We investigate the controlled manipulation of the Goos-Hänchen (GH) shift in probe light beams, encompassing both plane and Gaussian beams, when introduced into a cavity housing a highly resonant five-level atomic system exhibiting a combined tripod and $\mathrm{\Lambda }$ (CTL) configuration. This complex scheme arises from the interaction of three atomic ground states with two excited states through five distinct light fields. Such a system effectively reduces to a $\mathrm{\Lambda }$- or N-shaped configuration by manipulating the light fields, resulting in the alteration of the dispersion behavior of the probe beam, ultimately inducing either a positive or negative GH shift. This unique behavior is a direct consequence of the closed-loop structure inherent to the five-level atomic scheme. For both plane and Gaussian beams, we demonstrate the superiority of CTL over $\mathrm{\Lambda }$ and $N$ schemes in achieving substantial positive GH shifts. When considering Gaussian probe light, we observe a critical role played by the beam width in controlling the magnitude and sign of the GH shifts. Our proposed approach for studying the GH shift carries significant practical implications, particularly in its capacity to monitor media with either left-handed characteristics displaying negative permittivity and permeability or right-handed characteristics displaying positive permittivity and permeability through the manipulation of externally controlled parameters. This approach may find applications in various fields, including optical heterodyne sensors used to measure beam angle, displacement, temperature, and refractive index, thereby advancing our understanding and control of optical phenomena.

Noiseless measurement of a single quadrature in systems of parametrically coupled oscillators is theoretically possible by pumping at the sum and difference frequencies of the two oscillators, realizing a backaction-evading (BAE) scheme. Although this would hold true in the simplest scenario for a system with pure three-wave mixing, implementations of this scheme are hindered by unwanted higher-order parametric processes that destabilize the system and add noise. We show analytically that detuning the two pumps from the sum and difference frequencies can stabilize the system and fully recover the BAE performance, enabling operation at otherwise inaccessible cooperativities. We also show that the acceleration demonstrated in a weak-signal-detection experiment [Jiang et al., PRX Quantum 4, 020302 (2023)] was only achievable because of this detuning technique.

We propose a method to achieve a coherent switch of optomagnonic entanglement in a cavity optomagnonic system with non-Hermitian coupling. The strength of photon-photon and photon-magnon entanglement can be controlled by tuning the relative phase angle of two nanoparticles and optimizing the detuning of two optical modes. We show that the bipartite entanglement is significantly enhanced by selecting a suitable optomagnonics coupling strength in the presence of the exceptional points (EPs). The relative phase not only enhances the entanglement strength but also increases the entanglement domain over a wide range of detuning compared to the Hermitian system. By manipulating the system toward or away from EPs, versatile tunability of the tripartite entanglement, mean photon, and magnon numbers can be achieved. Additionally, the direction of asymmetric transmission can also be well tuned in a highly asymmetric way via non-Hermitian coupling. The study of controlled entanglement may provide the theoretical basis and reference for the research and development of new tunable quantum devices.

In their recent paper [Phys. Rev. A 97, 062322 (2018)], Wan et al. proposed a quantum algorithm to solve systems of linear equations $Ax=b$, where $A$ is an $n\times n$ Toeplitz matrix generated by the Fourier coefficients of a continuous, $2\pi$-periodic, and positive function $f$. For large enough $n$, they claimed that the algorithm is valid for all $b$. In this Comment we prove that, in general, this is not true.

We study a non-Hermitian Su-Schrieffer-Heeger model with nonreciprocal hopping under periodic driving, and show that the Floquet topological nature and non-Hermiticity can have rich interplay in this non-Hermitian Floquet topological system. We find that both the topological characteristics and the non-Hermitian skin effect are affected by the Floquet driving and can be associated with the quasienergy spectrum topology. For general choice of system and driving parameters, we derive a non-Bloch bulk-boundary correspondence to successfully describe the Floquet topological edge states with non-Hermitian skin effects. We observe interesting bipolar non-Hermitian skin effect by periodically driving the short-range non-Hermitian system, and establish its connection to the winding of Bloch quasienergy spectrum. Finally, we propose to implement the non-Hermitian quantum system with asymmetric hopping in cold atomic gases. Our work demonstrates the impact of periodic driving on non-Hermitian topological systems, and suggests a route to search for richer non-Hermitian skin effects through Floquet engineering.

We calculate the decoherence caused by photon emission for a charged particle traveling through an interferometer; the decoherence rate gives a quantitative measure of how much “which-path” quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and subleading soft photons, and show that it can be extracted entirely from information about the end points of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading-order soft photons then give no contribution to decoherence, and carry no quantum information. The subleading soft photons in contrast may carry finite which-path information, and the subleading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at subleading order; we discuss the possibility of answering this question experimentally.

