqrt{1-\rho }-\sqrt{\rho }}\right)$ executions, which betters existing approaches when the errors are high. In the multiple-weight decision problem, the input is an $n$-bit Boolean function $f\left(\right)$ given as a black box and the objective is to determine the number of $x$ for which $f\left(x\right)=1$, denoted $wt\left(f\right)$, given some possible values $\{w_1,...,w_k\}$ for $wt\left(f\right)$. When our technique is applied to this problem, we obtain the correct answer, maybe with a negligible error, using $O\left({log}_{2}k\sqrt{2^n}\right)$ calls to $f\left(\right)$, which shows a quadratic speedup over classical approaches and currently known quantum algorithms.

We propose different experimental methods to measure the analog of the Debye length in a very large magneto-optical trap, which should characterize the spatial correlations in the atomic cloud. An analytical, numerical, and experimental study of the response of the atomic cloud to an external modulation potential suggests that this Debye length, if it exists, is significantly larger than what was expected.

We propose a class of quantum simulators for antiferromagnetic spin systems based on coupled photonic cavities in the presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its nonequilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate with the antiferromagnetic coupling, the steady state presents properties which bear full analogy with those typical of the spin-liquid phases arising in frustrated magnets.

The Hong-Ou-Mandel effect is considered a signature of the quantumness of light, as the dip in coincidence probability using semiclassical theories has an upper bound of 50%. Here we show, theoretically and experimentally, that, with proper phase control of the signals, classical pulses can mimic a Hong-Ou-Mandel-like dip. We demonstrate a dip of $(99.635\pm 0.002)\%$ with classical microwave fields. Quantumness manifests in wave-particle complementarity of the two-photon state. We construct quantum and classical interferometers for the complementarity test and show that while the two-photon state shows wave-particle complementarity the classical pulses do not.

We extend classical Maxwell field theory to a first quantized theory of the photon by deriving a conserved Lorentz four-current whose zero component is a positive-definite number density. Fields are real and their positive (negative) frequency parts are interpreted as absorption (emission) of a positive-energy photon. With invariant plane-wave normalization, the photon position operator is Hermitian with instantaneously localized eigenvectors that transform as Lorentz four-vectors. Reality of the fields and wave function ensure causal propagation and zero net absorption of energy in the absence of charged matter. The photon probability amplitude is the real part of the projection of the photon's state vector onto a basis of position eigenvectors and its square implements the Born rule. Manifest covariance and consistency with quantum field theory is maintained through use of the electromagnetic four-potential and the Lorenz gauge.

Nonadiabatic holonomic quantum computation (NHQC) offers a way to realize geometric quantum gates beyond the adiabatic regime. To extend the flexibility and control robustness, many NHQC schemes have been proposed. Here, we propose to use quantum optimal control theory to search control sequences that can realize holonomic gates. Given a target gate and the corresponding computational subspace, our optimization algorithm can find the control sequence automatically. Furthermore, by defining an averaged target function, our method can improve the robustness of the holonomic gates against the errors such as thermal noises and amplitude errors. As an application, we search the control sequences for the Hadamard, not, and cnot gates in a nitrogen-vacancy-center system.

We report on a generic cooling technique for atoms trapped in optical lattices. It consists in modulating the lattice depth with a proper frequency sweeping. This filtering technique removes the most energetic atoms and provides, with the onset of thermalization, a cooling mechanism reminiscent of evaporative cooling. However, the selection is here performed in quasimomentum space rather than in position space. Interband selection rules are used to protect the population with a zero quasimomentum, namely the Bose Einstein condensate. Direct condensation of thermal atoms in an optical lattice is also achieved with this technique. It offers an interesting complementary cooling mechanism for quantum simulations performed with quantum gases trapped in optical lattices.

We study the Bloch-Messiah reduction of parametric down-conversion of light in the pulsed regime with a nondegenerate phase matching providing generation of twin beams. We find that in this case every squeezing eigenvalue has multiplicity at least two. We discuss the problem of ambiguity in the definition of the squeezing eigenmodes in this case and develop two approaches to unique determination of the latter. First, we show that the modal functions of the squeezing eigenmodes can be tailored from the Schmidt modes of the signal and idler beams. Alternatively, they can be found as a solution of an eigenvalue problem for an associated Hermitian squeezing matrix. We illustrate the developed theory by an example of frequency nondegenerate collinear twin beams generated in beta barium borate crystal. In this example we demonstrate how the squeezing eigenmodes can be approximated analytically on the basis of the Mehler's formula, extended to complex kernels. We show how the multiplicity of the eigenvalues and the structure of the eigenmodes are changed when the phase matching approaches the degeneracy in frequency.