We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.

The relativistic spin correlation function was calculated for a pair of electrons originating from Møller scattering of two polarized electron beams. The results were discussed in view of a possible measurement of the correlation function and the corresponding probabilities. The special case of scattering off a stationary target (both polarized and unpolarized) was also analyzed. It was shown that the Clauser-Horne-Shimony-Holt (CHSH) inequality may be violated in the relativistic energy range when both scattering electrons are highly polarized.

As a ubiquitous quantum effect, tunneling has attracted attention ever since the dawn of quantum mechanics. However, recent evidence suggests that nonadiabatic atomic tunneling near a conical intersection (CI) behaves differently from its adiabatic counterpart, producing lifetime differences of up to two orders of magnitude. Using two-dimensional models, we demonstrate here that the failure of the adiabatic model in describing tunneling near a CI can be attributed largely to the neglect of the geometric phase, which is associated with the adiabatic electronic wave function transported around a CI. The geometric phase–induced destructive interference among wave functions following different paths around the CI, manifested as a node in the adiabatic wave function, retards tunneling.

We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a heliumlike two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced by harmonic potentials. The electron-electron interaction potential is taken to be both screened (decaying faster than the inverse of the interparticle separation) and regularized (in the limit of zero separation). We reveal the exactly solvable few-electron ground state, which explicitly includes electron correlation, for certain values of the harmonic containment.

We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines distinct propagation regimes. A realistic model for the environment is considered by introducing non-Gaussian noise as time-dependent fluctuations of the tunneling amplitudes between adjacent sites. We observe that the combined effect of particle interaction and fast noise (weak coupling with the environment) provides a faster propagation compared to the noiseless case. This effect can be understood in terms of the band structure of the Hubbard model, and a detailed analysis as a function of both noise and system parameters is presented.

We propose the implementation of a switch of particle statistics with an embedding quantum simulator. By encoding both Bose-Einstein and Fermi-Dirac statistics into an enlarged Hilbert space, the statistics of the simulated quantum particles may be changed in situ during the time evolution, from bosons to fermions and from fermions to bosons, as many times as desired before a measurement is performed. We illustrate our proposal with few-qubit examples, although the protocol is straightforwardly extendable to larger numbers of particles. This proposal can be implemented on different quantum platforms such as trapped ions, quantum photonics, and superconducting circuits, among others. The possibility to implement permutation symmetrization and antisymmetrization of quantum particles enhances the toolbox of quantum simulations for unphysical operations as well as for symmetry transformations.

We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in the vicinity of a constriction of nanometric dimensions, the coupling constant can be as high as 5–10 kHz. This coupling affects the amplitude of the field reflected by the resonator and the integrated homodyne signal allows detection of a single spin with unit signal-to-noise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time-dependent homodyne signal improves this figure by $\sim 30\%$ for typical parameters.

We propose to use quantum coherence as the ultimate proof of the quantum nature of the radiation that appears by means of the dynamical Casimir effect in experiments with superconducting microwave waveguides. We show that, unlike previously considered measurements such as entanglement and discord, quantum coherence does not require a threshold value of the external pump amplitude and is highly robust to thermal noise.

The energy-level spectrum of the protactinium atom (Pa, $Z=91$) is simulated with a configuration interaction calculation. Levels belonging to the separate manifolds of a given total angular momentum and parity $J^{\pi }$ exhibit distinct properties of many-body quantum chaos. Moreover, an extremely strong enhancement of small perturbations takes place. As an example, effective three-electron interaction is investigated and found to play a significant role in the system. Chaotic properties of the eigenstates allow one to develop a statistical theory and predict probabilities of different processes in chaotic systems.

The single-center adiabatic-nuclei convergent close-coupling method is used to investigate positron collisions with molecular hydrogen (${\mathrm{H}}_2$) in the ground and first vibrationally excited states. Cross sections are presented over the energy range from 1 to 1000 eV for elastic scattering, vibrational excitation, total ionization, and the grand total cross section. The present adiabatic-nuclei positron-${\mathrm{H}}_2$ scattering length is calculated as $A=-2.70a_0$ for the ground state and $A=-3.16a_0$ for the first vibrationally excited state. The present elastic differential cross sections are also used to “correct” the low-energy grand total cross-section measurements of the Trento group [A. Zecca et al., Phys. Rev. A 80, 032702 (2009)] for the forward-angle-scattering effect. In general, the comparison with experiment is good. By performing convergence studies, we estimate that our $R_m=1.448a_0$ fixed-nuclei results are converged to within $\pm 5\%$ for the major scattering integrated cross sections.

We report the electron impact integrated and differential cross sections for excitation to the $b{}^3{\mathrm{\Sigma }}_u^{+}, a{}^3{\mathrm{\Sigma }}_g^{+}, c{}^3{\mathrm{\Pi }}_u, B{}^1{\mathrm{\Sigma }}_u^{+}, E,F{}^1{\mathrm{\Sigma }}_g^{+}, C{}^1{\mathrm{\Pi }}_u, e{}^3{\mathrm{\Sigma }}_u^{+}, h{}^3{\mathrm{\Sigma }}_g^{+}, d{}^3{\mathrm{\Pi }}_u, B^{\prime }{}^1{\mathrm{\Sigma }}_u^{+}, D{}^1{\mathrm{\Pi }}_u, B^{\prime }{}^{\prime }{}^1{\mathrm{\Sigma }}_u^{+}$, and $D^{\prime }{}^1{\mathrm{\Pi }}_u$ states of molecular hydrogen in the energy range from 10 to 300 eV. Total scattering and total ionization cross sections are also presented. The calculations have been performed by using the convergent close-coupling method within the fixed-nuclei approximation. Detailed convergence studies have been performed with respect to the size of the close-coupling expansion and a set of recommended cross sections has been produced. Significant differences with previous calculations are found. Agreement with experiment is mixed, ranging from excellent to poor depending on the transition and incident energies.

