Focused structured light fields with spatially nonuniform correlation can exhibit multiple focal points in the longitudinal direction, which suggests that they are suitable for longitudinal optical trapping. Due to the controllable nature of the longitudinal intensity distribution, this class of structured light fields not only can trap two high-index particles simultaneously, but also can manipulate them in the longitudinal direction.

The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behavior which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient—which characterizes the long-time current fluctuations—directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.

We propose to control spin-mixing dynamics in a gas of spinor atoms, via the combination of two off-resonant Raman transition pathways, enabled by a common cavity mode and a bichromatic pump laser. The mixing rate, which is proportional to the synthesized spin-exchange interaction strength, and the effective atomic quadratic Zeeman shift (QZS), can both be tuned by changing the pump laser parameters. Quench and driving dynamics of the atomic collective spin are shown to be controllable on a faster timescale than in existing experiments based on inherent spin-exchange collision interactions. The results we present open a promising avenue for exploring spin-mixing physics of atomic ensembles accessible in current experiments.

Linear optics imposes a relation that is more general than the second law of thermodynamics: For modes undergoing a linear evolution, the full mean occupation number, i.e., the photon number for optical modes, does not decrease, provided the evolution starts from a (generalized) diagonal state. This relation connects to noise increasing (or heating) and is akin to the second law and holds for a wide set of initial states. Also, the Bose entropy of modes increases, though this relation imposes additional limitations on the initial states and on linear evolution. We show that heating can be reversed via nonlinear interactions between the modes. They can cool, i.e., decrease the full mean occupation number and the related noise, an equilibrium system of modes provided their frequencies are different. Such an effect cannot exist in energy cooling, where only a part of an equilibrium system is cooled. We describe the cooling setup via both efficiency and coefficient of performance and relate the cooling effect to the Manley-Rowe theorem in nonlinear optics.

In quantum state discrimination, one aims to identify unknown states from a given ensemble by performing measurements. Different strategies such as minimum-error discrimination or unambiguous state identification find different optimal measurements. Maximum-confidence measurements (MCMs) maximize the confidence with which inputs can be identified given the measurement outcomes. This unifies a range of discrimination strategies including minimum-error and unambiguous state identification, which can be understood as limiting cases of MCM. In this work we investigate MCMs for general ensembles of qubit states. We present a method for finding MCMs for qubit-state ensembles by exploiting their geometry and apply it to several interesting cases, including ensembles of two and four mixed states and ensembles of an arbitrary number of pure states. We also compare MCMs to minimum-error and unambiguous discrimination for qubits. Our results provide interpretations of various qubit measurements in terms of MCM and can be used to devise qubit protocols.

We demonstrate that several metastable excited states in Hf ii, Hf iv, and W vi ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. The cooling electric dipole ($E1$) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using ${\mathrm{Ca}}^{+}$ or ${\mathrm{Sr}}^{+}$ ions. Energy levels; Landé $g$ factors; transition amplitudes for electric dipole ($E1$), electric quadrupole ($E2$), and magnetic dipole ($M1$) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory ($\mathrm{CI}+\mathrm{SD}$), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{-16}$ and ${10}^{-18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{−}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\alpha$ and may be used to search for dark matter producing this variation of $\alpha$. The enhancement coefficient for the $\alpha$ variation reaches $K=8.3$. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.

Experiments dedicated to the measurement of the electric dipole moment of the neutron require outstanding control of the magnetic-field uniformity. The neutron electric dipole moment (nEDM) experiment at the Paul Scherrer Institute uses a ${}^{199}\mathrm{Hg}$ co-magnetometer to precisely monitor temporal magnetic-field variations. This co-magnetometer, in the presence of field nonuniformity, is, however, responsible for the largest systematic effect of this measurement. To evaluate and correct that effect, offline measurements of the field nonuniformity were performed during mapping campaigns in 2013, 2014, and 2017. We present the results of these campaigns, and the improvement the correction of this effect brings to the neutron electric dipole moment measurement.

We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of $N$ spin-$j$ particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the $z$ and $x$ basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.

Ultracold spinor atoms in the weak and strong interaction regimes have been extensively investigated, while the behavior in the intermediate regime is less understood. We numerically investigate one-dimensional ultracold spinor atomic ensembles of finite size in the intermediate interaction regime and reveal the evolution of the eigenstates from the strong to the intermediate regime. In the strong interaction regime, it is well known that the eigenstates can be categorized into different manifolds, and the categorization is protected by the energy gaps between manifolds. In the intermediate interaction regime, it is found that the eigenenergy spectrum becomes gapless, while categorization of the eigenstates is still preserved even without the protection from the intermanifold gaps. The categorization in the intermediate regime is found due to the minigap induced by the finite-size effect, which prevents the intermanifold coupling. The gap vanishing in the spectrum induces both direct and avoided crossings between close-lying manifolds, of which the combined symmetries determine the type of the crossings. A modified $t\text{−}J$ model is derived to describe the low-lying eigenstates in the intermediate regime, which can capture the formation and crossings of the manifolds. State preparation through avoided crossings is also investigated.

