Free motion of a quantum particle with the wave function entirely comprised of plane waves with non-negative momenta may be accompanied by negative probability current, an effect called quantum backflow. The effect is weak and fragile and has not yet been observed experimentally. Here we show that quantum backflow becomes significantly more pronounced and more amenable to experimental observation if, instead of letting the particle move along a straight line, one forces it to move in a circular ring.

In the presence of Lindblad decoherence, i.e., dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by non-Hermitian Hamiltonians with the Lindblad equation, for which the parity-time-reversal (PT) symmetry is conserved. First, the density matrix formalism for $\mathcal{PT}$-symmetric non-Hermitian Hamiltonian systems is developed. It is shown that the Lindblad operators $L_j^{}$ are pseudo-Hermitian, namely, $\eta L_j^{}{\eta }^{-1}=L_j^{†}$ with $\eta$ being a linear and positive-definite metric, and respect the $\mathcal{PT}$ symmetry as well. We demonstrate that the generalized density matrix ${\rho }_{\mathrm{G}}^{}\left(t\right)\equiv \rho \left(t\right)\eta$, instead of the normalized density matrix ${\rho }_{\mathrm{N}}^{}\left(t\right)\equiv \rho \left(t\right)/\mathrm{tr}\left[\rho \left(t\right)\right]$, should be implemented for the calculation of the transition probabilities in accordance with the linearity requirement. Second, the density matrix formalism is used to derive the transition probabilities in general cases of $\mathcal{PT}$-symmetric non-Hermitian Hamiltonians. In some concrete examples, we calculate compact analytical formulas for the transition probabilities and explore their main features with numerical illustrations. We also make a comparison between our present results and our previous ones using state vectors in the absence of Lindblad decoherence.

According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle natures. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath interference experiment that has a which-path detector in a quantum superposition of being present and absent. We show that a tight multipath wave-particle duality relation is respected in all such situations, and complementarity holds well. The apparent violation of complementarity may be due to incorrect evaluation of path distinguishability in such scenarios.

We investigate the possibility of multiple uses of a single copy of a three-qubit state for detecting genuine tripartite Einstein-Podolsky-Rosen (EPR) steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger (GHZ) type or $W$ type is shared between two fixed observers in two wings and a sequence of multiple observers in the third wing who perform unsharp or nonprojective measurements. The measurement settings of each of the multiple observers in the third wing are independent and uncorrelated with the measurement settings and outcomes of the previous observers. In such setup, we investigate all possible types of ($2\to 1$) and ($1\to 2$) genuine tripartite EPR steering. For each case, we obtain an upper limit on the number of observers on the third wing who can demonstrate genuine EPR steering through the quantum violation of an appropriate tripartite steering inequality. We show that the GHZ state allows for a higher number of observers compared to the $W$ state. Additionally, ($1\to 2$) genuine steering is possible for a larger range of sharpness parameters compared to ($2\to 1$) genuine steering cases.

The identification of time-varying parameters (e.g., directly inaccessible in situ signals in vacuum and low-temperature environments) is prevalent for characterizing the dynamics of quantum processes. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with specially designed probe systems can the parameters be explicitly read out, and a rigorous identifiability analysis is lacking, i.e., whether the measurement data are sufficient for unambiguous identification. In this paper we formulate this problem as the invertibility of the input-output mapping associated with the quantum system for which an algebraic identifiability criterion is derived based on the system's relative degree. The invertibility analysis also leads to an inversion-based algorithm for numerically identifying the parameters, which is computationally much more efficient than nonlinear regression methods. The effectiveness of the criterion are demonstrated by numerical examples.

We report on the improved determination of the center frequency of a hydrogen deuteride vibration-rotation transition. As a result of a refined analysis of cavity ring-down absorption spectra, it was possible to quantify the influence of the hyperfine structure on the line center frequency of the weak 2-0 $R\left(1\right)$ line, as retrieved in the Doppler-limited regime. It turns out that ignoring the hyperfine structure leads to an underestimation of the center frequency of about 350 kHz. The updated determination gives an absolute frequency of the $R\left(1\right)$ centroid of 217 105 181.936 MHz with a global uncertainty of 76 kHz.

