A quantum analog of the fundamental classical not gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question of under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalization of partly unknown single- and two-qubit quantum states. A state orthogonal to an input state is conditionally prepared by quantum filtering, and the only required information about the input state is a mean value of a single arbitrary operator. We show that perfect orthogonalization of partly unknown two-qubit entangled states can be performed by applying the quantum filter to one of the qubits only.

We calculate scalar static polarizabilities for lanthanides and actinides, the atoms with open $4f$ or $5f$ subshells. We show that polarizabilities of the low states are approximately the same for all states of a given configuration, and we present a way of calculating them reducing valence space to just two or three valence electrons occupying $6s$ and $5d$ states for lanthanides or $7s$ and $6d$ states for actinides, while $4f$ and $5f$ states are considered to be in the core. The configuration interaction technique is used to calculate polarizabilities of lanthanides and actinides for all states of the $4f^{n}6s^2$ and $4f^{n-1}6s^{2}5d$ configurations of lanthanides and all states of the $5f^{n}7s^2$ and $5f^{n-1}7s^{2}6d$ configurations of actinides. Polarizability of the electron core (including $f$ orbitals) has been calculated in the random-phase approximation.

Polarizable dipoles, such as atoms, molecules, or nanoparticles, subject to laser radiation may attract or repel each other. We derive a general formalism in which such laser-induced dipole-dipole interactions (LIDDIs) in any geometry and for any laser strength are described in terms of the resonant dipole-dipole interaction (RDDI) between dipoles dressed by the laser. This approach provides a simple route towards the analysis of LIDDI in a general geometry. Our general results reveal LIDDI effects due to nonlinear dipolar response to the laser, previously unaccounted for. The origin of these nonlinear effects is discussed. Our general formalism is illustrated for LIDDI between atoms in a cavity.

Detailed two-dimensional particle-in-cell (PIC) simulations and numerical calculations of electron density profiles, based on a simplified model, were performed to show that underdense plasma, induced by two pairs of counterpropagating femtosecond-laser pulses in a gas, could be manipulated by ponderomotive-optical lattices to form periodic structures. These phenomena facilitate the localization and enhancement of the generating laser pulse intensities by the self-induced plasma photonic lattices (PPLs) and exhibit unique spatiotemporal dynamics. Variation of the initial plasma density profile and the configuration of the interacting pulses enabled control over the attainable PPL structures. It is predicted that by using a nonuniform initial plasma density, light emission in a preferred direction could be obtained.

A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting polaritons as natural collective eigenstates. We derive polariton-polariton kinematic interactions by applying a bosonization procedure to transform excitation spin-$\frac{1}{2}$ operators into interacting bosons. In solving the scattering problem we extract the effective potential, which is shown to be modulated by using the excitation-photon detuning as a control parameter. We examine the regime in which polaritons behave as a dilute degenerate boson gas and in the limit where polaritons can be treated as weakly interacting photons we propose the system for realizing superfluidity of photons. We implement the kinematic interaction as a mechanism for nonlinear optical processes that provide an observation tool for the system properties, e.g., the interaction strength produces a blue shift in pump-probe experiments.

Identifying an accurate model for the dynamics of a quantum system is a vexing problem that underlies a range of problems in experimental physics and quantum information theory. Recently, a method called quantum Hamiltonian learning has been proposed by the present authors that uses quantum simulation as a resource for modeling an unknown quantum system. This approach can, under certain circumstances, allow such models to be efficiently identified. A major caveat of that work is the assumption of that all elements of the protocol are noise free. Here we show that quantum Hamiltonian learning can tolerate substantial amounts of depolarizing noise and show numerical evidence that it can tolerate noise drawn from other realistic models. We further provide evidence that the learning algorithm will find a model that is maximally close to the true model in cases where the hypothetical model lacks terms present in the true model. Finally, we also provide numerical evidence that the algorithm works for noncommuting models. This work illustrates that quantum Hamiltonian learning can be performed using realistic resources and suggests that even imperfect quantum resources may be valuable for characterizing quantum systems.

Experiments in coherent nuclear and electron magnetic resonance and quantum computing in general correspond to control of quantum-mechanical systems, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here, we derive a time-optimal sequences as fundamental building blocks to synthesize unitary transformations. Such sequences can be widely implemented on various physical systems, including the simulation of effective Hamiltonians for topological quantum computing on spin lattices. Experimental demonstrations are provided for a system consisting of three nuclear spins.