The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact was extended to higher partial waves; in particular, the $p$-wave contacts have been experimentally probed in recent experiments. So far, discussions on $p$-wave contacts have been limited to three dimensions. In this paper, we generalize the $p$-wave contacts to two dimensions and derive a series of universal relations, including the adiabatic relations, high-momentum distribution, virial theorem, and pressure relation. At the high-temperature and low-density limit, we calculate the $p$-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing-mode frequency and the $p$-wave contacts is given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three- and two-dimensional Fermi gases and discuss possible experimental realization of a two-dimensional Fermi gas with $p$-wave interactions.

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a ${\mathbb{Z}}_3$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

The effect of turbulence on a pair of photons propagating together through the same medium is analyzed. The behavior is compared to the case where these photons propagate separately through different turbulent media. The analysis is done with a multiple phase screen approach, by deriving and solving an infinitesimal propagation equation. We apply these results to the case where the initial photons are entangled in their spatial degrees of freedom with the aid of spontaneous parametric down-conversion. It is found that for this input state, the decay of entanglement in correlated media under the weak scintillation approximation is quicker than in uncorrelated media. Beyond the weak scintillation approximation, the entanglement in correlated media decays slower when it is close to zero—approaching zero asymptotically as a function of scintillation strength. This is contrary to the case in uncorrelated media where entanglement becomes zero at a finite scintillation strength.

In this study, a standing wave in an optical nanocavity with Bose-Einstein condensate (BEC) constitutes a one-dimensional optical lattice potential in the presence of a finite two bodies atomic interaction. We report that the interaction of a BEC with a standing field in an optical cavity coherently evolves to exhibit Fano resonances in the output field at the probe frequency. The behavior of the reported resonance shows an excellent compatibility with the original formulation of asymmetric resonance as discovered by Fano [U. Fano, Phys. Rev. 124, 1866 (1961)]. Based on our analytical and numerical results, we find that the Fano resonances and subsequently electromagnetically induced transparency of the probe pulse can be controlled through the intensity of the cavity standing wave field and the strength of the atom-atom interaction in the BEC. In addition, enhancement of the slow light effect by the strength of the atom-atom interaction and its robustness against the condensate fluctuations are realizable using presently available technology.

We study adiabatic light transfer in systems of two coupled waveguides with spatially varying detuning of the propagation constants, providing an analogy to the quantum phenomena of rapid adiabatic passage (RAP) and two-state stimulated Raman adiabatic passage (two-state STIRAP). Experimental demonstration using a photoinduction technique confirms the robust and broadband character of the structures that act as broadband directional couplers and broadband beam splitters, respectively.

We propose to utilize symmetry-protected zero modes of a photonic lattice to realize a single-mode, fixed-frequency, and spatially tunable laser. These properties are the consequence of the underlying non-Hermitian particle-hole symmetry, with which the energy spectrum satisfies ${\varepsilon }_m=-{\varepsilon }_n^{*}$. Unlike in the Hermitian case, the symmetric phase of particle-hole symmetry is no longer restricted to $\varepsilon =0$ but extends along the imaginary-$\varepsilon$ axis, which is set by the single-cavity frequency and symmetry-protected against position and coupling disorder of the photonic lattice. By selectively pumping different cavities in the photonic lattice, we control the spontaneous symmetry restoration process, which provides a convenient method to tune the spatial profile of the laser without changing its frequency.

We propose a scheme of enhancement of Rabi coupling between two identical atomic ensembles trapped inside an optical cavity in a membrane-in-the-middle setup. The cavity modes dispersively interact with the ensembles and the effective interaction between the ensembles is governed by the tunneling rate of the cavity modes through the oscillating membrane. We have shown that this interaction can be made large enough such that the Rabi oscillation occurs in a time scale much smaller than the relevant decay time scales of the cavity modes and of the membrane. We present the detailed analytical and numerical results and assess the feasibility of the scheme using currently available technology.

The experimental realization of many-body entangled states is one of the main goals of quantum technology as these states are a key resource for quantum computation and quantum sensing. However, increasing the number of photons in an entangled state has been proved to be a painstakingly hard task. This is a result of the nondeterministic emission of current photon sources and the distinguishability between photons from different sources. Moreover, the generation rate and the complexity of the optical setups hinder scalability. Here we present a scheme that is compact, requires a very modest number of components, and avoids the distinguishability issues by using only one single-photon source. States of any number of photons are generated with the same configuration, with no need for increasing the optical setup. The basic operation of this scheme is experimentally demonstrated, and its sensitivity to imperfections is considered.

For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a conditional amplitude, which depends functionally on the interelectronic distance $r_{12}$ and parametrically on $r_1$ and $r_2$. Applying the variational principle, we derive pseudoeigenvalue equations for these two amplitudes, which cast the internal Schrödinger equation in a form akin to the Born-Oppenheimer separation of nuclear and electronic degrees of freedom in molecules. The marginal equation involves an effective radial Hamiltonian, which contains a nonadiabatic potential energy surface that takes into account all interparticle correlations in an averaged way, and whose unique eigenvalue is the internal energy. At each point $(r_1,r_2)$, such surface is, in turn, the unique eigenvalue in the conditional equation. Employing the ground state of He as prototype, we show that the nonadiabatic potential energy surface affords a molecularlike interpretation of the structure of the atom, and aids in the analysis of energetic and spatial aspects of the Coulomb correlation, in particular correlation-induced symmetry breaking and quantum phase transition.