The manipulation of low-energy beams of neutral atoms and molecules via their de Broglie wavelength is a branch of atom optics often referred to as de Broglie matter wave optics. The application areas include fundamental quantum mechanics, atom interferometry, and the development of new microscopy instrumentation. The focusing of de Broglie matter waves with a Fresnel zone plate was used to demonstrate the first neutral helium microscopy imaging. The ultimate resolution of such a microscope is limited by the width of the outermost zone. Because a Fresnel zone plate for atoms cannot be fabricated on a substrate (the low-energy atom beams would not be able to penetrate the substrate material), this gives a fabrication determined limit for the first-order focus of around 30–50 nm. Therefore, it is important to search for alternative optical elements that enable higher resolution. Photon sieves consist of a large number of pinholes, arranged suitably relative to the Fresnel zones. The great advantages are that the width of the pinholes can be larger than the respective Fresnel zones and a free-standing pinhole is much easier to fabricate than a free-standing zone. Thus, with a photon-sieve structure applied for de Broglie matter wave manipulation, the fabrication limit for focusing is reduced to potentially around 3–5 nm. Here we present a realization of such an “atom sieve,” which we fabricated out of a silicon nitride (SiN) membrane, using electron-beam lithography and reactive ion etching. Our atom sieve is 178 $\mu \mathrm{m}$ in diameter and has 31 991 holes. The diameter of the holes varies from 1840 to 150 nm. Using a beam of neutral, ground-state helium atoms with an average wavelength of 0.055 nm, we demonstrate helium atom focusing down to a spot size of less than 4 $\mu \mathrm{m}$. The focus size is limited by the intrinsic velocity spread of the helium beam.

We show that in the regime of ground-state cooling, simple expressions can be derived for the performance of resolved-sideband cooling—an example of coherent feedback control—and optimal linear measurement-based feedback cooling for a harmonic oscillator. These results are valid to leading order in the small parameters that define this regime. They provide insight into the origins of the limitations of coherent and measurement-based feedback for linear systems, and the relationship between them. These limitations are not fundamental bounds imposed by quantum mechanics, but are due to the fact that both cooling methods are restricted to use only a linear interaction with the resonator. We compare the performance of the two methods on an equal footing—that is, for the same interaction strength—and confirm that coherent feedback is able to make much better use of the linear interaction than measurement-based feedback. We find that this performance gap is caused not by the back-action noise of the measurement but by the projection noise. We also obtain simple expressions for the maximal cooling that can be obtained by both methods in this regime, optimized over the interaction strength.

We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: (i) The classical part associated with the Fisher information of the probability distribution of the states contributing to the decomposition, and (ii) the quantum part given by the average quantum Fisher information of the states in this decomposition. Next we use a non-Hermitian extension of a symmetric logarithmic derivative in order to obtain another upper bound on quantum Fisher information, which helps to derive a closed form for the bound in evolutions having the semigroup property. We enhance the extended convexity with this concept of a non-Hermitian symmetric logarithmic derivative (which we show is computable) to lay out a general metrology framework where the dynamics is described by a quantum channel and derive the ultimate precision limit for open-system quantum metrology. We illustrate our results and their applications through two examples where we also demonstrate how the extended convexity allows identifying a crossover between quantum and classical behaviors for metrology.

We analyze the random unitary evolution of a qubit within the memory kernel approach. We provide sufficient conditions which guarantee that the corresponding memory kernel generates physically legitimate quantum evolution. Interestingly, we are able to recover several well-known examples and to generate new classes of nontrivial qubit evolution. Surprisingly, it turns out that a class of quantum evolutions with a memory kernel generated by our approach gives rise to the vanishing of a non-Markovianity measure based on the distinguishability of quantum states.

Digital signatures guarantee the authenticity and transferability of messages and are widely used in modern communication. The security of currently used classical digital signature schemes, however, relies on computational assumptions. In contrast, quantum digital signature (QDS) schemes offer information-theoretic security guaranteed by the laws of quantum mechanics. We present two QDS protocols which have the same experimental requirements as quantum key distribution, which is already commercially available. We also give a security proof for the presented QDS schemes against coherent forging attacks.

Using the inelastic x-ray scattering with a high resolution of 70 meV, squared form factors of molecular carbon monoxide have been determined from the ground state $X{}^1{\Sigma }^{+}$ to the vibronic states of $A{}^1\Pi$ and $B{}^1{\Sigma }^{+}$. Since the first Born approximation is satisfied in inelastic x-ray scattering, the inelastic squared form factors of the valence-shell excitations of carbon monoxide measured by this work not only provide the experimental benchmark data but also serve as the high-energy limit for the electron impact method. Based on the present experimental results, the validity conditions of the previous electron impact works are discussed. It is found that for the excitations of $A{}^1\Pi ({\nu }^{\prime }=0\text{–}6)$ the first Born approximation is reached in the region of $q^2<0.7$ a.u. at an impact electron energy of 1.5 keV, while for $B{}^1{\Sigma }^{+}({\nu }^{\prime }=0)$ the first Born approximation does not fully hold at the impact electron energy of 1.5 keV except for the $q^2<0.15$ a.u. The large discrepancies between the present inelastic x-ray scattering results and the theoretical calculations for most transitions suggest that the formerly reported calculations are not accurate enough.

