The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. It is based on the combined application of the eigendecomposition (EID) and singular value decomposition (SVD) of the two matrices associated to the Bogoliubov transformation of the given Gaussian unitary, with the constraint that the unitary matrices appearing in the SVDs must verify a stringent condition, called in the paper “rotation condition”. Thus, for a correct evaluation of the BM reduction, one has to choose, among the possible SVD pairs, the pair that meets this condition. The paper develops an approach to this problem, which is based on the introduction of a balancing matrix in the SVDs to fulfill the rotation condition. The theory is illustrated with a few application examples.

One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems, the main reason for this being the rigid layout of their quantum bits as well as their sparse connectivity. In particular, the implementation of constraints has become a major bottleneck in the embedding of practical problems, because the latter is typically achieved by adding harmful penalty terms to the problem Hamiltonian, a technique that often requires an all-to-all connectivity between the qubits. Recently, a novel technique designed to obviate the need for penalty terms was suggested; it is based on the construction of driver Hamiltonians that commute with the constraints of the problem, rendering the latter constants of motion. In this work we propose general guidelines for the construction of such driver Hamiltonians given an arbitrary set of constraints. We illustrate the broad applicability of our method by analyzing several diverse examples, namely, graph isomorphism, not-all-equal three-satisfiability, and the so-called Lechner-Hauke-Zoller constraints. We also discuss the significance of our approach in the context of current and future experimental quantum annealers.

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics. Our first result is a remainder term for the entropy gain of a quantum channel. This result implies that a small increase in entropy under the action of a subunital channel is a witness to the fact that the channel's adjoint can be used as a recovery map to undo the action of the original channel. We apply this result to pure-loss, quantum-limited amplifier, and phase-insensitive quantum Gaussian channels, showing how a quantum-limited amplifier can serve as a recovery from a pure-loss channel and vice versa. Our second result regards the information gain of a quantum measurement, both without and with quantum side information. We find here that a small information gain implies that it is possible to undo the action of the original measurement if it is efficient. The result also has operational ramifications for the information-theoretic tasks known as measurement compression without and with quantum side information. Our third result shows that the loss of Holevo information caused by the action of a noisy channel on an input ensemble of quantum states is small if and only if the noise can be approximately corrected on average. We finally establish that the reduced dynamics of a system-environment interaction are approximately completely positive and trace preserving if and only if the data processing inequality holds approximately.

As a further test of advanced theoretical methods to describe electron-impact single-ionization processes in complex atomic targets, we extended our recent work on $\mathrm{Ne}(2p$) ionization [X. Ren, S. Amami, O. Zatsarinny, T. Pflüger, M. Weyland, W. Y. Baek, H. Rabus, K. Bartschat, D. Madison, and A. Dorn, Phys. Rev. A 91, 032707 (2015)] to $\mathrm{Ar}(3p$) ionization at the relatively low incident energy of $E_0=66$ eV. The experimental data were obtained with a reaction microscope, which can cover nearly the entire $4\pi$ solid angle for the secondary electron emission. We present experimental data for detection angles of 10, 15, and ${20}^{\circ }$ for the faster of the two outgoing electrons as a function of the detection angle of the secondary electron with energies of 3, 5, and 10 eV, respectively. Comparison with theoretical predictions from a $B$-spline $R$-matrix (BSR) with pseudostates approach and a three-body distorted-wave (3DW) approach, for detection of the secondary electron in three orthogonal planes as well as the entire solid angle, shows overall satisfactory agreement between experiment and the BSR results, whereas the 3DW approach faces difficulties in predicting some of the details of the angular distributions. These findings are different from our earlier work on $\mathrm{Ne}(2p$), where both the BSR and 3DW approaches yielded comparable levels of agreement with the experimental data.

We report an experimental and theoretical study of low-energy electron-impact ionization of tetrahydrofuran, which is a molecule of biological interest. The experiments were performed using an advanced reaction microscope specially built for electron-impact ionization studies. The theoretical calculations were performed within the molecular three-body distorted-wave model. Reasonably good agreement is found between experiment and theory.

