Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter systems. We present a simple, scalable, top-down method of entangling the quantum optical frequency comb into hypercubic-lattice continuous-variable cluster states of a size of about ${10}^4$ quantum field modes, using existing technology. A hypercubic lattice of dimension $D$ (linear, square, cubic, hypercubic, etc.) requires but $D$ optical parametric oscillators with bichromatic pumps whose frequency splittings alone determine the lattice dimensionality and the number of copies of the state.

We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.

We demonstrate the nondestructive imaging of a lattice gas of ultracold bosons. Atomic fluorescence is induced in the simultaneous presence of degenerate Raman sideband cooling. The combined influence of these processes controllably cycles an atom between a dark state and a fluorescing state while eliminating heating and loss. Through spatially resolved sideband spectroscopy following the imaging sequence, we demonstrate the efficacy of this imaging technique in various regimes of lattice depth and fluorescence acquisition rate. Our work provides an important extension of quantum gas imaging to the nondestructive detection, control, and manipulation of atoms in optical lattices. In addition, our technique can also be extended to atomic species that are less amenable to molasses-based lattice imaging.

Topological superfluids are recently discovered quantum matter that hosts topologically protected gapless edge states known as Majorana fermions—exotic quantum particles that act as their own antiparticles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the x-y plane and a large out-of-plane (perpendicular) Zeeman field along the z direction. Here we propose an alternative setup, where the topological superfluid phase is driven by applying an in-plane Zeeman field. This scheme offers a number of different features, notably Cooper pairings at finite center-of-mass momentum (i.e., Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, gapless topological quantum matter with an inhomogeneous pairing order parameter appears. It features unidirectional Majorana surface states at boundaries, which propagate in the same direction and connect two Weyl nodes in the bulk. We demonstrate the emergence of such exotic topological matter and the associated Majorana fermions in spin-orbit coupled atomic Fermi gases, and we determine its parameter space. The implementation of our scheme in semiconductor/superconductor heterostructures is briefly discussed.

We consider an equilibrium single-species homogeneous Bose gas from which a proportion of the atoms are instantaneously and coherently transferred to a second species, thereby forming a binary Bose gas in a non-equilibrium initial state. We study the ensuing evolution towards a new equilibrium, mapping the dynamics and final equilibrium state out as a function of the population transfer and the interspecies interactions by means of classical field methods. While in certain regimes, the condensate fractions are largely unaffected by the population transfer process, in others, particularly for immiscible interactions, one or both condensate fractions are vastly reduced to a new equilibrium value.

The contact interaction is often used in modeling ultracold atomic gases, although it leads to pathological behavior arising from the divergence of the many-body wave function when two particles coalesce. This makes it difficult to use this model interaction in quantum Monte Carlo and other popular numerical methods. Researchers therefore model the contact interaction with pseudopotentials, such as the square well potential, whose scattering properties deviate markedly from those of the contact potential. In this article, we propose a family of pseudopotentials that reproduce the scattering phase shifts of the contact interaction up to a hundred times more accurately than the square well potential. Moreover, the pseudopotentials are smooth, resulting in significant improvements in efficiency when used in numerical calculations.

We propose to go beyond the usual Hubbard model description of atoms in optical lattices and show how few-body physics can be used to simulate many-body phenomena, e.g., an electron-phonon system. We take one atomic species to be trapped in a deep optical lattice at full-filling and another to be untrapped spin-polarized fermions (which do not see the optical lattice) but to have an $s$-wave contact interaction with the first species. For large positive scattering length on the order of lattice spacing, the usual two-body bound (dimer) states overlap forming giant orbitals extending over the entire lattice, which can be viewed as an “electronic” band for the untrapped species while the trapped atoms become the “ions” with their own on-site dynamics, thereby simulating an electron-phonon system with renormalization of the phonon frequencies and Peierls transitions. This setup requires large scattering lengths but minimizes losses, does not need higher bands, and adds degrees of freedom which cannot easily be described in terms of lattice variables, thus opening up intriguing possibilities to explore interesting physics at the interface between few-body and many-body systems.