Using the Wigner-Vlasov formalism, an exact three-dimensional solution of the Schrödinger equation for a scalar particle in an electromagnetic field is constructed. Electric and magnetic fields are nonuniform. According to the exact expression for the wave function, the search for two types of Wigner function is conducted. The first function is the usual Wigner function with a kinetic momentum. The second Wigner function is constructed on the basis of the Weyl-Stratonovich transform [Javanainen et al., Phys. Rev. A 35, 2791 (1987); Nedjalkov et al., Phys. Rev. B 99, 014423 (2019)]. It turns out that the second function, unlike the first one, has areas of negative values for wave functions with the Gaussian distribution (Hudson's theorem). An example of an electromagnetic quantum system described by a non-Gaussian wave function has successfully been found. The second Wigner function is positive over the whole phase space for the non-Gaussian wave function. This result is analogous to the Hudson theorem for the gauge invariant Wigner function. On the one hand, knowing the Wigner functions allows one to find the distribution of the mean momentum vector field and the energy spectrum of the quantum system. On the other hand, within the framework of the Wigner-Vlasov formalism, the mean momentum distribution and the magnitude of the energy are initially known. Consequently, the mean momentum distributions and energy values obtained according to the Wigner functions can be compared with the exact momentum distribution and energy values. This paper presents this comparison and describes the differences. The Vlasov-Moyal approximation of average acceleration flow has been built in phase space for a quantum system with an electromagnetic field. The obtained approximation makes it possible to cut the Vlasov chain off at the second equation and also to analyze the Boltzmann H-function evolution. By averaging the Vlasov-Moyal approximation over momentum space we can derive an expression for the electromagnetic force of the classical system. This averaging makes the high-order quantum terms disappear from the “motion equation.”

We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations, that is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations considered here are the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality and the violation of the $F_3$ inequality for Einstein-Podolsky-Rosen steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomena for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violations of CHSH inequality and $F_3$ inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid center. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and furthermore two-qubit states with locally inaccessible maximal hidden quantum correlations.

Typical measures of nonstabilizerness of a system of $N$ qubits require computing $4^N$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension $2^N$. For permutationally invariant systems, this exponential overhead can be reduced to just $O\left(N^3\right)$ expectation values on a state with a dimension $O\left(N\right)$. We exploit this simplification to study the nonstabilizerness phase transitions of systems with hundreds of qubits.

Utilizing a tritter with variable parameter $T$ and induced by vacuum–one-photon superpositions $|0\rangle +\alpha |1\rangle$ with $\alpha =\left|\alpha \right|e^{i\varphi }$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${|\psi \rangle }_{123}=c_0|000\rangle +c_1|100\rangle +c_2|010\rangle +c_3|001\rangle$. The coefficients $(c_0,$ $c_1,$ $c_2, \text{and} c_3)$ can be manipulated through interaction parameters $\left(\right|\alpha |,$ $\varphi , \text{and} T)$. In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${|\psi \rangle }_{123}$ by using the measure of concurrence fill. Drawing on Hao et al.'s research [Phys. Rev. Lett. 128, 120402 (2022)], we examine tripartite steering for ${|\psi \rangle }_{123}$ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state ${|\psi \rangle }_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.

Quantitative characterization of two-qubit entanglement purification protocols is introduced. Our approach is based on the concurrence and the hit-and-run algorithm applied to the convex set of all two-qubit states. We demonstrate that pioneering protocols are unable to improve the estimated initial average concurrence of almost uniformly sampled density matrices; however, as it is known, they still generate pairs of qubits in a state that is close to a Bell state. We also develop a more efficient protocol and investigate it numerically together with a recent proposal based on an entangling rank-2 projector. Furthermore, we present a class of variational purification protocols with continuous parameters and optimize their output concurrence. These optimized algorithms turn out to surpass former proposals and our protocol by means of not wasting too many entangled states.

Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using what is referred to as the adiabatic condition derived from the adiabatic theorem. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most $\mathrm{\Theta }\left(L\right)$, where $L$ is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. For concrete examples, we consider the adiabatic Grover search and the ferromagnetic $p$-spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap, we are able to achieve a success probability considerably higher than that of conventional QA. Moreover, in concrete examples, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA. Our findings pave the way for a better understanding of QA performance.

In noisy quantum systems, achieving high-fidelity state preparation using the adiabatic approach faces a dilemma: either extending the evolution time to reduce diabatic transitions or shortening it to mitigate decoherence effects. Here we present a quantum shortcut to adiabaticity for state preparation in a finite-sized Jaynes-Cummings lattice by applying counterdiabatic (CD) driving along given adiabatic trajectories. Leveraging the symmetry of eigenstates in our system, we convert the CD driving to an implementable Hamiltonian that only involves local qubit-cavity couplings for a two-site lattice with one polariton excitation. Additionally, we derive a partial analytical form of the CD driving for the lattice with two excitations. Our numerical results demonstrate that circuit errors and environmental noise have negligible effects on our scheme under practical parameters. We also show that our scheme can be characterized through the detection of qubit operators. This approach can lead to a promising pathway to high-fidelity state preparation in a significantly reduced timescale when compared to conventional adiabatic methods.