Demagnetization cooling relies on spin-orbit coupling that brings motional and spin degrees of freedom into thermal equilibrium. In the case of a gas, one has the advantage that the spin degree of freedom can be cooled very efficiently using optical pumping. We investigate demagnetization cooling of a chromium gas in a deep optical dipole trap over a large temperature range and reach high densities up to $5\times {10}^{19}$ m${}^{-3}$. We study the loss mechanism under such extreme conditions and identify excited-state collisions as the main limiting process. We discuss that in some systems demagnetization cooling has a realistic potential of reaching degeneracy by optical cooling only.

In this article we apply the intermediate-energy $R$-matrix method to photo-double-ionization of the metastable $1s2s{}^{1,3}{S}^e$ and $1s2p{}^{1,3}{P}^o$ states of He, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$, along with the $1s^{2}2s2p{}^{1,3}{P}^o$ and $1s^{2}2s3s{}^{1,3}{S}^e$ states of Be, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$. We compare our results with other theoretical data where possible and achieve excellent agreement. We examine trends between the various excited states and ground states of the systems.

We study the effect of the synthetic spin-orbit coupling in a two-component Bose-Hubbard model in one dimension by employing the density-matrix renormalization group method. A ferromagnetic long-range order emerges in both Mott-insulator and superfluid phases resulting from the spontaneous breaking of the $Z_2$ symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the intercomponent interaction is smaller than the intracomponent one as well. This effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments.

An analytical approach is reported that describes previously observed fast-light regimes in linear and passive Mach-Zehnder interferometers (MZI) where the optical path difference is due to a different length of the branches. Approximate expressions are developed for the transmission coefficient and group delay spectral functions valid for frequencies close to the transmission minima ${\omega }_{\min }$, where these regimes occur. It is found that the group delay at ${\omega }_{\min }$ verifies a simple scaling law. We demonstrate that slow light cannot arise in this system, and that tunneling and superluminal regimes appear only for low-loss devices, where the attenuation drives the change in the propagation regimes. The propagation of a sinusoidally modulated pulse train through the MZI is described, and relevant figures of merit, which are intrinsic to the system and universal for any operative spectral range, are determined. The theoretical approach is illustrated by simulations of a silicon-based interferometer designed for advancing pulses at 1.55 μm. Also, previously reported experimental results in the radiofrequency range are interpreted in the framework of the model.

We derive an analytical description for quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation using correlated light fields, photon addition, and photon subtraction processes. Using a postselection procedure to a particular number of clicks of the detector system, the output states reveal a variety of quantum features. The rigorous description allows the identification and characterization of fundamentally unavoidable attenuations within given processes. We also generalize a known scenario of noiseless amplification with click detectors for the purpose of the preparation of various types of nonclassical states of light. Our exact results are useful for a choice of experimental parameters to realize a target state.

We investigate the zero-temperature properties of a diluted homogeneous Bose gas made of $N$ particles interacting via a two-body square-well potential by performing Monte Carlo simulations. We tune the interaction strength to achieve arbitrary positive values of the scattering length and compute by Monte Carlo quadrature the energy per particle $E/N$ and the condensate fraction $N_0/N$ of this system by using a Jastrow ansatz for the many-body wave function, which avoids the formation of the self-bound ground state and describes instead a (metastable) gaseous state with uniform density. In the unitarity limit, where the scattering length diverges while the range of the interatomic potential is much smaller than the average distance between atoms, we find a finite energy per particle [$E/N=0.70{\hslash }^2{\left(6{\pi }^{2}n\right)}^{2/3}/2m$, with $n$ the number density] and a quite large condensate fraction ($N_0/N=0.83$).

In this paper, we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner [Phys. Rev. Lett. 90, 157904 (2003)] who characterized the correlation polytope for $2\times 2$ measurement settings with binary outcomes plus one bit of communication. Here, we derive a complete set of Bell inequalities for $3\times 2$ measurement settings and a shared bit of communication. When the communication direction is fixed, nine Bell inequalities characterize the correlation polytope, whereas when the communication direction is bidirectional, 143 inequalities describe the correlations. We then prove a tight lower bound on the amount of communication needed to simulate all no-signaling correlations for a given number of measurement settings.

