We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum circuit representations of the algebraic generators of the relevant Lie algebras allowing the direct implementation of a Cartan decomposition on a quantum computer. The construction is recursive and allows us to expand any circuit down to generators and rotation matrices on individual qubits, where through our recursive algorithm we find that the generators themselves can be expressed with controlled-not (cnot) and swap gates explicitly. Our approach is independent of the standard cnot implementation and can be easily adapted to other cross-qubit circuit elements. In addition to its versatility, we also achieve near-optimal counts when working with cnot gates, achieving an asymptotic cnot cost of $\frac{21}{16}{4}^n$ for $n$ qubits.

The excitation spread caused by Rydberg facilitation in a gas of laser-driven atoms is an interesting model system for studying epidemic dynamics. We derive a mean-field approach to describe this facilitation process in the limits of high and low temperatures, which takes into account Rydberg blockade and the network character of excitation spreading in a low-temperature gas. As opposed to previous mean-field models, our approach accurately predicts all stages of the facilitation dynamics from the initial fast epidemic growth, an extended saturation period, to the final relaxation phase.

A $\mathcal{P}\mathcal{T}$-symmetric optical waveguide has a dielectric function with symmetric and antisymmetric real and imaginary parts, respectively. It is well known that if the amplitude $\sigma$ of the imaginary part of the dielectric function (representing the balanced gain and loss) is small, the $\mathcal{P}\mathcal{T}$-symmetric waveguide can have real guided modes that are confined around the waveguide core and have a real frequency and a real propagation constant. Many studies on $\mathcal{P}\mathcal{T}$-symmetric waveguides are concerned with the dependence of guided modes on $\sigma$ for a fixed frequency. In particular, $\mathcal{P}\mathcal{T}$-symmetric waveguides have exceptional points (EPs) where typically two guided modes coalesce to a single degenerate mode. We analyze the dispersion curves of the real guided modes in a $\mathcal{P}\mathcal{T}$-symmetric waveguide, show that for any positive $\sigma$ the number of dispersion curves is always finite and, when $\sigma$ is increased, each dispersion curve goes through two transitions and finally disappears on the light line. The EPs in $\mathcal{P}\mathcal{T}$-symmetric waveguides are normally studied for a fixed frequency with $\sigma$ being the parameter. We show that the dispersion curves of the real guided modes have local extremum points that are EPs with alternative parameters. The evolution of real dispersion curves (as $\sigma$ is increased) is accompanied by the appearance and disappearance of different types of EPs. Although our study is based on a simple $\mathcal{P}\mathcal{T}$-symmetric slab waveguide, similar results are expected for other $\mathcal{P}\mathcal{T}$-symmetric waveguides.

In this work, we explore the $\mathcal{PT}$-symmetric quantum Rabi model, which describes a $\mathcal{PT}$-symmetric qubit coupled to a quantized light field. By employing the adiabatic approximation (AA), we are able to solve this model analytically in the parameter regime of interest and analyze various physical aspects. We investigate the static and dynamic properties of the model, using both the AA and numerical diagonalization. Our analysis reveals a multitude of exceptional points (EPs) that are closely connected with the exactly solvable points in the Hermitian counterpart of the model. Intriguingly, these EPs vanish and revive depending on the light-matter coupling strength. Furthermore, we discuss the time evolution of physical observables under the non-Hermitian Hamiltonian. Rich and exotic behaviors are observed in both strong and ultrastrong coupling regimes. Our work extends the theory of $\mathcal{PT}$ symmetry into the full quantum light-matter interaction regime and provides insights that can be readily enlarged to a broad class of quantum optical systems.

We investigate the radiation of optical angular momentum by a dipole gas under uniform magnetic field with an unpolarized source at its center. Conservation of angular momentum implies a torque on both the source and the surrounding environment. We study the separate spin and orbital contributions to the radiated angular momentum.

We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time evolution and that it can describe a nonquantum hydrogenlike system which is stable, has discrete energy levels, and includes the Zeeman effect. This allows us to study dynamical effects such as excitations of the hydrogenlike system by a resonant laser and Rutherford scattering. Our construction demonstrates that classical theory and quantum theory can be seen as specific choices of general probabilistic theory in phase space and that other probabilistic theories also lead to measurable predictions.

We present a scheme for the charging of a quantum battery based on the dynamics of an open quantum system undergoing coherent quantum squeezing and affected by an incoherent squeezed thermal bath. We show that quantum coherence, as instigated by the application of coherent squeezing, is key in the determination of the performance of the charging process, which is efficiency-enhanced at low environmental temperatures and under a strong squeezed driving.