We show numerically that a rotating, harmonically trapped mixture of two Bose-Einstein-condensed superfluids can—contrary to its single-species counterpart—contain a multiply quantized vortex in the ground state of the system. This giant vortex can occur without any accompanying single-quantum vortices, may either be coreless or have an empty core, and can be realized in a ${}^{87}\mathrm{Rb}\text{−}{}^{41}\mathrm{K}$ Bose-Einstein condensate. Our results not only provide a rare example of a stable, solitary multiquantum vortex but also reveal exotic physics stemming from the coexistence of multiple, compositionally distinct condensates in one system.

We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic traps with external spin-orbit potentials and short-range two-body interactions. Using a truncated basis of total angular momentum eigenstates, nonperturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.

We use time-domain numerical simulations of a two-dimensional scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a low electric-field intensity, we observe strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a higher intensity induces a nonlinear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in nonlinear Rabi oscillations. The transition between the two regimes is observed and an analytical model is proposed which accurately describes our numerical observations.

A study of the mode-locking lasing pulse formation in closed cavities is presented within a statistical-mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into the system. Electromagnetic modes are represented by classical degrees of freedom of a Hamiltonian model at equilibrium in an effective ensemble corresponding to the stationary laser regime. By means of optimized Monte Carlo numerical simulations, the system properties are analyzed while varying mode interaction dilution, gain profile, and number of modes. Properties of the resulting mode-locking laser phase are presented that were not observed in previous approaches based on mean-field approximations. For strong dilution of the nonlinear interaction network, power condensation occurs as the total optical intensity is taken by a few electromagnetic modes, whose number does not depend on the size of the system. For all reported cases, laser thresholds, intensity spectra, phase waves, and ultrafast electromagnetic pulses are computed.

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a nonguess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and nonguess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.

We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.

Analytical expressions are derived for the fidelity and for the quantum Loschmidt echo in the broken phase of the Lipkin-Meshkov-Glick (LMG) model for large particle number $N$. A detailed comparison is given between this model and some other models for the decaying behaviors of the two quantities in the neighborhood of critical points. The two quantities show qualitatively different decaying behaviors on the two sides of the critical point. Specifically, in the broken phase they behave in a way similar to those in models such as the one-dimensional Ising chain in a transverse field. In contrast, in the symmetric phase, the similarity is to those in models such as the Dicke model.

We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are the worst possible pure states, so our solutions have an operational interpretation as being highly nonstabilizer. The optimal strategy for a qudit version of the Clauser-Horne-Shimony-Holt game in prime dimensions is achieved by measuring maximally entangled states that are isomorphic to single-qudit magic states. These magic states have an appealingly simple form, and our proof shows that they are “balanced” with respect to all but one of the mutually unbiased stabilizer bases. Of all equatorial qudit states, magic states minimize the average entropic uncertainties for collision entropy and also, for small prime dimensions, min-entropy, a fact that may have implications for cryptography.

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitates successful optimization.

We propose an efficient method to filter out single atoms from trapped ensembles with unknown numbers of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg excitation of all the other atoms within the ensemble. This triggers the excitation of Rydberg-blockaded atoms to short-lived intermediate states and their subsequent decay to untrapped states. Using an auxiliary microwave field to carefully engineer the dissipation, we obtain a nearly deterministic single-atom source. Our method is applicable to small atomic ensembles in individual microtraps and in lattice arrays.

We study the evolution of a system of interacting ultracold bosons which presents nonlinear, chaotic behaviors in the limit of a very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches—exact diagonalization, the truncated Husimi method, and the mean-field (Gross-Pitaevskii) approximation—we put into evidence the destructive impact of quantum noise on the emergence of nonlinear dynamics.

A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent “anomalous” velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.

By properly driving a qubit-resonator system in the strong dispersive regime, we implement an “impedance-matched” $\Lambda$ system in the dressed states, where a resonant single photon deterministically induces a Raman transition and excites the qubit. Combining this effect and a fast dispersive readout of the qubit, we realize a detector of itinerant microwave photons. We theoretically analyze the single-photon response of the $\Lambda$ system and evaluate its performance as a detector. We achieve a high detection efficiency without relying on precise temporal control of the input pulse shape and under a conservative estimate of the system parameters. The detector can also be reset quickly by applying microwave pulses, which allows a short dead time and a high repetition rate.

We propose an interferometric method for statistically discriminating between nonorthogonal states in high-dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases.