Quantum optimal control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: numerical approaches iteratively work toward a given target by parametrizing the applied time-dependent fields with a finite set of variables. The effectiveness of the resulting optimization depends on the complexity of the problem and the number of variables. We consider different parametrizations in terms of basis functions, asking whether the choice of the applied basis affects the quality of the optimization. Furthermore, we consider strategies to choose the most suitable basis. For comparison, we test three different randomizable bases—introducing the sinc and sigmoid bases as alternatives to the Fourier basis—on QOC problems of varying complexity. For each problem, the basis-specific convergence rates result in a unique ranking. Especially for expensive evaluations, e.g., in closed loop, a potential speedup by a factor of up to 10 may be crucial for the optimization's feasibility. We conclude that a problem-dependent basis choice is an influential factor for QOC efficiency and provide advice for its approach.

Quantum fluctuations are inherent in open quantum systems and they affect not only the statistical properties of the initial state but also the time evolution of the system. Using a generic minimal model, we show that quantum noise smooths the transition between a stationary and a dynamical phase corresponding to a limit cycle (LC) in the semiclassical mean-field approximation of a generic open quantum system. Employing truncated Wigner approximation, we show that the inherent quantum noise pushes the system to exhibit signatures of LCs for interaction strengths lower than the critical value predicted by the standard mean-field theory, suggesting a noise-induced emergence of temporal ordering. Our work demonstrates that the apparent crossover-like behavior between stationary phases brought by finite-size effects from quantum fluctuations also apply to transitions involving dynamical phases. To demonstrate this on a specific physical system, we consider a transversely pumped atom-cavity setup, wherein LCs have been observed and identified as continuous time crystals. We compare the oscillation frequencies of the LCs in the one-dimensional (1D) and two-dimensional regimes, and find that the frequencies have larger shot-to-shot fluctuations in 1D. This has an important consequence in the effectiveness of entrainment of LCs for a periodically driven pump intensity or light-matter coupling strength.

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.

In the convergent close-coupling method for calculating electron-atom scattering, excitation and ionization are associated with cross sections of negative- and positive-energy target states, respectively. We show that the zero-energy boundary can be continuously accessed from either the negative- or positive-energy side, thereby enabling the estimation, via interpolation, of cross sections of arbitrarily high-level Rydberg target states for the target orbital angular momentum included in the calculations.

We find a chiral superfluid (CSF) phase in a one-dimensional Bose-Fermi Hubbard model with significant mass and density imbalance between the two species. In the CSF phase, bosons condensate at nonzero momentum $\pm 2\pi /L$ with chain length $L$. To capture the essential physics of this phenomenon, we study an alternative simplified model that only features competition between single-fermion hopping and hopping of composite particles composed of a fermion and a boson. This model captures the low-energy physics of the Hubbard model and hosts a robust CSF phase. Our numerical studies show that in the CSF phase, the local superfluid order parameter continuously rotates along the chain, indicating that time-reversal symmetry is spontaneously broken. This symmetry breaking generates an emergent flux in the background, effectively optimizing the system's ground-state energy. We provide a physical understanding at the mean-field level. Furthermore, we have explored the potential realization of this phase in cold-atom experiments.

While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. Using multichannel quantum-defect theory, we derive a multichannel expression for the Smith lifetime $Q$ matrix that is valid far away from scattering resonances. For collisions mediated by short-range interaction potentials of the form $-C_6/R^6$, we obtain the average time delay in the incident $s$-wave collision channel in the limit of zero collision energy $E$ as $Q_{11}=A/\sqrt{E}+B$, where $A$ and $B$ are constants. We show that the time delay is dominated by elastic scattering and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the $S$ matrix and shortens with increasing the short-range loss parameter $y$.

We present an entangled photon source that produces polarization entanglement in highly nondegenerate photon pairs, generated through Type-0 spontaneous parametric down conversion using bulk periodically poled lithium niobate. This source is specifically designed for entanglement-based quantum key distribution between ground and satellite, as part of the Quantum Encryption and Science Satellite mission funded by the Canadian Space Agency. Through the utilization of birefringent beam displacers in a Sagnac interferometer scheme, we ensure high polarization contrast and stable interference of highly nondegenerate photon pairs. However, this approach causes substantial spatial and temporal walk-offs of the photon paths, posing a formidable challenge. We introduce an effective compensation method using birefringent crystal wedges to eliminate spatial and temporal walk-offs simultaneously. With only $1.0\mathrm{m}\mathrm{W}$ of pump power, we observed a coincidence rate of $(33.33\pm 0.05)\mathrm{kHz}$, a significant improvement compared to the rate of $(4.20\pm 0.01)\text{kHz}$ without spatial compensation. Additionally, we observed an estimated pair generation rate of $(2.92\pm 0.12)\text{MHz}$ and an entanglement visibility of $(97.1\pm 0.3)\%$, making this a promising source for long-distance quantum communication in ground-to-satellite and fiber optic links.