The structure of a two-dimensional honeycomb optical lattice potential with small inversion asymmetry is characterized using coherent diffraction of ${}^{87}\mathrm{Rb}$ atoms. We demonstrate that even a small potential asymmetry, with peak-to-peak amplitude of $\le 2.3\%$ of the overall lattice potential, can lead to pronounced inversion asymmetry in the momentum-space diffraction pattern. The observed asymmetry is explained quantitatively by considering both Kapitza-Dirac scattering in the Raman-Nath regime and also either perturbative or full-numerical treatment of the band structure of a periodic potential with a weak inversion-symmetry-breaking term. Our results have relevance for both the experimental development of coherent atom optics and the proper interpretation of time-of-flight assays of atomic materials in optical lattices.

The recent experimental realization of one-dimensional (1D) equal Rashba-Dresselhaus spin-orbit coupling (ERD-SOC) for cold atoms provides a disorder-free and highly controllable platform for the implementation and observation of Majorana fermions (MFs), analogous to the broadly studied solid-state nanowire-superconductor heterostructures. However, the corresponding 1D chains of cold atoms possess strong quantum fluctuation, which may destroy the superfluids and MFs. In this paper, we show that such 1D topological chains with MFs may be on demand generated in a two- or three-dimensional nontopological optical lattice with 1D ERD-SOC by modifying local potentials on target locations using experimentally already implemented atomic gas microscopes or patterned (e.g., double- or triple-well) optical lattices. All ingredients in our scheme have been experimentally realized, and the combination of them may pave the way for the experimental observation of MFs in a clean system.

We study spatial coherence near a classical environment by loading a Bose-Einstein condensate into a magnetic lattice potential and observing diffraction. Even very close to a surface ($5\mu \mathrm{m}$), and even when the surface is at room temperature, spatial coherence persists for a relatively long time ($\ge 500\mathrm{ms}$). In addition, the observed spatial coherence extends over several lattice sites, a significantly greater distance than the atom-surface separation. This opens the door for atomic circuits, and may help elucidate the interplay between spatial dephasing, interatomic interactions, and external noise.

We have developed the general grid method for multichannel scattering of bosonic atoms inside a harmonic waveguide with transverse anisotropy. This approach is employed to analyze elastic as well as inelastic multichannel confined scattering. For the elastic scattering, the effects of the range and form of interatomic potential and the waveguide anisotropy on the confinement-induced resonance are studied. We have also investigated quantitatively the reactive rate constant in confined atom-atom collisions. It is found that a slight anisotropy to the confining trap considerably enhances the reactive rate constant in multichannel regime.

We study the effect of a change in size and spatial profile of the pump beam in an atomic-based four-wave mixing process on the size of the coherence area of the generated entangled twin beams. We perform experiments and develop a theoretical model to obtain a measure of the linear extent or “radius” of the coherence area from noise measurements of the twin beams as a function of transmission through a variable size slit. Our results show that an increase in the size of the pump reduces the size of the coherence area. More interestingly, we find that the use of a flat-top pump beam of the same size as a Gaussian pump beam leads to a reduction by a factor of more than 2 in the linear extent of the coherence area. This in turn leads to an increase by a factor of more than 4 in the number of spatial modes that make up the twin beams and a resolution enhancement of the entangled images that can be generated with the four-wave mixing process.

Quantum optomechanics opens a possibility to mediate a physical connection between quantum optics and classical thermodynamics. We propose and theoretically analyze a one-way chain starting from various quantum states of radiation. In the chain, the radiation state is first ideally swapped to a sufficiently large mechanical oscillator (membrane). Then the membrane mechanically pushes a classical almost massless piston, which is pressing a gas in a small container. As a result, we observe strongly nonlinear and nonmonotonic transfer of the energy stored in classical and quantum uncertainty of radiation to mechanical work. The amount of work and even its sign depend strongly on the uncertainty of the radiation state. Our theoretical prediction would stimulate an experimental proposal for such optomechanical connection to thermodynamics.