Using the strong-field-approximation theory beyond the dipole approximation we investigate above-threshold ionization induced by the monochromatic and bichromatic laser fields. Particular emphasis is on the approach based on the saddle-point method and the quantum-orbit theory which provides an intuitive picture of the underlying process. In particular, we investigate how the solutions of the saddle-point equations and the corresponding quantum orbits and velocities are affected by the nondipole effects. The photoelectron trajectories are two dimensional for linearly polarized field and three dimensional for two-component tailored fields, and the electron motion in the propagation direction appears due to the nondipole corrections. We show that the influence of these corrections is not the same for all contributions of different saddle-point solutions. For a linearly polarized driving field, we focus our attention only on the rescattered electrons. On the other hand, for the tailored driving field, exemplified by the $\omega$–$2\omega$ orthogonally polarized two-color field, which is of the current interest in the strong-field community, we devote our attention to both the direct and the rescattered electrons. In this case, we quantitatively investigate the shift which appears in the photoelectron momentum distribution due to the nondipole effects and explain how these corrections affect the quantum orbits and velocities which correspond to the saddle-point solutions.

A density matrix approach was recently developed by Yuen and Lin to study the dissociative sequential double ionization (SDI) of ${\text{N}}_2$ molecules induced by an intense few-cycle infrared laser pulse [Phys. Rev. A 106, 023120 (2022)]. Despite the positions and relative ratios of peaks in the simulated kinetic energy release (KER) spectrum agreeing very well with experiments, the experimental KER spectrum is considerably broader than that obtained from the simulation where both laser couplings between ${\text{N}}_2{}^{2+}$ states and the nuclear vibration distribution of neutral ${\text{N}}_2$ molecules were neglected. Here, we revisit to simulate the experiment by Voss et al. [J. Phys. B: At. Mol. Opt. Phys. 37, 4239 (2004)] and Wu et al. [J. Phys. Chem. A 114, 6751 (2010)] and find that the agreement between the simulated KER spectra and the experiments is improved significantly by considering the laser couplings between ${\text{N}}_2{}^{2+}$ states and nuclear vibration distribution of neutral ${\text{N}}_2$ molecules. This work provides further insights into the SDI dynamics and the influences of nuclear motion on the SDI of molecules.

We investigate the transformation of Rayleigh speckle patterns by an atomic cesium vapor. After propagation through the atomic vapor, the incident exponentially decaying intensity distribution of the Rayleigh speckles is transformed with enhancement of high intensities probabilities (extreme events). The measured intensity distributions are fitted by Weibull distributions. The nonlinear interaction between the atomic vapor and the optical field leads to intensity-dependent refraction and absorption, resulting in changes of the speckle spots' intensities with propagation. We measure the inverse of the shape parameter of the Weibull distributions as a function of laser detuning and interpret the results by modeling the speckle propagation.

We experimentally demonstrate spatial confinement of atomic excitation by narrow-band composite pulse (NCP) sequences in a rare-earth ion-doped ${\text{Pr}}^{3+}\text{:}{\text{Y}}_2{\text{SiO}}_5$ crystal. The experimental data confirm that NCP sequences localize excitation far below the diameter of the driving laser pulse, with potential to proceed below the diffraction limit. We reach significant improvement of the spatial confinement compared to previous implementations. To this end, we derive several new classes of composite pulses that significantly outperform previously known sequences for the objectives of this study. In particular, the new NCP sequences are applicable also in inhomogeneously broadened ensembles, where most conventional composite pulse sequences fail. We systematically investigate the performance of the different classes of sequences and compare the results with numerical simulations, which agree very well with our experimental data. The findings serve as a step towards novel applications of composite pulse sequences to precisely prepare and manipulate excitation patterns in space, e.g., in quantum technology to address qubits with large spatial resolution.

Quantum state preparation and measurement of photonic and phononic Schrödinger cat states have gathered significant interest due to their implications for alternative encoding schemes in quantum computation. These schemes employ coherent state superpositions, leveraging the expanded Hilbert space provided by cavity or mechanical resonators in contrast to two-level systems. Moreover, such cat states also serve as a platform for testing fundamental quantum phenomena in macroscopic systems. In this study, we generate four bipartite phononic cat states using an entanglement swapping scheme achieved through projective Bell-state measurements on two superconducting qubits. Employing two superconducting qubits allows for the creation of bipartite phononic cat states remotely, where the two phononic resonators are separated by a far distance. Subsequently, we conduct a Bell inequality test on the bipartite cat state using the Clauser-Horne-Shimony-Holt formulation. Given that the entangled cat states are generated through entanglement swapping, our approach holds promising applications for the advancement of complex quantum network processors based on continuous-variable systems.

Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing a number-conserving operation (NCO), i.e., $a{a}^{†}$ and $a^{†}a$, inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of the NCO on the phase sensitivity, the quantum Fisher information (QFI), and the quantum Cramér-Rao bound under both ideal and photon-loss scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the QFI and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the $a^{†}a$ scheme exhibits superior improvement in both the ideal and photon-loss cases in terms of phase sensitivity. Moreover, in the ideal case, the $a{a}^{†}$ scheme slightly outperforms the $a^{†}a$ scheme in terms of the QFI. However, in the presence of high photon losses, the $a^{†}a$ scheme demonstrates a greater advantage.