In this paper we present a protocol to engineer interactions confined to subspaces of the Fock space in trapped ions: we show how to engineer upper-bounded, lower-bounded, and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upper-bounded (lower-bounded) interaction acting upon Fock subspaces ranges from $|0\rangle$ to $|M\rangle$ ($|N\rangle$ $\text{to}\infty$), and the sliced one confined to Fock subspace ranges from $|M\rangle$ to $|N\rangle$, whatever $M<N$. Whereas the upper-bounded JC or AJC interaction is shown to drive any initial state to a steady Fock state $|N\rangle$, the sliced one is shown to produce steady superpositions of Fock states confined to the sliced subspace $\left\{\right|N\rangle \text{,}|N+1\rangle \}$.

Linear and nonlinear (especially coherent) electromagnetic interactions of moving many-electron atoms are investigated using a reduced-density-matrix description, which is applied to electromagnetically induced transparency and related resonant pump-probe optical phenomena. External magnetic fields are included on an equal footing with the electromagnetic fields and spin-Zeeman interactions are taken into account. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix description are self-consistently developed. The general nonperturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. The macroscopic electromagnetic response is described semiclassically, employing a perturbation expansion of the reduced-density operator in powers of the classical electromagnetic field. Our primary results are compact Liouville-space operator expressions for the linear and general ($n\text{th}$-order) nonlinear macroscopic electromagnetic-response tensors, which can be evaluated for nonlocal and nonstationary optical media described by multilevel atomic-system representations. Interactions among atoms and with environmental photons are treated as line-broadening effects by means of a general Liouville-space self-energy operator, for which the tetradic-matrix elements are explicitly evaluated in the diagonal, lowest-order, and Markov approximations. The compact Liouville-space operator expressions that are derived for the macroscopic electromagnetic-response tensors are introduced into the dynamical description of the electromagnetic-field propagation. It is pointed out that a quantized-electromagnetic-field approach will be required for a fully self-consistent quantum-mechanical treatment of local-field effects and radiative corrections.

We report on the observation of terahertz radiation in a noncentrosymmetric insulating oxide, paratellurite $\left(\alpha \text{−}{\mathrm{TeO}}_2\right)$, by irradiation of a femtosecond laser pulse at room temperature. In the power spectrum of the terahertz radiation, an intensity fringe pattern with a period of $\sim 0.25$ THz shows up below 3 THz. It can be reproduced by taking into account the effective generation length for the terahertz radiation with a poor phase-matching condition. In addition, a temporal oscillation component appears in the radiated terahertz wave with a frequency of $\sim 3.71$ THz, which is in good agreement with the center frequency of the Raman active longitudinal optical $E$ mode. On the basis of comprehensive polarized optical and Raman spectroscopic studies, we explain the generation mechanism of the temporal oscillation component in terms of the coherent phonon generation via impulsive stimulated Raman scattering.

In nonrelativistic quantum mechanics, Hudson's theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpositions of particles and antiparticles, while the existence of positive WFs exclusive composed of particles is conjectured. These observations may open new directions in relativistic quantum information theory.

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a non-negligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem: state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal generalized measurement. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

We show how to extract the scaling behavior of quantum walks using the renormalization group (RG). We introduce the method by efficiently reproducing well-known results on the one-dimensional lattice. For a nontrivial model, we apply this method to the dual Sierpinski gasket and obtain its exact, closed system of RG recursions. Numerical iteration suggests that under rescaling the system length, $L^{\prime }=2L$, characteristic times rescale as $t^{\prime }=2^{d_w}t$, with the exact walk exponent $d_w={log}_2\sqrt{5}=1.1609...$ Despite the lack of translational invariance, this value is very close to the ballistic spreading, $d_w=1$, found for regular lattices. However, we argue that an extended interpretation of the traditional RG formalism will be needed to obtain scaling exponents analytically. Direct simulations confirm our RG prediction for $d_w$ and furthermore reveal an immensely rich phenomenology for the spreading of the quantum walk on the gasket. Invariably, quantum interference localizes the walk completely, with a site-access probability that decreases with a power law from the initial site, in contrast to a classical random walk, which would pass all sites with certainty.

