We propose an all-optical method to reconstruct the transition dipole moment of solid materials. Our method is realized by high-order harmonic generation driving by a multicycle laser pulse. The relations between the transition dipole moment and the harmonic yield are established. It is found that the transition dipole phase is related to the intensity ratio of the neighboring odd and even harmonics, and the modulus of the transition dipole moment is related to the odd harmonics. We investigate the high-order harmonic generation in symmetric crystals and asymmetric crystals by solving the semiconductor Bloch equations and use these relations to successfully reconstruct their relative transition dipole moments.

We consider two noninteracting two-level emitters that are coupled weakly to a one-dimensional nonlinear waveguide. Due to the Kerr-like nonlinearity, the waveguide considered supports—in addition to the scattering continuum—a two-body bound state. As such, the waveguide models a bath with nontrivial mode structure. Solving the time-dependent Schrödinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert-space formulations, which result in effective emitter separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional waveguide did not contain a nonlinearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schrödinger equation based results provide critical guidance for the development of master equation approaches.

We experimentally show that resonance spectra of optical microcavities have a fine structure that resembles the one observed in atoms. We can identify the polarization-resolved modes in the spectrum and distinguish between two intrinsic effects that cause fine structure: (1) an optical spin-orbit coupling and (2) nonparaxial propagation and reflection. The measured effects are intrinsic to cavities and are therefore present in any cavity, in contrast to accidental effects like astigmatism. The analogy of fine structure with atomic physics is surprisingly fruitful and gives accurate theoretical predictions which agree which experiments. This analogy can even predict further splittings like a hyperfine splitting, which in our microcavities is explained by a Bragg effect.

We investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between dispersion and saturable nonlinearity, which we extend in the context of the $\mathcal{PT}$-symmetric coupler. Our investigations of power-controlled and phase-sensitive switching show richer soliton switching dynamics than the currently existing conventional counterparts, which may lead to ultrafast and efficient all-optical switching dynamics at very low power owing to the combined effects of $\mathcal{PT}$ symmetry and saturable nonlinearity. In addition to the input power, the relative phase of the input solitons and saturable coefficient are additional controlling parameters that efficiently tailor the switching dynamics. Also, we provide a suitable range of system and pulse parameters that would be helpful for the practical realization of the coupler to use in all-optical switching devices and photonic circuits. Finally, we develop a variational approach to analytically investigate the switching dynamics in such $\mathcal{PT}$-symmetric couplers that excellently predicts the numerical findings.

Quantum engineering of photons is a key requirement for the development of quantum technology. Here, we put forward a scheme to investigate extensively quantum statistical characteristics of the photons and their engineering in a hybrid nanoparticle-emitter-cavity architecture through placing a nanoparticle (NP) and a quantum emitter (QE), called NP-QE molecule, into an optical cavity, where the coherent tripartite coupling emerges in the interactions among the NP, QE, and cavity. The photons are collected from the two different channels, i.e., the cavity emission and the NP-QE molecule scattering. Due to the composite nature of the tripartite dressed excitations of our fully coupled system and the destructive interference between different transition pathways for the two-photon excitation, the nontrivial quantum statistical properties, such as unconventional single-photon blockade and strong photon superbunching, can be achieved even within the bad cavity limit (without the need of the strong-coupling condition) when the NP-QE molecule is driven by an external laser not interacting the cavity mode. It is also revealed that the photon autocorrelation and cross-correlation properties are well modified by regulating the size-dependent system parameters, such as the NP-to-QE distance and the NP radius. The small-coupling strength required, the ease of parameter tuning, the relaxation of high-cavity quality factor, and the robustness to the dephasing rate in realistic scenarios all benefit the generation of single-photon sources, which has potential applications in quantum information and quantum communication.

Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It is found that the entanglement of photon pairs over the Schmidt modes is one of the sources of distinguishability. The distinguishability is quantified by the symmetric part of the internal state of $n$ pairs of photons over the spectral Schmidt modes, whose normalization $q_{2n}$ is the probability that $2n$ photons interfere as indistinguishable. For two pairs of photons $q_4=(1+2\mathbb{P})/3$, where $\mathbb{P}$ is the purity of the squeezed states ($K=1/\mathbb{P}$ is the Schmidt number). For a fixed purity $\mathbb{P}$, the probability $q_{2n}$ decreases exponentially fast in $n$. For example, in the experimental Gaussian boson sampling of H.-S. Zhong et al., [Science 370, 1460 (2020)], the achieved purity $\mathbb{P}\approx 0.938$ for the average number of photons $2n\ge 43$ gives $q_{2n}\lesssim 0.5$, i.e., close to the middle line between $n$ indistinguishable and $n$ distinguishable pairs of photons. In derivation of all the results, the first-order quantization representation based on the particle decomposition of the Hilbert space of identical bosons serves as an indispensable tool. The approach can be applied also to the generalized (non-Gaussian) squeezed states, such as those recently generated in the three-photon parametric down-conversion.

