Quantum thermodynamics often deals with the dynamics of small quantum machines interfacing with a large and complex environment. Virtual qubits, collisional models, and reset master equations have become highly useful tools for predicting the qualitative behavior of two-dimensional target systems coupled to few-qubit machines and a thermal environment. While few successes in matching the simplified model parameters for all possible physical systems are known, the qualitative predictions still allow for a general design of quantum machines irrespective of the implementation. We generalise these tools by introducing multiple competing virtual qubits for modeling multidimensional systems coupled to larger and more complex machines. By simulating the full physical dynamics for targets with three dimensions, we uncover general properties of reset models that can be used as “dials” to correctly predict the qualitative features of physical changes in a realistic setup and thus design autonomous quantum machines beyond a few qubits. We then present a general analytic solution of the reset model for arbitrary-dimensional systems coupled to multiqubit machines. Finally, we showcase an improved three-level laser as an exemplary application of our results.

The hybrid tensor network approach allows us to perform calculations on systems larger than the scale of a quantum computer. However, when calculating transition amplitudes, there is the problem that the number of terms to be measured increases exponentially with that of the contracted operators. This problem is caused by the fact that the contracted operators are represented as non-Hermitian operators. In this study, we propose a method for hybrid tensor network calculation that contracts non-Hermitian operators without an exponential increase in the number of terms. In the proposed method, transition amplitudes are calculated by combining the singular value decomposition of the contracted non-Hermitian operators with a Hadamard test. The method significantly extends the applicability of the hybrid tensor network approach.

A general relativistic distorted-wave expression of the multipole cross sections for anisotropic excitation of ions by impact with an electron beam is derived by taking into account the coherence between magnetic sublevels. These multipole cross sections are required in the analysis of the intensity and polarization of lines emitted from plasmas with cylindrically symmetric electron velocity distributions. To calculate such cross sections for highly charged target ions, we need to adapt the distorted-wave excitation program of the Flexible Atomic Code by making some modifications. Detailed computations are performed for transitions in the Be-like ion ${\mathrm{O}}^{4+}$ from the ground $2s^2$ and metastable triplet $2s2p$ levels. A selected series of results for transitions from $2s2p{}^{3}P_{1,2}$ to $2s3p{}^{3}P_{1,2}$ and $2s3d{}^{3}D_{2,3}$ levels, which may be of interest for the solar atmosphere and tokamak plasmas, are given to illustrate the application of the modified program suggested here. Indepth analysis of the numerical results and preliminary comparison with available data in the literature provide a systematic consistency of the modified program, paving the way for computations of a large amount of multipole cross sections's data with a considerable saving of time.

We investigate the transverse-spin relaxations of ${}^{129}\mathrm{Xe}$ due to diffusion in the presence of magnetic-field gradients in relation to the dimensions of a sub-cm sized cubiclike atomic gas cell with a stem. The transverse-spin-relaxation rate $\left({\mathrm{\Gamma }}_{\mathrm{\Delta }B}\right)$ of ${}^{129}\mathrm{Xe}$ is measured as a function of various magnetic-field gradients, $\partial B_z/\partial x$, $\partial B_z/\partial y$, $\partial B_z/\partial z$, and $\partial B_y/\partial y$. From the measured transverse-spin-relaxation rates in five atomic gas cells with different stem sizes, the quadratic coefficients of ${\mathrm{\Gamma }}_{\mathrm{\Delta }B}$ with respect to the magnetic-field gradients are extracted. To investigate the effect of the dimensions of the stem, we calculate the ratio between the quadratic coefficients in each atomic gas cell, which is invariant under scaling in the cell size and change in the diffusion coefficient. We compare these ratios with those obtained analytically from a rectangular parallelepiped model for the atomic gas cells and with those obtained numerically from a more precise model taking the stems directly into account. Using a scaling argument, we provide a scheme for estimating the quadratic coefficient of a cubic atomic cell with a stem. Finally, we determine the diffusion coefficient from the measured quadratic coefficient. Compared to the analytical method for a rectangular parallelepiped, numerical analysis considering the stem provides the diffusion coefficient as a value close to the value given by Fuller's equation. We estimate the diffusion coefficients of ${}^{129}\mathrm{Xe}$ in the gas mixture of nitrogen, ${}^{129}\mathrm{Xe}$, and ${}^{131}\mathrm{Xe}$ as 0.13 ${\mathrm{cm}}^2/\mathrm{s}$ at the standard temperature and pressure condition.