The natural widths of atomic resonances do not broaden spectral lines of emitted particles, which makes the corresponding spectroscopies suitable for high-resolution studies of x-ray absorption. While resonant inelastic x-ray scattering (RIXS) results in a narrow-band x-ray signal which primarily depends on the charge of the emitter, the resonant Auger (RA) emission is more dispersed and promises the separation of individual atomic resonances. To disentangle the $1s^{-1}3p^{-1}nl{n}^{\prime }{l}^{\prime }$ absorption spectrum in Ar, we have measured a sequence of $K{M}_{23}-L_{23}^2{M}_{23}$ RA spectra with a high experimental resolution. Although only parts of the RA spectra were reliably isolated due to the strong overlap with the intense $K-L^2$ Auger emission from ions, the data analysis shows contributions from separate groups of resonances to the Auger signal in greater detail compared to the previous high-resolution absorption and RIXS studies. The calculated differential cross sections are consistent with the available experimental results when the angular dependence of RA emission and the interference of absorption-emission paths through different resonances are accounted for.

Quantum optomechanical systems enable the study of fundamental questions on the quantum nature of massive objects. For that a strong coupling between light and mechanical motion is required, which presents a challenge for massive objects. In particular, large interferometric sensors with low-frequency oscillators are difficult to bring into the quantum regime. Here we propose unbalancing the central beam splitter in the Michelson-Sagnac interferometer, which allows us to boost the optomechanical coupling strength compared with a balanced beam splitter. This unbalancing allows us to enhance the cooperative action of two types of optomechanical coupling present in the system: dissipative and dispersive. We analyze two different configurations, in which the optomechanical cavity is formed by the mirror for the laser pump field (power recycling) and by the mirror for the signal field (signal recycling). We show that the imbalance of the beam splitter allows us to dramatically increase the optical cooling of the test-mass motion. We also formulate the conditions for observing quantum radiation-pressure noise and ponderomotive squeezing. Our configuration could serve as the basis for more complex modifications of the interferometer that would utilize the enhanced coupling strength. This would allow us to efficiently reach the quantum state of large test masses, opening the way to studying the fundamental aspects of quantum mechanics and the experimental search for quantum gravity.

We demonstrate a key ingredient in a bottom-up approach to building complex quantum matter using thermal atomic vapors. We isolate and track very slowly moving individual atoms without the aid of laser cooling. Passive filtering enables us to carefully select atoms whose three-dimensional velocity vector has a magnitude below $\overline{v}/20$, where $\overline{v}$ is the mean velocity of the ensemble. Using a photon correlation technique, we can extract the velocity distributions. We can also follow the trajectory of slowly moving single atoms for more than $1\mu \mathrm{s}$ within a $25\text{−}\mu \mathrm{m}$ field of view, with no obvious limit to the tracking ability while simultaneously observing Rabi oscillations of these single emitters. In addition, we measure the third-order correlation function of single thermal atoms. Our results demonstrate the power and scalability of thermal ensembles for utilization in quantum memories, imaging, and other quantum information applications through bottom-up approaches.

We propose a technique to improve the probability of single-photon emission with an electrically pumped quantum dot in an optical microcavity by continuously monitoring the dot's energy state and using feedback to control when to stop pumping. The goal is to boost the probability of single-photon emission while bounding the probability of two or more photons. We model the system by a stochastic master equation that includes postmeasurement operations. Ideally, feedback should be based on the entire continuous measurement record, but in practice, it may be difficult to do such processing in real time. We show that even a simple threshold-based feedback scheme using measurements at a single time can improve performance over deterministic (open-loop) pumping. This technique is particularly useful for strong dot-cavity coupling with lower rates of pumping, as can be the case for electrical pumping. It is also numerically tractable since we can perform ensemble averaging with a single master equation rather than averaging over a large number of quantum trajectories.

Conventional methods of measuring entanglement in a two-qubit photonic mixed state require detection of both qubits. We generalize a recently introduced method which does not require detection of both qubits, by extending it to cover a wider class of entangled states. Specifically, we present a detailed theory that shows how to measure entanglement in a family of two-qubit mixed states, obtained by generalizing Werner states, without detecting one of the qubits. Our method is interferometric and does not require any coincidence measurement or postselection. We also perform a quantitative analysis of anticipated experimental imperfections. We show that the method is resistant to a decrease in the interference visibility resulting from such imperfections.