The Dirac equation for ${\mathrm{H}}_2^{+}$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. D 11, 15 (1989)]. The four-component wave function is expanded in a newly introduced kinetically balanced exponential basis set. The ground-state relativistic energy is obtained with an accuracy of ${10}^{-20}$, which represents an improvement by several orders of magnitude, and is shown to be in good agreement with results obtained from perturbation theory. Highly accurate relativistic wave functions are obtained, which is a first step towards nonperturbative calculations of the one-loop self-energy correction in hydrogen molecular ions.

Homogeneous quantum gases open up new possibilities for studying many-body phenomena and have now been realized for a variety of systems. For gases with short-range interactions the way to make the cloud homogeneous is, predictably, to trap it in an ideal (homogeneous) box potential. We show that creating a close to homogeneous dipolar gas in the roton regime, when long-range interactions are important, actually requires trapping particles in soft-walled (inhomogeneous) box-like potentials. In particular, we numerically explore a dipolar gas confined in a pancake trap which is harmonic along the polarization axis and a cylindrically symmetric power-law potential $r^p$ radially. We find that intermediate $p$'s maximize the proportion of the sample that can be brought close to the critical density required to reach the roton regime, whereas higher $p$'s trigger density oscillations near the wall even when the bulk of the system is not in the roton regime. We characterize how the optimum density distribution depends on the shape of the trapping potential and find it is controlled by the trap wall steepness.

High-dimensional entangled states are of crucial importance, as they provide higher channels for quantum information. Angular position, as a continuous variable, provides an infinite Hilbert space theoretically. It is usually represented in discrete bases experimentally because of the convenient modulation of the width of the angular aperture. Thus the combination of the angular apertures will conveniently shape the two photon states. And the entanglement of the two photon states can be naturally demonstrated by Hardy's paradox. Here, by testing Hardy's paradox for two-setting high-dimensional angular subspaces with dimension ranging from 2 to 7 and for multisetting three-dimensional subspaces with setting ranging from 3 to 5, we reveal the high-dimensional entanglement in the angular-position degree of freedom. We show that the high-dimensional angular-position entanglement can yield a much sharper contradiction between the quantum mechanics and classical theories. Our work shows that the angular variable can be considered as an alternative discrete base to provide the high-dimensional entangled states. Thus it may be used as a new platform for quantum information.

Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging collective effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half-filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in Zanner et al. [Nat. Phys. 18, 538 (2022)] and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.

We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate the error and disturbance of the model and examine the uncertainty relations. We find that, for the coherent light meter in pure polarization, both the error and disturbance behave like the cyclic oscillations due to the Faraday rotation in both the light and spin polarizations. We also examine a class of polarization-squeezed light meter, where we apply the phase-space approximation and characterize the role of squeezing. We derive the error-disturbance relations for these cases and find that the Heisenberg-Arthurs-Kelly uncertainty is violated while the tight Branciard-Ozawa uncertainty always holds. We note that, in the limit of weak interaction strength, the error and disturbance come to obey the unbiasedness condition and hence the Heisenberg-Arthurs-Kelly relation holds. The work contributes to our understanding of the quantum measurement of spin systems under the atom-light interface framework and may hold potential applications in quantum metrology, quantum state estimation, and control.

We analyze the continuous monitoring of a qudit coupled to a cavity using both phase-preserving and phase-sensitive amplification. The quantum trajectories of the system are described by a stochastic master equation, for which we derive the appropriate Lindblad operators. The measurement back-action causes spiraling in the state coordinates during collapse, which increases as the system levels become less distinguishable. We discuss two examples: a two-level system and an $N$-dimensional system and meter with rotational symmetry in the quadrature space. We also provide a comparison of the effects of phase-preserving and phase-sensitive detection on the master equation and show that the average behavior is the same in both cases, but individual trajectories collapse at different rates depending on the measurement axis in the quadrature plane.

The dispersion of a three-way waveguide is engineered to exhibit exceptional modal characteristics. Two coupled waveguides with parity-time ($\mathcal{P}\mathcal{T}$) symmetry have been previously demonstrated to exhibit second order exceptional points of degeneracy (EPDs). In this work, we introduce and investigate a particular class of EPDs, applicable from radio frequency to optical wavelengths, whereby three coupled waveguides satisfy glide-time ($\mathcal{G}\mathcal{T}$) symmetry to exhibit a third order modal degeneracy with a real-valued wave number. $\mathcal{G}\mathcal{T}$ symmetry involves glide symmetry of lossless and gainless components of the waveguide in addition to changing the sign of passive and active elements while applying a glide-symmetry operation. This $\mathcal{G}\mathcal{T}$-symmetry condition allows three Floquet-Bloch eigenmodes of the structure to coalesce to a real-valued wave number at a single frequency, in addition to having one branch of the dispersion diagram with a purely real wave number. The proposed scheme may have applications including but not limited to distributed amplifiers, radiating arrays, and sensors, from radio frequency to optics.