Relative phases of atomic above-threshold ionization wave packets were investigated in an experiment [L. J. Zipp, A. Natan, and P. H. Bucksbaum, Optica 1, 361 (2014)] exploiting interferences between different pathways in a weak probe field at half the frequency of the strong ionization pulse. In this work we explore theoretically the extraction of phase delays and time delays of attosecond wave packets formed in strong-field ionization. We perform simulations solving the time-dependent Schrödinger equation and compare these results with the strong-field and Coulomb-Volkov approximations. In order to disentangle short- from long-range effects of the atomic potential, we also perform simulations for atomic model potentials featuring a Yukawa-type short-range potential. We find significant deviations of the ab initio phase delays between different photoelectron pathways from the predictions by the strong-field approximation even at energies well above the ionization threshold. We identify similarities to but also profound differences from the well-known interferometric extraction of phase and time delays in one-photon ionization.

We demonstrate the transfer of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ molecules from a closed-channel-dominated Feshbach-molecule state to the absolute ground state. The Feshbach molecules are initially created from a gas of sodium and potassium atoms via adiabatic ramping over a Feshbach resonance at 78.3 G. The molecules are then transferred to the absolute ground state using stimulated Raman adiabatic passage with an intermediate state in the spin-orbit-coupled complex $|c^3{\mathrm{\Sigma }}^{+},v=35,J=1\rangle \sim |B^1\mathrm{\Pi },v=12,J=1\rangle$. Our measurements show that the pump transition dipole moment linearly increases with the closed-channel fraction. Thus, the pump-beam intensity can be two orders of magnitude lower than is necessary with open-channel-dominated Feshbach molecules. We also demonstrate that the phase noise of the Raman lasers can be reduced by filter cavities, significantly improving the transfer efficiency.

We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $\left|\psi \right(0)\rangle =|\cdots 2020\cdots \rangle$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the hopping energy. We derive the effective spin-1/2 $XXZ$ Hamiltonian for the strongly interacting regimes by using a perturbation method. On the basis of the effective Hamiltonian, we show that the trapping potential is effectively strengthened by the on-site interaction, leading to the enhancement of the nonergodic behavior. We also calculate the real-time dynamics under the effective Hamiltonian and find that the entanglement entropy grows logarithmically in time.

We propose and analyze a protocol for observing a violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated Bose-Einstein condensates (BECs). To prepare the Bell correlated state, spin-changing collisions are used to first prepare a two-mode squeezed BEC. This is then split into two BECs by controlling the spatial wave function, e.g., by modifying the trapping potential. Finally, spin-changing collisions are also exploited locally, to compensate local squeezing terms. The correlators appearing in the inequality are evaluated using three different approaches. In the first approach, correlators are estimated using normalized expectation values of number operators, in a similar way to evaluating continuous-variable Bell inequalities. An improvement to this approach is developed using the sign binning of total spin measurements, which allows for the construction of two-outcome measurements and violations of the CHSH inequality without auxiliary assumptions. Finally, we show a third approach where maximal violations of the CH inequality can be obtained by assigning zero values to local vacua outcomes under a no-enhancement assumption. The effect of loss and imperfect detection efficiency is investigated, and the observed violations are found to be robust to noise.

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The nonequilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulations. We consider a semiclassical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a $Z_2$ symmetry out of the symmetry-unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.

The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of stationary, shape-invariant states propagating at constant velocity are explicitly found and compared to the known solution of the Gross-Pitaevskii equation. The typical features attributed to nonlinearity are thus recovered in a purely linear theory, provided the full many-particle physics is correctly accounted for. However, the formation dynamics predicted by the Gross-Pitaevskii approximation considerably differs from the exact many-body evolution.

Contextuality is an intriguing feature of quantum theory that excludes any noncontextual hidden variable theory of our nature. It is therefore a natural and important pursuit to detect as larger contextuality as possible. In the scenario to reveal contextuality through violation of noncontextuality inequality, the pursuit is to construct such inequality with large violations. In this paper, we present a simple method to extend arbitrary state-(in)dependent noncontextuality inequalities into ones with larger violations. By recursively applying the method, one can obtain noncontextuality inequalities with an arbitrary large violation. Moreover, the method also constructs quantum measurements and states to violate the new inequality.

We expand the quantum variant of the popular game Sudoku by introducing the notion of cardinality of a quantum Sudoku (SudoQ), equal to the number of distinct vectors appearing in the pattern. Our considerations are focused on the genuinely quantum solutions—the solutions of size $N^2$ that have cardinality greater than $N^2$, and therefore cannot be reduced to classical counterparts by a unitary transformation. We find the complete parametrization of the genuinely quantum solutions of a $4\times 4$ SudoQ game and establish that in this case the admissible cardinalities are 4, 6, 8, and 16. In particular, a solution with the maximal cardinality equal to 16 is presented. Furthermore, the parametrization enabled us to prove a recent conjecture of Nechita and Pillet [I. Nechita and J. Pillet, Quantum Inf. Comput. 21, 781 (2021)] for this special dimension. In general, we proved that for any $N$ it is possible to find an $N^2\times N^2$ SudoQ solution of cardinality $N^4$, which for a prime $N$ is related to a set of $N$ mutually unbiased bases of size $N^2$. Such a construction of $N^4$ different vectors of size $N$ yields a set of $N^3$ orthogonal measurements.

By properly considering the propagation dynamics of the dipole field, we obtain the full magnetic dipolar interaction between two quantum dipoles for general situations. With the help the Maxwell equation and the corresponding Green function, this result applies for general boundary conditions and naturally unifies all the interaction terms between permanent dipoles, resonant or nonresonant transition dipoles, and even the counter-rotating interaction terms altogether. In particular, we study the dipolar interaction in a rectangular three-dimensional cavity with discrete field modes. When the two dipoles are quite near to each other and far from the cavity boundary, their interaction simply returns the free-space result; when the distance between the two dipoles is comparable to their distance to the cavity boundary and the field mode wavelength, the dipole images and near-resonant cavity modes bring in significant changes to the free-space interaction. This approach also provides a general way to study the interaction mediated by other kinds of fields.

We prove two simple theorems about squeezing induced by bilinear spin-spin interactions that conserve spin parity—including a vast majority of quantum spin models implemented by state-of-the-art quantum simulators. In particular we show that squeezing captures the first form of quantum correlations which are produced (1) at equilibrium, by adiabatically turning on the spin-spin interactions starting from a factorized state aligned with an external, arbitrary field; and (2) away from equilibrium, by evolving unitarily the same state with the interacting Hamiltonian.

We consider geometric phases of mobile quantum vortices in superfluid Bose–Einstein condensates (BECs). Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, ${\gamma }_{\mathcal{C}}=2\pi N_{\mathcal{C}}$, of such a vortex is determined by the number of condensate atoms $N_{\mathcal{C}}$ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase: (i) A topologically protected edge current of vortices at the condensate boundary and (ii) a superfluid displacement current. Our results generalize to and pave the way for experimental measurements of vortex geometric phases using scalar and spinor BECs and superfluid Fermi gases.

Quantum-mechanical scattering involving continuum states coupled to a scatterer with a discrete spectrum gives rise to Fano resonances. Here we consider scatterers that possess internal vibrational degrees of freedom in addition to discrete states. Entanglement between the scattered excitation and vibrational modes complicates analytical and numerical calculations considerably. For the example of one-dimensional scattering we develop a multichannel quantum scattering approach which can determine reflection and transmission probabilities in the presence of vibrations. Application to a linear chain coupled to a control unit containing vibrating sites shows that vibrational degrees of freedom can have a profound effect on quantum transport. For suitable parameters, spectral regions which are opaque in the static case can be rendered transparent when vibrations are included. The formalism is general enough to be applicable to a variety of platforms for quantum transport including molecular aggregates, cold atom chains, quantum-dot arrays and molecular wires based on conjugated polymers.

In this paper we answer the question of how one can quantify the amount of entanglement necessary to create a given steering assemblage when the original state and measurements are unknown. To do this, we extend the concepts of entanglement cost and entanglement of formation to steering assemblages and provide easy-to-calculate upper and lower bounds. We prove that the entanglement of formation for assemblages is not generally continuous and not a flat roof extension (in contrast with the state-based quantity), and we use numerical analysis to illustrate these properties. Finally, we discuss the consequences of these results for assemblage-to-assemblage conversion and suggest potential applications.

The continuous-time quantum walk is a particle evolving by Schrödinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems, however, the Hamiltonian is proportional to the adjacency matrix instead. It is well known that these quantum walks are equivalent when the graph is regular, i.e., when each vertex has the same number of neighbors. If the graph is irregular, however, the quantum walks evolve differently. In this paper, we show that for some irregular graphs, if the particle is initially localized at a certain vertex, the probability distributions of the two quantum walks are identical, even though the amplitudes differ. We analytically prove this for a graph with five vertices and a graph with six vertices. By simulating the walks on all 1 018 689 568 simple, connected, irregular graphs with 11 vertices or less, we found 64 graphs with this notion of equivalence. We also give eight infinite families of graphs supporting these equivalent walks.

In this paper, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator, assumed as an entanglement quantifier. The resulting expression depends on sets of four trajectories, originated from the underlying classical description, and having mutually connected final phase-space points. Such classical elements, which are capable to reproduce the quantum entanglement even for long values of propagation time, arise when we assume a proper analytical continuation of the classical phase space onto a complex domain. We apply this theory to a particular physical system, showing that taking into account only a few sets of complex trajectories is enough to get an excellent agreement between the semiclassical linear entropy of the reduced density operator and its quantum counterpart.