The static dipole polarizabilities of the first three lowest states of hydrogen molecules ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ are calculated using variationally generated wave functions in Hylleraas coordinates without using the Born-Oppenheimer approximation. Our results for ${\mathrm{H}}_2$ and HD are two orders of magnitude more accurate than the best literature values. We also improve the previous best results for ${\mathrm{D}}_2$.

Despite the increasing interest, the research field which studies the concepts of work and heat at the quantum level has suffered from two main drawbacks: first, the difficulty to properly define and measure the work, heat, and internal energy variation in a quantum system and, second, the lack of experiments. Here, we report a full characterization of the dissipated heat, work, and internal energy variation in a two-level quantum system interacting with an engineered environment. We use the IBMQ quantum computer to implement the driven system's dynamics in a dissipative environment. The experimental data allow us to construct quasiprobability distribution functions from which we recover the correct averages of work, heat, and internal energy variation in the dissipative processes. Interestingly, by increasing the environment coupling strength, we observe a reduction of the pure quantum features of the energy exchange processes that we interpret as the emergence of the classical limit. This makes the present approach a privileged tool to study, understand, and exploit quantum effects in energy exchanges.

Certification and quantification of correlations for multipartite states of quantum systems appear to be a central task in quantum information theory. We give here a unitary quantum-mechanical perspective of both entanglement and Einstein-Podolsky-Rosen (EPR) steering of continuous-variable multimode states. This originates in the Heisenberg uncertainty relations for the canonical quadrature operators of the modes. Correlations of two-party $\left(N\text{vs}1\right)$-mode states are examined by using the variances of a pair of suitable EPR-like observables. It turns out that the uncertainty sum of these nonlocal variables is bounded from below by local uncertainties and is strengthened differently for separable states and for each one-way unsteerable state. The analysis of the minimal properly normalized sums of these variances yields necessary conditions of separability and EPR unsteerability of $\left(N\text{vs}1\right)$-mode states in both possible ways of steering. When the states and the performed measurements are Gaussian, then these conditions are precisely the previously known criteria of separability and one-way unsteerability.

The concept of thermal machines has evolved from the canonical steam engine to the recently proposed nanoscopic quantum systems as working fluids. The latter obey quantum open system dynamics and frequently operate in nonequilibrium conditions. However, the role of this dynamics in the overall performance of quantum heat engines remains an open problem. Here we analyze and optimize the efficiency and power output of two-stage quantum heat engines fueled by nonequilibrium steady states. In a charging first stage, the quantum working fluid consisting of a qutrit or two coupled qubits is connected to two reservoirs at different temperatures, which establish a heat current that stores ergotropy in the system; the second stage comprises a coherent driving force that extracts work from the machine in finite a amount of time; finally, the external drive is switched off and the machine enters a new cycle.

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.

We present a theoretical investigation of coherent dynamics of a spin qubit encoded in hyperfine sublevels of an alkali-metal atom in a far off-resonant optical dipole trap. The qubit is prepared in the “clock transition” utilizing the Zeeman states with zero projection of the spin angular momentum. We focus on various dephasing processes such as the residual motion of the atom, fluctuations of the trapping field and its incoherent scattering, and their effects on the qubit dynamics. We implement the most general fully quantum treatment of the atomic motion, so our results remain valid in the limit of close-to-ground-state cooling with a low number of vibrational excitations. We support our results by comparison with an experiment showing reasonable correspondence with no fitting parameters.

Continuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted “two-level” recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities and analyze the role of phase for optimal code designs. We extend the principle of phase engineering to bosonic codes defined in other bases and multiqubit codes, demonstrating its broad applicability in quantum error correction.

In this paper we show that for sufficiently strong atomic interactions, there exist analytical solutions of current-carrying nonlinear Bloch states at the Brillouin zone edge to the model of spin-orbit-coupled Bose-Einstein condensates (BECs) with symmetric spin interaction loaded into optical lattices. These simple but generic exact solutions provide an analytical demonstration of some intriguing properties which have neither an analog in the regular BEC lattice systems nor in the uniform spin-orbit-coupled BEC systems. It is an analytical example for understanding the superfluid and other related properties of the spin-orbit-coupled BEC lattice systems.

We semianalytically and numerically investigate the static and dynamical characteristics of quantum-dot (QD) lasers directly grown on silicon by considering the Shockley-Read-Hall (SRH) recombination. The static characteristics are studied through small-signal analysis, including the ${\alpha }_H$ factor, damping factor, and modulation dynamics. In addition, the feedback dynamics are analyzed through improved corpuscular rate equations based on the classical Lang-Kobayashi (LK) model with time series, bifurcation diagrams, and phase portraits. We find that a smaller ${\alpha }_H$ factor but larger damping factor are obtained by decreasing the nonradiative recombination lifetime. On top of that, in both the short- and long-external-cavity regimes, any decrease of the SRH recombination lifetime obliterates significantly chaotic regions and shifts the first Hopf bifurcation point to higher feedback values. Overall, this work provides insights into the understanding of QD laser physics, hence highlighting the influence of the SRH lifetime on the reflection sensitivity of epitaxial QD lasers on silicon. These results are qualitatively consistent with recent experiments and are therefore helpful for designing feedback-resistant lasers for future photonic integrated circuits operating without optical isolation.