The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these “weak trajectories” with single photons.

In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves a time-reversal procedure to assess the effect of perturbations in a quantum excitation dynamics. However, when addressing macroscopic systems one is repeatedly confronted with limitations that seem insurmountable. This led to the formulation of the central hypothesis of irreversibility stating that the timescale of decoherence, $T_3$, is proportional to the timescale of the many-body interactions we reversed, $T_2$. We test this by implementing two experimental schemes based on Floquet Hamiltonians where the effective strength of the dipolar spin-spin coupling, i.e., $1/T_2$, is reduced by a variable scale factor $k$. This extends the perturbation timescale, $T_{\mathrm{\Sigma }}$, in relation to $T_2$. Strikingly, we observe the superposition of the normalized Loschmidt echoes for the bigger values of $k$. This manifests the dominance of the intrinsic dynamics over the perturbation factors, even when the Loschmidt echo is devised to reverse that intrinsic dynamics. Thus, in the limit where the reversible interactions dominate over perturbations, the LE decays within a timescale, $T_3\approx T_2/R$ with $R=(0.15\pm 0.01)$, confirming the emergence of a perturbation independent regime. These results support the central hypothesis of irreversibility.

In this paper, we investigate quantum decoherence dynamics of a two-level system in colored environments described by stochastic processes. We present the extension of the theoretical framework of the stochastic Liouville approach, and we employ the approach in studying the decoherence dynamics of the two-level system in typical colored environments: the Ornstein-Uhlenbeck environment, a simple fluctuating bottleneck environment, and the dichotomic (two-state) environment. The analytical expressions of the decoherence factor of a two-level system in colored environments are obtained by introducing the marginal average operator, whose eigenvalues and eigenfunctions provide different viewpoints from which to understand the behavior of the decoherence factor. In addition, the investigations provide us a potential way to manipulate the decoherence of the quantum system in colored environments.

A quantum internet connects remote quantum processors that need to interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes operate at the wavelength ranges unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom bands is crucial for long-distance quantum networks based on optical fiber. Here, we propose wavelength conversion devices for single-photon polarization qubits using continuous-variable quantum teleportation that can efficiently convert qubits between near-infrared (780–795 nm suitable for interacting with atomic quantum nodes) and telecom wavelength (1300–1500 nm suitable for long-distance transmission). The teleportation uses entangled photon fields (i.e., nondegenerate two-mode squeezed state) that can be generated by four-wave mixing in a rubidium atomic gas using a diamond configuration of atomic transitions. The entangled fields can be emitted in two orthogonal polarizations with locked relative phase, making them especially suitable for interfacing with single-photon polarization qubits. Our work may pave the way for the realization of long-distance quantum networks.

Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization, and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make an efficient use of the current generation of quantum hardware. However, optimizing variational quantum algorithms is a challenge as it is an nondeterministic polynomial time-hard problem that in general requires an exponential time to solve and can contain many far from optimal local minima. Here, we present a current term NISQ algorithm for solving SDPs. The classical optimization program of our NISQ solver is another SDP over a lower dimensional ansatz space. We harness the SDP-based formulation of the Hamiltonian ground-state problem to design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex and can be solved in polynomial time with the number of ansatz parameters, and every local minimum is a global minimum. We find numeric evidence that NISQ SDP can improve the estimation of ground-state energies in a scalable manner. Further, we efficiently solve constrained problems to calculate the excited states of Hamiltonians, find the lowest energy of symmetry constrained Hamiltonians, and determine the optimal measurements for quantum state discrimination. We demonstrate the potential of our approach by finding the largest eigenvalue of up to $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.

We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal. Holographic codes are interesting examples of tensor-network codes, so we first test out this parallel decoding strategy on the max-rate holographic Steane (heptagon) code. For holographic codes with a constant number of logical qubits, the tensor-network decoder was shown to be efficient with complexity polynomial in $n$, the number of physical qubits. Here we show that, by using the parallel decoding scheme, the complexity is also linear in $k$, the number of logical qubits. We then calculate the bulk threshold (the threshold for logical qubits a fixed distance from the code center) under depolarizing noise for the max-rate holographic Steane code to be $9.4\%$. We also introduce some further holographic error-correcting codes and calculate their thresholds under depolarizing noise. One example is based on an 11-qubit code due to Gottesman, which has asymptotic rate 0.114 and threshold 13.8%. Another code we consider is an asymptotically zero-rate holographic code, which performs extremely well under dephasing noise in the $X, Y$, or $Z$ basis with a threshold of $50\%$.

We present an investigation of the performance of the relativistic multireference Fock-space coupled-cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the ${}^{19}\mathrm{F}$ HFS constant in the ground and excited states of BaF. The ab initio values were compared to the recent experimental results, and good overall agreement within the theoretical uncertainties was found. This work demonstrates the predictive power of the FSCC method and the reliability of the established uncertainty estimates, which can be crucial in cases where the calculated property cannot be directly compared to experiment.