We propose two different setups to generate single photons on demand using an atom in front of a mirror, along with either a beam splitter or a tunable coupling. We show that photon-generation efficiency of $\sim 99\%$ is straightforward to achieve. The proposed schemes are simple and easily tunable in frequency. The operation is relatively insensitive to dephasing and can be easily extended to generate correlated pairs of photons. They can also, in principle, be used to generate any photonic qubit of the form $\mu \left|0\right.〉+\nu \left|1\right.〉$ in arbitrary wave packets, making them very attractive for quantum communication applications.

We analyze experimentally and theoretically the spatiotemporal dynamics of a highly multimode semiconductor laser with coherent optical injection. Due to the particular geometry of the device (a 1-m-long ring cavity), the multimode dynamics can be resolved in real time and we observe stable chiral solitons and domain dynamics. The experiment is analyzed in the framework of a set of effective semiconductor Maxwell-Bloch equations. We analyze the stability of stationary solutions and simulate both the complete model and a reduced rate equation model. This allows us to predict domain shrinking and the stability of only one chiral charge that we ascribe to the finite active medium response time.

We propose a scheme to generate and control atomic spin squeezing via atomic coherence induced by the strong coupling and probe fields in the Λ-type electromagnetically-induced-transparency configuration in an atomic ensemble. Manipulation of squeezing of the two components in the plane orthogonal to the mean atomic spin direction and generation of nearly perfect squeezing in either component can be achieved by varying the relative intensities of the coupling and probe fields. This method provides a flexible and convenient way to create and control atomic spin squeezing, which may find potential applications in high-precision atomic-physics measurement, quantum coherent control, and quantum information processing.

We investigate theoretically the effects of vacuum-induced coherence (VIC) on magneto-optical rotation (MOR). We carry out a model study to show that VIC in the presence of a control laser and a magnetic field can lead to large enhancement in the rotation of the plane of polarization of a linearly polarized weak laser with vanishing circular dichroism. This effect can be realized in cold molecular gases and may be used as a sensitive probe for VIC. Such a large MOR angle can also be used to detect weak magnetic field with large measurement sensitivity.

The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.

In photoionization microscopy experiments, an atom is placed in static external fields, it is ionized by a laser, and an electron falls onto a position-sensitive detector. The current of electrons arriving at various points on the detector depends upon the initial state of the atom, the excited states to which the electron is resonantly or nonresonantly excited, and the various paths leading from the atom to the final point on the detector. We report here quantum-mechanical computations of photoionization microscopy in parallel electric and magnetic fields. We focus especially on the patterns resulting from resonant excited states. We show that the magnetic field substantially modifies some of these resonant states, confining them in the radial direction, and that it has a strong effect on the interference pattern at the detector.

Using an efficient cluster approach, we study the physics of two-dimensional lattice bosons in a strong magnetic field in the regime where the tunneling is much weaker than the on-site interaction strength. We study both the dilute, hard-core bosons at filling factors much smaller than unity occupation per site and the physics in the vicinity of the superfluid-Mott lobes as the density is tuned away from unity. For hard-core bosons, we carry out extensive numerics for a fixed flux per plaquette $\varphi =1/5$ and $\varphi =1/3$. At large flux, the lowest-energy state is a strongly correlated superfluid, analogous to He-4, in which the order parameter is dramatically suppressed, but nonzero. At filling factors $\nu =1/2,1$, we find competing incompressible states which are metastable. These appear to be commensurate density wave states. For small flux, the situation is reversed and the ground state at $\nu =1/2$ is an incompressible density wave solid. Here, we find a metastable lattice supersolid phase, where superfluidity and density wave order coexist. We then perform careful numerical studies of the physics near the vicinity of the Mott lobes for $\varphi =1/2$ and $\varphi =1/4$. At $\varphi =1/2$, the superfluid ground state has commensurate density wave order. At $\varphi =1/4$, incompressible phases appear outside the Mott lobes at densities $n=1.125$ and $n=1.25$, corresponding to filling fractions $\nu =1/2$ and 1, respectively. These phases, which are absent in single-site mean-field theory, are metastable and have slightly higher energy than the superfluid, but the energy difference between them shrinks rapidly with increasing cluster size, suggestive of an incompressible ground state. We thus explore the interplay between Mott physics, magnetic Landau levels, and superfluidity, finding a rich phase diagram of competing compressible and incompressible states.