We theoretically demonstrate that the hallmarks of correlation and fermionization in a one-dimensional exciton-polariton gas can be observed with state-of-the-art technology. Our system consists of a chain of excitonic quantum dots coupled to a photonic waveguide, with a low filling of polaritons. We analytically identify the Tonks-Girardeau, Tavis-Cummings, and mean-field limits and relate them to different regimes of excitonic anharmonicity and photonic bandwidth. Using matrix-product states, we numerically calculate the ground-state energies, correlation functions, and dynamic structure factor of the system. In particular, the latter has a finite weight in the Lieb-Liniger hole branch, and the density-density correlator displays Friedel-like oscillations for realistic parameters, which reveal the onset of fermionization close to the Tonks-Girardeau regime. Our work encourages future experiments aimed at observing, for the first time and in spite of the moderate excitonic anharmonicity, strongly correlated exciton-polariton physics.

Floquet theory and other established semiclassical approaches are widely used methods to predict the state of externally driven quantum systems, yet they do not allow the prediction of the state of the photonic driving field. To overcome this shortcoming, the photon-resolved Floquet theory (PRFT) was developed recently [Phys. Rev. Res. 6, 013116 (2024)], which deploys concepts from full-counting statistics to predict the statistics of the photon flux between several coherent driving modes. In this paper, we study in detail the scaling properties of the PRFT in the semi-classical regime. We find that there is an ambiguity in the definition of the moment-generating function, such that different versions of this function produce the same photonic probability distribution in the semiclassical limit, and generate the same leading-order terms of the moments and cumulants. Using this ambiguity, we establish a simple expression for the Kraus operators, which describe the decoherence dynamics of the driven quantum system appearing as a consequence of the light-matter interaction. The PRFT will pave the way for improved quantum sensing methods, e.g., for spectroscopic quantum sensing protocols, reflectometry in semiconductor nanostructures, and other applications, where the detailed knowledge of the photonic probability distribution is necessary.

Photon-resolved Floquet theory keeps track of the photon exchange of a quantum system with a coherent driving field. It thus complements the standard full-counting statistics that counts the number of photons exchanged with incoherent photon modes giving rise to dissipation. In this paper, we introduce a unifying framework describing both situations. We develop methods suitable for an analytical evaluation of low-order cumulants of photonic probability distributions. Within this framework we analyze the two-mode Jaynes-Cummings model to demonstrate that the photon-resolved Floquet theory and the standard full-counting statistics make consistent statistical predictions. Interestingly, we find that the photon-flux fluctuations diverge for vanishing dissipation, which can be related to an entanglement effect between the driven matter system and the driving field. To substantiate our results, we use our framework to describe efficient photon up-conversion in an ac-driven lambda system, that is characterized by a high signal-to-noise ratio. Because the framework is nonperturbative and predicts fluctuations, it paves the way toward nonperturbative spectroscopy, which will assist to improve metrological methods.

The Stern-Gerlach experiment (SGE) has been known for decades, but a complete theory that explains all facets of it remains enigmatic. In its classic realization, each spin state of an atom follows a unique path or trajectory in an SGE. The enigmatic part is the final output of SGE. Feynman envisaged the outcome to be an entangled state, a superposition of $|\text{spin}\text{state}\rangle \otimes |\text{corresponding}\text{path}\rangle$. Later works described the final state of SGE as a mixed state, a weighted average of states belonging to separate beams or trajectories. Notably, Schwinger, Englert, and Scully compared the difficulty of obtaining a coherent output (a pure state) to “putting together Humpty Dumpty” again. Yet recent experiments using Bose-Einstein condensates indicate the emerging beams are partly coherent, favoring Feynman's description. In this work, we revisit SGE using a recent version of the quantum master equation. We show that both outcomes are probable depending on the time of flight and the timescale of the environmental fluctuations. We predict the output is initially coherent and grows gradually into a mixed state. Moreover, we also estimate how the magnetic-field gradient helps broaden the beam waist. Moreover, our treatment implies that the wave function of an atom passing through a Stern-Gerlach device does not undergo an instantaneous collapse; rather, a gradual decay of coherences results in a mixed state, resulting in an irreversible process.