We analyze the robust character against the nonstatic noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in ${}^{87}\mathrm{Rb}$. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the deco- herence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (sinusoidal driving) field of control can be appropriately chosen to force the nonstatic random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_{\text{out}}\propto \sqrt{N}$ scaling of the number of surviving photons $N_{\text{out}}$ in the number of input photons $N$. We numerically verify this result using a tensor network algorithm with $\mathrm{U}\left(1\right)$ symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.

Many quantum algorithms demand a large number of repetitions to obtain reliable statistical results. Thus, at each repetition it is necessary to reset the qubits efficiently and precisely in the shortest possible time, so that quantum computers actually have advantages over classical ones. In this work, we perform a detailed analysis of three different models for information resetting in superconducting qubits. Our experimental setup consists of a main qubit coupled to different auxiliary dissipative systems, which are employed in order to perform the erasure of the information of the main qubit. Our analysis shows that it is not enough to increase the coupling and the dissipation rate associated with the auxiliary systems to decrease the resetting time of the main qubit, a fact that motivates us to find the optimal set of parameters for each studied approach, allowing a significant decrease in the reset time of the three models analyzed.

In the standard weak measurement, the imaginary part of the weak value is usually constructed with a specific pre- or postselection state to cause a large shift of the frequency-domain pointer. In this paper we demonstrate that the purely real weak value can also shift the frequency-domain pointer when using a broad-spectrum light source. The reason for the deflection of the frequency-domain pointer in this scheme is that the postselection probability of different frequency is different, which causes the rearrangement of the amplitudes of the spectrum. The weak measurement with real weak value can be used for the estimation of time delay, and it is found that it can reach the same high resolution as the standard weak measurement in some sensitive regions.

Developing effective methods to measure the enantiomeric excess of chiral mixtures is one of the major topics in chiral molecular research but remains challenging. An enantiodetection method via two-dimensional (2D) spectroscopy based on a four-level model containing a cyclic three-level system (CTLS) of chiral molecules was recently proposed and demonstrated, but with a strict condition of one-photon resonance (where three driving fields are exactly resonantly coupled to the three electric dipole transitions) in the CTLS and narrow-band probe-pulse assumption. Here, we extend the 2D spectroscopy method to more general experimental conditions, with three-photon resonance (where the sum of the two smaller frequencies among the three driving fields equals the third one) and a broadband probe pulse. Our method remains effective on enantiodetection with the help of experimental techniques such as the chop-detection method, which is used to eliminate the influence of the other redundant levels that exist in the real system of chiral molecules. Under these more general conditions, the enantiomeric excess of the chiral mixture is estimated by taking an easily available standard sample (usually the racemic mixture) as the reference.

Associative ionization in collisions of ${\mathrm{H}}^{+}+{\mathrm{H}}^{-}$ as well as $\mathrm{H}\left(1s\right)+\mathrm{H}\left(ns\right)$ with $n=2,3,4$ is studied theoretically. Relevant adiabatic potential curves and nonadiabatic couplings are calculated ab initio and the autoionization from the lowest electronic resonant states in the ${}^1{\mathrm{\Sigma }}_{g/u}^{+}$ and ${}^3{\mathrm{\Sigma }}_{g/u}^{+}$ symmetries are considered. The cross sections are obtained by solving the coupled Schrödinger equation, including a complex potential matrix, in a strict diabatic representation. The importance of using a nonlocal description of autoionization is investigated. Associative ionization is also studied for different isotopes of hydrogen. Calculated cross sections are compared with results from measurements.

We perform detailed calculations of the electronic structure of the ${\mathrm{Os}}^{16+}$ ion and demonstrate that it has several metastable states which can be used for very accurate optical clocks. The clocks are highly sensitive to manifestations of the physics beyond the standard model, such as time variation of the fine-structure constant $\alpha$, interaction with scalar and pseudoscalar (axion) dark matter fields, local Lorentz invariance and local position invariance violations, and interaction of atomic electrons with a nucleus mediated by a new boson. The latter can be studied by analyzing the King plot for isotope shifts and its possible nonlinearities since Os has five stable isotopes with zero nuclear spin. Similar calculations for the ${\mathrm{Ir}}^{17+}$ ion spectra demonstrate good agreement between theory and experiment. This helps to validate the method of the calculations and demonstrate that both ions are excellent candidates for the search for new physics.