We consider large rings of weakly coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e., in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, nonzero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $\pi /2$ and $3\pi /2$ and interparticle interaction in condensates exceeds a critical interaction value $u_c$, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero are generally offset by a critical timescale $t_c$, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical timescale in detail in a broad parameter range.

We exploit the interplay between uncertainty, disturbance, nonlocality, and self-duality within the framework of generalized probabilistic theories (GPTs). We first introduce an operational uncertainty-disturbance relation that reveals the discrepancies of GPTs in uncertainty and disturbance exhibited by one single measurement. We then apply the relation to Bell's scenarios and derive upper bounds for the basic spatial Clauser-Horne-Shimony-Holt and the temporal Leggett-Garg inequalities with and without the assumption of strong self-duality, respectively. It turns out that self-duality, though being thought of as one pillar of the axiomatization of quantum theory and implying additional constraints, is insufficient to explain the quantum violations. These insights may serve as a seed for a universal understanding of these basic properties in GPTs.

Two spatially separated observers, Alice and Bob, share a bipartite two-qubit entangled state and perform measurements to witness entanglement. After their measurements, they pass their qubits to a subsequent pair of observers who try to perform the same task independently, and so on. Here we ask: what is the maximum number of such pairs that can perform this task successfully? It has previously been conjectured that not more than one pair of observers can detect Clauser-Horne-Shimony-Holt “Bell-nonlocal” correlations in this setup. We prove that, on the contrary, entanglement can be witnessed by arbitrarily many pairs of observers. The dissimilar nature between entanglement and Bell-nonlocal correlations is therefore uncovered in a rather radical way, when considering sequentially acting pairs of observers. We prove this statement to be true when the initial shared state is any pure entangled state, a class of Bell-nonlocal mixed states, or a class of Bell-local entangled states.

Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian function of the system Hamiltonian. A hybrid quantum-classical algorithm feasible on near-term quantum computers is developed, which implements the quantum Gaussian filter as a linear combination of Hamiltonian evolution at various times. Remarkably, the linear combination coefficients are determined classically and can be optimized in the postprocessing procedure. Compared to the existing filter algorithms whose coefficients are given in advance, our method is more flexible in practice under given quantum resources with the help of postprocessing on classical computers. We demonstrate the quantum Gaussian filter algorithm for the quantum Ising model with numeral simulations under noises. We also propose an alternative full quantum approach that implements a QGF with an ancillary continuous-variable mode.

One notion of nonlocality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many-body systems which cannot be accessed locally. We show, however, that, remarkably, two-dimensional subspaces do not have this property: Any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multipartite structure, may be performed locally. Further, this requires only local measurement and feed-forward of classical information, readily achievable in many experimental platforms. As an application to quantum secret sharing we suggest a twist on a well-known quantum information splitting protocol, which ensures that no receiving party ever has access to the full state sent, but parties must work together to perform measurements on the state. These results may have practical applications to the measurement of encoded qubits in, e.g., quantum secret sharing, quantum error correction, and reveal a fundamental property unique to two-dimensional subspaces.

The direct counterfactual quantum-communication protocol involving double-chained Mach-Zehnder interferometers requires a single-photon input. Here, we show that even with multiphoton light sources, including a strong coherent light source as input, the counterfactual communication can be achieved with success probability approaching unity in the ideal asymptotic limit. The path evolution of multiple photons is nonlocally controlled. Thus, information is transmitted without any photons, or any other auxiliary information carriers, appearing in the public transmission channel. The effect is quantum since quantum measurements are an essential requirement for this protocol. Furthermore, a modified scheme is proposed in which the number of interferometers is reduced.

We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.

Molecular photoelectron spectra are commonly obtained theoretically in Fermi's Golden Rule framework, where the stationary continuum wave function is represented by slowly converging series such as the celebrated partial wave expansion. In this paper, we employ an alternative approach to address the photoionization cross section. While it gives the same cross section as the Golden Rule, this method follows a different route and has a number of advantages. The cross section is computed directly from the probability current density having the (conjugated) Dyson orbital as its source. With this, one arrives at an intuitive interpretation of the photoionization process and avoids employing a long expansion series since the continuum solution is transition-specific and thus unique. We expect this methodology to be particularly beneficial in the case of complexly shaped and delocalized Dyson orbitals.

Grover multiports are higher-dimensional generalizations of beam splitters, in which input to any one of the four ports has equal probability of exiting at any of the same four ports, including the input port. In this paper, we demonstrate that interferometers built from such multiports have novel features. For example, when combined with two-photon input and coincidence measurements, it is shown that such interferometers have capabilities beyond those of standard beam-splitter-based interferometers, such as easily controlled interpolation between Hong-Ou-Mandel (HOM) and anti-HOM behavior. Further, it is shown that the Grover-based analog of the Mach-Zehnder interferometer can make three separate phase measurements simultaneously. By arranging the transmission lines between the two multiports to lie in different planes, the same interferometer acts as a higher-dimensional Sagnac interferometer, allowing rotation rates about three different axes to be measured with a single device.