Wehrl entropy is an entropy associated with the Husimi quasiprobability distribution. We discuss how it can be used to formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. We show that the Wehrl-Lieb inequality is closer to equality than the usual Białynicki-Birula–Mycielski entropic uncertainty relation almost everywhere. Furthermore, we show how Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement, which additionally provides a lower bound on the entanglement entropy.

The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time relativistic formalism of single-particle operators. Starting from the premise that physical variables associated with the proper-time gauge have a prominent role in the specification of position, since they do not depend on classical parameters connected to an external observer, we obtain a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper time. Among the consequences of this result, we emphasize that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.

High-fidelity quantum teleportation is necessary to configure a cubic phase gate that enables the processing of the nonclassicality in an input quantum state. The noise variance of the antisqueezing component, which increases rapidly with a higher pump factor, contaminates the squeezing component due to the phase fluctuation and results in a reduction of the fidelity. Here, we balance the influence of the extraction loss and phase fluctuation on the fidelity and optimize the performance of quantum teleportation. As a result, a fidelity $F=0.905\pm 0.022$ is experimentally achieved. The ultrahigh fidelity is expected to configure a cubic phase gate involving four-time sequential teleportation to perform universal continuous-variable quantum information processing.

The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by implementing a coherent time-delayed feedback mechanism. Simulating the non-Markovian dynamics within the matrix product state framework, we find that the visibility for two photons emitted from a three-level system (3LS) in ladder configuration can be enhanced significantly for a wide range of parameters by decelerating the decay of the upper level of the 3LS.

Algorithmic cooling techniques provide tools to increase the purity of quantum states. It is known that the cooling with these techniques is limited. However, the physical root of the limit is still unclear. Here we show that the unitarity of the compression operation imposes the cooling limit of heat-bath algorithmic cooling. Specifically, we prove that the unitarity of the compression operation does not allow increasing the purity beyond the maximum of the individual purities. We formalize the limitations imposed by the unitarity of the compression operation in two theorems. We then introduce an optimal cooling technique and show that without the limitations of the unitary operations the cooling technique would exceed the limit of heat-bath algorithmic cooling. We also show that the limitations of unitarity lead to the exact cooling limit of algorithmic cooling. This work opens up new avenues to understanding the limits of dynamic cooling.

We present a quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's algorithm and may be successfully executed on noisy intermediate-scale quantum devices. We prove that our algorithm is optimal in the total number of elementary gates up to a multiplicative constant. As many NP-hard problems are, in fact, not unstructured, we also describe the partial uncompute technique which exploits the oracle structure and allows a significant reduction in the number of elementary gates required to find the solution. Combining these results allows us to use an asymptotically smaller number of elementary gates than Grover's algorithm in various applications, keeping the number of queries to the oracle essentially the same. We show how the results can be applied to solve hard combinatorial problems, for example, Unique $k$-SAT. Additionally, we show how to asymptotically reduce the number of elementary gates required to solve the unstructured search problem with multiple marked elements.

We present experimental results that show the secondary-ion yield depends on the structure and orientation of incident cluster ions. A beam of carbon-cluster ions ${{\mathrm{C}}_n}^{+}$ ($n\le 4$) with an energy of 0.9 MeV per atom, which were obtained from a tandem electrostatic accelerator, was incident on a glycine target deposited on a carbon foil. The structure and orientation of the cluster ions after passing through the target were determined by the Coulomb explosion imaging method, and the positive secondary ions were simultaneously measured by time-of-flight mass spectrometry. When looking at the orientation dependence of linear structured ${{\mathrm{C}}_2}^{+}, {{\mathrm{C}}_3}^{+}$, and ${{\mathrm{C}}_4}^{+}$ projectiles, parallel orientations with respect to the beam direction were found to enhance the secondary-ion yield compared with perpendicular orientations. Additionally, comparison of the structure dependence of ${{\mathrm{C}}_3}^{+}$ and ${{\mathrm{C}}_4}^{+}$ projectiles with linear and ring structures showed that the secondary-ion yield was larger for linear structures. Interestingly, there was a clear correlation between the secondary-ion yield and the deposited energy density in the cluster-ion track. The energy density was calculated with electronic stopping power for incident cluster ions using linear-response dielectric theory and the cross section of the track of the incident cluster considering its geometrical structure and orientation. These results suggest that the deposited energy density in the cluster-ion track is a key parameter in the secondary-ion emission process induced by swift cluster-ion impacts.