The $X$-wave formation during the propagation of bichromatic femtosecond laser pulses in an air plasma filament and THz radiation generation has been investigated both experimentally and theoretically. We found that in this case the pump waves as well as THz radiation propagate as $X$ waves at the same group velocity. Therefore, the cone angle of generated THz radiation could be estimated using the $X$-wave dispersion law. Hence, the proposed model allows an alternative characterization of generated THz radiation based on the frequency-angular spectra of pump waves registered after propagation in the created plasma filament.

We investigate the influence of relativistic nondipole effects on the photoelectron spectra of argon, particularly in the low-kinetic-energy region (0–1 eV). In our experiment, we use intense, linearly polarized 800-nm laser pulses to ionize Ar from a jet and we record photoelectron energy and momentum distributions using a reaction microscope. Our measurements show that nondipole effects can cause an energy-dependent asymmetry along the laser propagation direction in the photoelectron energy and momentum spectra. Model simulation based on the time-dependent Dirac equation can reproduce our measurement results. Moreover, the electron trajectory analysis based on the classical model reveals that the photoelectrons obtain a negative momentum shift in the laser propagation direction due to the interplay between the Lorentz-force-induced radiation pressure during its free propagation in the continuum and rescattering by the Coulomb potential of the parent ion when it is driven back by the laser field.

The dynamics of open quantum systems is often modeled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the outcome of ideal single experiments—the “clicks” of a perfect detector due to, e.g., spontaneous emission. The correct description of quantum jumps, which are related to random events characterizing a sudden change in the wave function of an open quantum system, is pivotal to the definition of quantum trajectories. In this article, we extend the formalism of quantum trajectories to open quantum systems with ultrastrong coupling (USC) between light and matter by properly defining jump operators in this regime. In such systems, exotic higher-order quantum-state and energy transfer can take place without conserving the total number of excitations in the system. The emitted field of such USC systems bears signatures of these higher-order processes, and significantly differs from similar processes at lower coupling strengths. Notably, the emission statistics must be taken at a single quantum trajectory level, since the signatures of these processes are washed out by the “averaging” of a master equation. We analyze the impact of the chosen unraveling (i.e., how one collects the output field of the system) for the quantum trajectories and show that these effects of the higher-order USC processes can be revealed in experiments by constructing histograms of detected quantum jumps. We illustrate these ideas by analyzing the excitation of two atoms by a single photon [Garziano et al., Phys. Rev. Lett. 117, 043601 (2016)]. For example, quantum trajectories reveal that keeping track of the quantum jumps from the atoms allows one to reconstruct both the oscillations between one photon and two atoms as well as emerging Rabi oscillations between the two atoms.

The interaction between matter and squeezed light has mostly been treated within the approximation that the field-correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the systems producing the light. We develop a general purpose input-output theory for a particular form of narrowband squeezed light, a squeezed wave-packet mode, that only concerns the statistics of the squeezed field and the shape of the wave packet. This formalism allows us to derive the input-output relations and the master equation. We also consider detecting the scattered field using photon counting and homodyne measurements, which necessitates the derivation of the stochastic master equation. The non-Markovian nature of the field manifests itself in the master equation as a coupled hierarchy of equations. We illustrate these with consequences for the decay and resonance fluorescence of two-level atoms in the presence of such fields.

Doppler-free three-photon coherence effects at a wavelength of $253.7\mathrm{nm}$ were observed in thermal mercury vapor. The experimental results are compared to simulations based on a detailed theoretical model reproducing the measured effects. Based on these results, we show by simulations that amplification without inversion in our setup is feasible, paving the way towards lasing without inversion in mercury.

The topological charge of a photonic vortex is an essential quantity in singular optics and the critical parameter to characterize the vorticity of twisted light. However, the definition of the photonic topological charge remains elusive. Here we put forth a theoretical formalism to provide a comprehensive treatment of photonic vortices. We introduce quantum operators for the photon current density and helicity current density based on the continuity equations from the paraxial Helmholtz equation. Our formalism allows us to introduce flow velocity and circulation for photonic currents in parallel to their counterparts in superfluids. The quantized circulation of the photonic currents is conserved during propagation and it gives an explicit definition of the photonic topological charge as the winding number of a photonic vortex. In particular, we predict helicity current generated pure-helicity vortices, in which the photon current vanishes. Finally, we show an interesting effect that the quantum statistics of twisted photon pairs are essentially determined by their spin states.

We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that such errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detection-induced coherent errors, the exact surface code becomes an approximate QECC.

The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that the Hilbert state dimension is known. It is explicitly proved that the maximum certifiable entropy that can be obtained through this set of protocols is $-{log}_2\left[\frac{1}{2}(1+\frac{1}{\sqrt{3}})\right]$ and the same is independent of the dimension witnesses used to certify the protocol. The minimum number of preparation and measurement settings required to achieve this entropy is also proven. An SDI protocol that generates the maximum output entropy with the least amount of input setting is provided. An analytical relationship between the entropy generated and the witness value is obtained. It is also established that certifiable entropy can be generated as soon as the dimension witness crosses the classical bound, making the protocol noise-robust and useful in practical applications.

The Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr interaction between a squeezed light and a superposition of Fock states. We numerically show that the GKP qubit with the 10 dB can be generated with mean fidelities of 99.99 and 99.9% at the success probabilities of 2.7 and 4.8%, respectively. Therefore, our method has the potential to generate the optical GKP qubit with a quality required for FTQC when we obtain the sufficient technologies for the preparation of ancillary Fock states and a cross-Kerr interaction.

In this work, we derive analytic formulas that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze and derive expressions for the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows that our formulas are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field inhomogeneities applies to laser-free systems.

We present a hybrid classical-quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources by splitting the workload between classical and quantum processors. This algorithm reduces the needed number of qubits at the expense of an increased number of quantum evaluations. We demonstrate the method for the Hubbard model and show how the conservation of the $z$ component of the total spin allows the spin-up and spin-down configurations to be computed on classical and quantum hardware, respectively. Other symmetries can be exploited in a similar manner.

Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this contribution, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic Ansätze are successful for dissipative dynamics as well, allowing for easier experimental implementations compared to Lindbladian Ansätze involving dissipation. Our approach not only guarantees improvements of open-system adiabaticity but also enhances the success probability of quantum annealing.

Controlled modifications of the magnetic response of a two-level system are produced in dressed systems by one high-frequency, strong, and nonresonant electromagnetic field. This quantum control is greatly enhanced and enriched by a harmonic, commensurable, and orthogonally oriented dual dressing, as discussed here. The secondary field enables a fine tuning of the qubit response, with control parameter amplitude, harmonic content, spatial orientation, and phase relation. Our analysis, mainly based on a perturbative approach with respect to the driving strength, includes also nonperturbative numerical solutions. The Zeeman response becomes anisotropic in a triaxial geometry and includes a nonlinear quadratic contribution. The long-time dynamics is described by an anisotropic effective magnetic field representing the handle for the system full engineering. Through the low-order harmonic mixing, the bichromatic driving generates a synthetic static field modifying the system dynamics. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. In the weak-field direction it compensates the static fields applied in different geometries. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations.

Using a two-dimensional model system for the proton-coupled electron-transfer process, the eigenvalues and nonadiabatic dynamics have been notably investigated by means of diabatic representation in the Born-Oppenheimer picture. Different from a previously reported diabatic model, which was approximately determined by the eigenstates of the differently defined electronic Hamiltonians, the rigorous diabatization was achieved by a fitting method based on the adiabatic energies and derivative couplings. As expected, the rigorous diabatic models were found to be able to accurately reproduce the eigenvalues or nonadiabatic dynamics in the adiabatic representation for three different models. Furthermore, we proposed an approximate diabatic scheme, which was built from fitting the adiabatic energies solely but with a fixed form for the off-diagonal terms in the diabatic potential energy matrix. This approximate diabatic model without the aid of the derivative coupling is shown to be as accurate as the rigorous one, which provides a simple and efficient way to accurately describe the complex proton-coupled electron-transfer processes due to accurately computing derivative couplings that are quite challenging for realistic systems.

We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded DC-superconducting quantum interference device (-SQUID). The DC-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change in the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or $\pi$, whose probability can be controlled by an externally injected signal.

The atom-waveguide interface mediates significant and long-range light-matter interactions through guided modes. In this one-dimensional system, we theoretically investigate the excitation localization of multiple atomic excitations under strong position disorder. Deep in the localization side, we obtain the time evolutions of quantum correlations via Kubo cumulant expansions, which arise initially and become finite and leveled afterward, overtaking those without disorder. This indicates two distinct regimes in time: before the onset of excitation localization, the disorder engage the disturbance of quantum correlations, which is followed by disorder-assisted buildup of quantum correlations that maintain at a later stage owing to the absence of excitations diffusion. The crossing of distinct regimes is pushed further in time for longer-range correlations, which indicates a characteristic timescale needed for disorder to sustain them. We also explore the effect of directionality of couplings and resonant dipole-dipole interactions, which can drive the system toward the delocalized side when it is under chiral couplings or large dipole-dipole interaction strengths. The time-evolved quantum correlations can give insights into the studies of few-body localization phenomenon and nonequilibrium dynamics in open quantum systems.

We consider the probability distribution when the monotonic function $F\left(X\right)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable $X$. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we found that after dividing the nonmonotone function $H\left(X\right)$ into multiple monotone intervals the problem of solving the maximum and minimum expected values of $H\left(X\right)$ can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve two problems in quantum metrology. When studying the quantum parameter estimation in a Mach-Zehnder interferometer, for an equal total input photon number, we found an optimal path-symmetric entangled state that makes the quantum Fisher information of the outcome state take the maximum value, and we proved that the NOON state is the path-symmetric entangled state that makes the quantum Fisher information of the outcome state take the minimum value. Finally, when studying the quantum parameter estimation in the Landau-Zener-Jaynes-Cummings model, we found the optimal initial state of the cavity field that makes the final state of the system obtain the maximum quantum Fisher information.

Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $\xi$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean-field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of the nonlinear terms. We observe the saturation of the cloud expansion of $N$ particles to a volume $\sim N\xi$. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean-field diffusion with the final saturation regime and is entirely controlled by particle number $N$. The temporal window of that regime grows exponentially with the localization length $\xi$.