Tunneling ionization of atoms and molecules plays a major role in strong field physics. In this paper we study the nuclear version of this phenomenon: tunneling dissociation of ${{\mathrm{H}}_2}^{+}$ and its isotopes in the interaction with THz pulses. We show strong evidence supporting the concept of tunneling dissociation by numerically solving the time-dependent Schrödinger equation (TDSE). In our simulations, we observe a significant dissociation probability as a function of the driving field compatible with tunneling dissociation. We also observe nuclear rescattering, which induces high nuclear momenta, in clear analogy to the electron rescattering, which is very important in strong-field physics. This study offers an alternate perspective on the molecular tunneling dissociation in long-wavelength laser fields.

A parametric two-photon process, involving stimulated emission of two cascaded photons from a bidoped poled material placed inside an optically pumped cavity, is proposed and assessed within the priming photon scheme. We show that, with a specific level configuration for the two dopants $A$ and $B$, and an appropriate cavity design, stimulated emission from dopant $A$ can provide the priming photons for stimulated two-photon emission from dopant $B$ through a parametric biphotonic cascade. We discuss how this process is driven by a ratchet effect introduced by the simultaneous breakdown of both the space and time inversion symmetries. The optical Stark shifts are shown to considerably impact the efficiency of such a cascaded two-photon process.

One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group—containing $\pi$, $\pi /2$, and Hadamard gates—have been characterized with high accuracy. Here, we show how the Platonic solids enable implementing and characterizing larger gate sets. We find that all gates can be implemented with low error. The results fundamentally imply arbitrary manipulation of the quantum state can be realized with high precision, providing practical possibilities for designing efficient quantum algorithms.

Recently, it has been shown that the momentum distribution of a metallic state of fermionic atoms in a lattice Fermi-Bose mixture exhibits coherent oscillations after a global quench that suppresses tunneling. The oscillation period is determined by the Fermi-Bose interaction strength. Here we show that similar coherent dynamics, but with a different functional form, occurs in the fermionic Hubbard model when we quench a noninteracting metallic state by introducing a Hubbard interaction and suppressing tunneling. The period is determined primarily by the interaction strength. Conversely, we show that one can accurately determine the Hubbard interaction strength from the oscillation period, taking into account corrections from any small residual tunneling present in the final Hamiltonian. Such residual tunneling shortens the period and damps the oscillations, the latter being visible in the Fermi-Bose experiment.

A simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian, which transports a given initial state to a given final state in minimal time, under additional conditions on the drivings. If one of the three possible drivings is unconstrained in strength the problem is analytically completely solvable. A surprise arises for a class of states when one driving is bounded by a constant $c$ and the other drivings are constant. Then, for large $c$, the optimal driving is of type bang-off-bang and for increasing $c$ one recovers the unconstrained result. However, for smaller $c$ the optimal driving can suddenly switch to bang-bang type. It is also shown that for general states one may have a multistep protocol. The present paper explicitly proves and considerably extends the author's results contained in Phys. Rev. Lett. 111, 260501 (2013).

We investigate the smallest set of requirements for inducing non-Markovian dynamics in a collisional model of open quantum systems. This is done by introducing correlations in the state of the environment and analyzing the divisibility of the quantum maps from consecutive time steps. Our model and results serve as a platform for the microscopic study of non-Markovian behavior as well as an example of a simple scenario of non-Markovianity with purely contractive maps, i.e., with no backflow of information between system and environment.

We formulate a series of nontrivial equalities which are satisfied by all no-signaling correlations, meaning that no faster-than-light communication is allowed with the resource of these correlations. All quantum and classical correlations satisfy these equalities since they are no-signaling. By applying these equalities, we provide a general framework for solving the multipartite “guess your neighbor's input” (GYNI) game, which is naturally no-signaling but shows conversely that general no-signaling correlations are actually more nonlocal than those allowed by quantum mechanics. We confirm the validity of our method for the number of players from 3 up to 19, thus providing convincing evidence that it works for the general case. In addition, we solve analytically the tripartite GYNI and obtain a computable measure of supraquantum correlations. This result simplifies the defined optimization procedure to an analytic formula, thus characterizing explicitly the boundary between quantum and supraquantum correlations. In addition, we show that the gap between quantum and no-signaling boundaries containing supraquantum correlations can be closed by local orthogonality conditions in the tripartite case. Our results provide a computable classification of no-signaling correlations.