In this work, we introduce a family of $\left[\right[6k,2k,2\left]\right]$ codes designed specifically to be compatible with adiabatic quantum computation. These codes support computationally universal sets of weight 2 logical operators and are particularly well suited for implementing dynamical decoupling error suppression. For Hamiltonians embeddable on a planar graph of fixed degree, our encoding maintains a planar connectivity graph and increases the graph degree by only two.

The Pauli exclusion principle requires the spectrum of the occupation numbers of the one-electron reduced density matrix (1-RDM) to be bounded by one and zero. However, for a 1-RDM from a wave function, there exist additional conditions on the spectrum of occupation numbers, known as pure $N$-representability conditions or generalized Pauli conditions. For atoms and molecules, we measure through a Euclidean-distance metric the proximity of the 1-RDM spectrum to the facets of the convex set (polytope) generated by the generalized Pauli conditions. For the ground state of any spin symmetry, as long as time-reversal symmetry is considered in the definition of the polytope, we find that the 1-RDM's spectrum is pinned to the boundary of the polytope. In contrast, for excited states, we find that the 1-RDM spectrum is not pinned. Proximity of the 1-RDM to the boundary of the polytope provides a measurement and classification of electron correlation and entanglement within the quantum system. For comparison, this distance to the boundary of the generalized Pauli conditions is also compared to the distance to the polytope of the traditional Pauli conditions, and the distance to the nearest 1-RDM spectrum from a Slater determinant. We explain the difference in pinning in the ground- and excited-state 1-RDMs through a connection to the $N$-representability conditions of the two-electron reduced density matrix.

There has been increasing interest in the energy spectrum of highly excited Rydberg states. The energy spectra of the $s$, $p$, and $d$ highly excited Rydberg states of a rubidium atom have been measured by different groups. However, there is a discrepancy between the reported data concerning the energy levels of highly excited $s$ and $d$ states of Rb. We address this issue by performing accurate calculations of Rb($ns,np,nd$) energy levels using the parametric one-electron valence potential [Marinescu, Sadeghpour, and Dalgarno, Phys. Rev. A 49, 982 (1994)] with spin-orbit coupling. We compare results with reference data from the National Institute of Standards and Technology and from available experiments. This enables us to recommend energy levels of highly excited Rydberg states of Rb that can be used as reference values.

We present a theoretical analysis of the atomic photoelectron emission spectra produced by a linearly polarized sculpted laser pulse of two colors with frequencies $\omega$ and $2\omega$. The spectrum of the “direct” electrons with intermediate energies prominently features both intracycle and intercycle interferences. We derive a simple analytic expression for this spectral range based on a semiclassical approximation of the time-dependent distorted wave strong-field approximation generalized to strong-field ionization by a two-color pulse. We verify its applicability to approximately represent the intricate interference patterns by comparison with the exact solutions of the time-dependent Schrödinger equation and with the strong-field approximation. We show that the interference patterns can be tuned and its contrast enhanced by the additional “knob” available, the relative phase between the two frequency components. The present results confirm that two-color ionization allows resolving interference structures originating from trajectories launched within a time interval of less than 100 as [X. Xie et al., Phys. Rev. Lett. 108, 193004 (2012)].

We study the state-resolved production of neon ion after resonant photoionization of Ne via the $2s$-$3p$ Fano resonance. We find that by tuning the photon energy across the Fano resonance, a surprisingly high control over the alignment of the final $2p$ hole along the polarization direction can be achieved. In this way, hole alignments can be created that are otherwise very hard to achieve. The mechanism responsible for this hole alignment is the destructive interference of the direct and indirect (via the autoionizing $2s^{-1}3p$ state) ionization pathways of $2p$. By changing the photon energy, the strength of the interference varies and $2p$ hole alignments with ratios up to 19:1 between $2p_0$ and $2p_{\pm 1}$ holes can be created—an effect normally only encountered in tunnel ionization using strong-field ir pulses. The inclusion of spin-orbit interaction does not change the qualitative feature and leads only to a reduction in the alignment by $2/3$. Our study is based on a time-dependent configuration-interaction singles approach, which solves the multichannel time-dependent Schrödinger equation.

We consider correlation-assisted tunnel ionization of a small molecule by an intense low-frequency laser pulse. In this mechanism, the departing electron excites the state of the ion via a Coulomb interaction. We show that the wave packets emerging from this process can have nontrivial spatial structure and give a measurable indicator of correlated multielectron dynamics during the tunneling step. We also show that the saddle-point approximation requires special attention in this geometric analysis.