Manipulating entanglement, which reflects nonlocal correlations in a quantum system and defines the complexity of describing its wave function, represents the extremely tough challenge in the fields of quantum computing, quantum information, and condensed matter physics. In this work, by the example of the well-structured Dicke states we demonstrate that the complexity of these real-valued wave functions can be accurately tuned by introducing a random-sign structure, which allows us to explore the regime of the volume-law entanglement. Importantly, setting nontrivial sign structure one can increase the entanglement entropy of the Dicke state to the values that are close to Page's estimates for Haar-random states. The practical realization of these random-sign Dicke states is possible on different physical platforms with shallow quantum circuits. On the level of the measurements the change in the quantum state complexity due to sign structure can be traced out with the dissimilarity measure that estimates multiscale variety of patterns in bit-string arrays.

The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions, given that certain symmetric measurements exist. They are based on the trace norm of correlations obtained from seminal families of quantum measurements, specifically symmetric informationally complete measurements and mutually unbiased bases. Our criteria are strictly stronger than both the well-known fidelity witness criterion and the computable cross-norm or realignment criterion.

The electromagnetic scattering amplitude of a dielectric wedge is not known in closed form. This makes the computation of the Casimir-Polder (CP) interaction between a polarizable particle and a dielectric wedge challenging. This geometry is a prototype for the effect of edges on fluctuation-induced interactions, and hence, it is important to employ new methods for this problem. Using a recently developed multiple-scattering expansion [Emig and Bimonte, Phys. Rev. Lett. 130, 200401 (2023)], here, we implement a basis-free numerical evaluation of this expansion to obtain precise estimates of the CP potential for a wedge over a wide range of dielectric constants. A remarkable finding is that the CP potential for a dielectric wedge with a smoothed edge is closely related to the potential of a sharp wedge made of a perfect electric conductor. The latter potential is known exactly, making this relation particularly useful in practice.

We study theoretically the high-order harmonic generation (HHG) driven by an optical laser pulse in singly ionized gallium using the time-dependent density functional theory (TDDFT). Our numerical calculations are in qualitative agreement with published experimental data that demonstrates enhancement of harmonics with a photon energy close to the energy of autoionizing state (AIS) $3d^{9}4s^{2}4p$. We show that this enhancement originates from the multielectron correlation during the recollision of a photoelectron ejected from the valence $4s$ orbital with an ion in the entire optical range of laser wavelengths. Also, at the resonant wavelengths, the HHG spectrum contains relatively intense harmonics beyond the plateau cutoff given by the classical three-step HHG scenario. Generation of such harmonics in gallium plasma was observed experimentally. We attribute it to the recombination of an electron, ejected by the laser field from the $4p$ level, into a vacancy in the deep $3d$ subshell. In our TDDFT approach with the LB94 approximation for exchange-correlation potential, the energy of the resonant harmonic is $23.4\mathrm{eV}$, which is $1\mathrm{eV}$ higher than the difference between $4p$ and $3d$ levels of stationary energies. The same shift is present in the resonant peak in the photoionization cross section. We explain this shift analytically as a result of the perturbation in electron-electron potential during the AIS resonant population. The same effect causes a shift in the region of below-threshold harmonics enhancement with the energy determined by the $4s\to 4p$ transition.

We develop a lattice model which exhibits topological transitions from $Z_2$ topological insulators to mirror-symmetry-protected topological crystalline insulators by introducing additional spin-orbit coupling terms. The topological phase is characterized by the mirror winding number, defined within the mirror-symmetry-invariant subspace, which ensures the protection of gapless edge states and zero-energy corner states under specific boundary conditions. Additionally, we propose a feasible scheme using ultracold atoms confined in a stacked hexagonal optical lattice with Raman fields to realize the two-dimensional topological crystalline insulators. Detection of the mirror winding number in these systems can be achieved by implementing a simple quench sequence and observing the evolution of the time-of-flight patterns.