The emission of below-threshold harmonics (BTHs) is a promising tool for producing vacuum-ultraviolet frequency combs. Nevertheless, the generation mechanism of BTHs is still an open question and a lot of efforts have been devoted to this issue. Here, with a developed trajectory-resolved fully quantum numerical scheme which allows us to “coherently” trace the motion of the rescattering electron, the complex roles of different rescattering trajectories, such as the first return or multiple returns in the origin of BTHs are identified unambiguously. We show that the emission of BTHs is influenced dramatically by laser intensity. At strong laser fields, multiple returns (especially the third return) play an important role in BTHs. At weak fields, effects related to multiphoton processes dominate. The interference of the different contributions to BTHs is also addressed.

By performing a slow adiabatic change between two traps of a quantum particle, it is possible to transform an eigenstate of the original trap into the corresponding eigenstate of the final trap. If no level crossings are involved, the process can be made faster than adiabatic by setting first the interpolated evolution of the wave function from its initial to its final form and inferring from this evolution the trap deformation. We find a simple and compact formula which gives the trap shape at any time for any interpolation scheme. It is applicable even in complicated scenarios where there is no adiabatic process for the desired state transformation, e.g., if the state changes its topological properties. We illustrate its use for the expansion of a harmonic trap, for the transformation of a harmonic trap into a linear trap and into an arbitrary number of traps of a periodic structure. Finally, we study the creation of a node exemplified by the passage from the ground state to the first excited state of a harmonic oscillator.

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

We investigate the potential for controlling a noninteracting Bose-Einstein condensate loaded into a one-dimensional optical superlattice. Our control strategy combines Bloch oscillations, originating from accelerating the lattice, with time-dependent control of the superlattice parameters. We investigate two experimentally viable scenarios, very low and very high potential depths, in order to gain a better understanding of matter wave control available within the system. Multiple lattice parameters and a versatile energy band structure allow us to obtain a wide range of control over energy band populations. Finally, we consider several examples of quantum state preparation in the superlattice structure that may be difficult to achieve in a regular lattice.

We study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum on both sides of this transition by using two microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both the density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value.

We calculate the phase diagram of identical fermions in a two-dimensional lattice immersed in a three-dimensional Bose-Einstein condensate (BEC). The fermions exchange density fluctuations in the BEC, which gives rise to an attractive induced interaction. The resulting zero-temperature phase diagram exhibits topological $p_x+i{p}_y$ superfluid phases as well as a phase separation region. We show how to use the flexibility of the Bose-Fermi mixture to tune the induced interaction, so that it maximizes the pairing between nearest-neighbor sites, whereas phase separation originating from long-range interactions is suppressed. Finally, we calculate the Berezinskii-Kosterlitz-Thouless critical temperature of the topological superfluid in the lattice and discuss experimental realizations.

We propose a cold-atom realization of a zigzag ladder. The two legs of the ladder correspond to a “synthetic” dimension given by two internal (spin) states of the atoms, so that tunneling between them can be realized as a laser-assisted process. The zigzag geometry is achieved by employing a spin-dependent optical lattice with the site position depending on the internal atomic state, i.e., on the ladder's leg. The lattice offers a possibility to tune the single-particle dispersion from a double-well to a single-minimum configuration. In contrast to previously considered semisynthetic lattices with a square geometry, the tunneling in the synthetic dimension is accompanied by spatial displacements of atoms. Therefore, the atom-atom interactions are nonlocal and act along the diagonal (semisynthetic) direction. We investigate the ground-state properties of the system for the case of strongly interacting bosons. In particular, we find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an interesting gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.

Invisibility in a diffusive-light-scattering medium has been recently demonstrated by employing a scattering-cancellation core-shell cloak. Unlike nondiffusive cloaks, such a device can be simultaneously macroscopic, broadband, passive, polarization independent, and omnidirectional. Unfortunately, it has been verified that this cloak, as well as more sophisticated ones based on transformation optics, fail under pulsed illumination, invalidating their use for a variety of applications. Here, we introduce a different approach based on unimodular transformations that enables the construction of unidirectional diffusive-light cloaks exhibiting a perfect invisibility effect, even under transient conditions. Moreover, we demonstrate that a polygonal cloak can extend this functionality to multiple directions with a nearly ideal behavior, while preserving all other features. We propose and numerically verify a simple cloak realization based on a layered stack of two isotropic materials. The studied devices have several applications not addressable by any of the other cloaks proposed to date, including shielding from pulse-based detection techniques, cloaking undesired scattering elements in time-of-flight imaging or high-speed communication systems for diffusive environments, and building extreme optical security features. The discussed cloaking strategy could also be applied to simplify the implementation of thermal cloaks.

We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on $N$ spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., $O\left(N^{-2}\right)$ precision, and derive the explicit circuit that accomplishes the simulation.

Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the previous schemes in this direction have been based on the conventional geometric phases, of which the dynamical phases need to be removed. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases, of which the dynamical phases do not need to be removed. Specifically, by using three physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of geometric gates nonadiabatically and unconventionally. Our scheme not only maintains all the merits of nonadiabatic geometric quantum computation in decoherence-free subspaces, but also avoids the additional operations required in the conventional schemes to cancel the dynamical phases.

The average fidelity of the teleportation of coherent states is calculated for general Gaussian bipartite systems shared by the partners of the protocol, Alice and Bob. It is considered that the shared Gaussian bipartite modes suffer independent attenuations before the processing of Alice and Bob. In addition, the classical communication between the partners can be controlled by a gain not necessarily unitary. Comparing with the classical fidelity threshold of measure-and-prepare methods, we establish several genuinely quantum teleportation conditions which depend on the gain and the local attenuations. If the gain can be tuned to maximize the bipartite state set capable of performing genuinely quantum teleportation, then a condition for teleportation robust against local attenuations is found. This condition is demonstrated to be essentially equivalent to the condition of robust Gaussian bipartite entanglement, obtained in previous articles, showing that the robustness against attenuations is an entanglement property relevant for characterization and application of bipartite systems. For the derivation of the robust teleportation conditions, the Gaussian operations onto the bipartite system are thoroughly studied, so that the transformations that maintain the fidelity invariant are found. Some scenarios for different Gaussian bipartite states are presented and discussed.

External potentials play a crucial role in modeling quantum systems, since, for a given interparticle interaction, they define the system Hamiltonian. We use the metric-space approach to quantum mechanics to derive, from the energy conservation law, two natural metrics for potentials. We show that these metrics are well defined for physical potentials, regardless of whether the system is in an eigenstate or if the potential is bounded. In addition, we discuss the gauge freedom of potentials and how to ensure that the metrics preserve physical relevance. Our metrics for potentials, together with the metrics for wave functions and densities from I. D'Amico et al. [Phys. Rev. Lett. 106, 050401 (2011)] paves the way for a comprehensive study of the two fundamental theorems of density-functional theory. We explore these by analyzing two many-body systems for which the related exact Kohn-Sham systems can be derived. First we consider the information provided by each of the metrics, and we find that the density metric performs best in distinguishing two many-body systems. Next we study for the systems at hand the one-to-one relationships among potentials, ground-state wave functions, and ground-state densities defined by the Hohenberg-Kohn theorem as relationships in metric spaces. We find that, in metric space, these relationships are monotonic and incorporate regions of linearity, at least for the systems considered. Finally, we use the metrics for wave functions and potentials in order to assess quantitatively how close the many-body and Kohn-Sham systems are: We show that, at least for the systems analyzed, both metrics provide a consistent picture, and for large regions of the parameter space the error in approximating the many-body wave function with the Kohn-Sham wave function lies under a threshold of 10%.

We model the one-dimensional (1D) to three-dimensional (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin imbalance. We calculate the mean-field phase diagram and study the relative stability of exotic superfluid phases as a function of interaction strength and temperature. For weak interactions and low density, we find 1D-like behavior, which repeats as a function of the chemical potential as new channels open. For strong interactions, mixing of single-particle levels gives 3D-like behavior at all densities. Furthermore, we map the system to an effective 1D model, finding significant density dependence of the effective 1D scattering length.

We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating-wave, two-level, Born, or Markov approximations. A well-behaved time-domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.

A quantum-eraser setup exploiting the time-energy complementarity relation in the x-ray regime is investigated theoretically. The starting point is the interference process between x-ray quanta driving two nuclear hyperfine transitions in a nuclear forward-scattering setup. We show that which-way information can be obtained by marking the scattering paths with orthogonal polarization states, thus leading to the disappearance of the interference pattern. In turn, erasure of the which-way information leads to the reappearance of the interference fringes. We put forward two schemes using resonant scattering off nuclear targets and design which-way marking procedures to realize the quantum-eraser setup for x-ray quanta.

We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak-coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe decoherence and suggests that a decoherence dynamical transition occurs in this two-qubit spin-boson model. We also demonstrate that the critical transition point can be characterized by the behavior of the frequency spectrum of the quantum coherence indicator.

The existing decoy-state measurement-device-independent quantum key distribution (MDI-QKD) theory assumes perfect control of the source states, which is an impossible task for any real setup. In this paper, we study the decoy-state MDI-QKD method with source errors without presuming any unverifiable error patterns. In our method we need the range of only a few parameters in the source state.

We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occurs on a large variety of regular graphs, including edge-transitive, expander, and high-degree graphs. As a corollary, high edge connectivity also implies localization of these states, since it is closely related to electric resistance.

A scheme for transferring classical information over a lossy bosonic channel is proposed by generalizing the proposal presented by Guha [Phys. Rev. Lett. 106, 240502 (2011)]. It employs code words formed by products of coherent states of fixed mean photon number with multiple phases which, through a passive unitary transformation, reduce to a pulse-position modulation code with multiple pulse phases. The maximum information rate achievable with optimal, yet difficult to implement detection schemes is computed and shown to saturate the classical capacity of the channel in the low-energy regime. An easy to implement receiver based on a conditional Dolinar detection scheme is also proposed, finding that while suboptimal, it allows for improvements in an intermediate photon-number regime with respect to previous proposals.

In recent years, the development of neutral helium microscopes has gained increasing interest. The low energy, charge neutrality, and inertness of the helium atoms makes helium microscopy an attractive candidate for the imaging of a range of samples. The simplest neutral helium microscope is the so-called pinhole microscope. It consists of a supersonic expansion helium beam collimated by two consecutive apertures (skimmer and pinhole), which together determine the beam spot size and hence the resolution at a given working distance to the sample. Due to the high ionization potential of neutral helium atoms, it is difficult to build efficient helium detectors. Therefore, it is crucial to optimize the microscope design to maximize the intensity for a given resolution and working distance. Here we present an optimization model for the helium pinhole microscope system. We show that for a given resolution and working distance, there is a single intensity maximum. Further we show that with present-day state-of-the-art detector technology (ionization efficiency $1\times {10}^{-3}$), a resolution of the order of 600 nm at a working distance of 3 mm is possible. In order to make this quantification, we have assumed a Lambertian reflecting surface and calculated the beam spot size that gives a signal 100 cts/s within a solid angle of $0.02\pi$ sr, following an existing design. Reducing the working distance to the micron range leads to an improved resolution of around 40 nm.