The discovery of laser-driven rescattering and high harmonic radiation out to a maximum photon energy of 3.17 times the ponderomotive energy laid the groundwork for attosecond pulse generation and coherent x rays. As the laser field drives the interaction to higher energies, relativity and the Lorentz force from the laser magnetic field enter into the dynamics. Recent studies of laser rescattering have included these effects to give a quantitative description of rescattering dynamics in the high-energy limit, i.e., recollision energies of order 1,000 hartree (27 keV). In this high-energy limit, we treat the emitted high harmonic radiation from rescattering as a bremsstrahlung process. We find the highest-energy photons in the radiated energy spectra follow the rescattering electron energy near the ultimate cutoff. The effective charge from the ion core shielding does not affect the radiation yield at cutoff; however, the overall energy radiated does scale quadratically with the atomic number of the parent ion.

We present a theoretical study of the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analog inflationary universe. As the system expands, we find that phonons in the BEC undergo redshift and damping due to quantum pressure effects, owing to the thinness of the ring. We predict that rapidly expanding toroidal BEC's can exhibit spontaneous particle creation, and study this phenomenon in the context of an initial coherent state wave function. We show how particle creation would be revealed in the atom density and density correlations, and discuss connections to the cosmological theory of inflation.

We investigate many-body localization of interacting spinless fermions in a one-dimensional disordered and tilted lattice. The fermions undergo energy-dependent transitions from ergodic to Stark many-body localization driven by the tilted potential, which are manifested by the appearance of mobility edges between delocalized states and Stark many-body localized states even when the disorder is weak. We can concretely diagnose these transitions rather than crossovers by finite-size scaling of energy-level statistics. Moreover, in the Stark many-body localization, the entanglement entropy obeys the area law scaling, in analogy to that in the conventional many-body localization.

Quantum electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the speed of light should be modified when the vacuum is stressed by intense electromagnetic fields. This optical phenomenon has not yet been observed. The DeLLight (deflection of light by light) experiment aims to observe the optically induced index change of vacuum, a nonlinear effect which has never been explored. The experiment is installed in the LASERIX facility at IJCLab, which delivers ultrashort intense laser pulses (2.5 J per pulse, each of 30 fs duration, with a 10 Hz repetition rate). The proposal is to measure the refraction of a probe laser pulse when crossing a transverse vacuum index gradient, produced by a very intense pump pulse. The refraction induces a transverse shift in the intensity profile of the probe, whose signal is amplified by a Sagnac interferometer. In this article we describe the experimental method and setup, and present the complete theoretical calculations for the expected signal. With a minimum waist at focus of $5\mu \mathrm{m}$ (corresponding to a maximum intensity of $\sim 3\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2$), and with the nonlinear vacuum index derived from QED, the expected refraction angle is 0.13 prad. First results of the interferometer prototype are presented. It is shown that an extinction factor $\mathcal{F}=0.4\times {10}^{-5}$ (corresponding to a signal amplification factor of 250) and a spatial resolution ${\sigma }_y=10\mathrm{nm}$ are achievable. The expected signal is then about 15 pm, and could be observed at a 5-sigma confidence level with about one month of collected data.

We study reservoir-engineered entanglement for a cascaded bosonic system consisting of three modes, where the adjacent pairs couple to each other via both the beam-splitter interaction and the coherent parametric interaction with the interaction strengths being tunable. We focus on an optomechanical realization of the model by combining a nondegenerate parametric amplifier and an auxiliary cavity. A great steady-state cavity-mechanical entanglement can be achieved by optimizing the ratio of the interaction strengths, where the optomechanical cavity enacts the cold reservoir, simultaneously laser cooling the pair of hybrid modes delocalized over the auxiliary cavity and the mechanical oscillator. In comparison with the case of cooling a single delocalized mode, the dual-mode cooling approach allows one to obtain a greater amount of entanglement with higher cooling efficiencies and to explore strong entanglement in much broader parameter regions, where the rotating-wave approximation fails for the single-mode cooling case. Moreover, we show that the steady-state cavity-mechanical entanglement is robust to the mechanical thermal noise of the high temperature. The improved reservoir engineering approach can potentially be generalized to other bosonic systems with asymmetric beam-splitter and parametric interactions.

The implementation of exceptional points (EPs), a special type of topological singularities, has emerged as a new paradigm for engineering the quantum-inspired or wave-based photonic systems. Even though there exists a range of investigations on EPs of order two and three (say, EP2s and EP3s, respectively), the hosting of fourth-order EPs (EP4s) in any real system and the exploration of associated topological features are lacking. Here we have designed a simple Fabry-Pérot type gain-loss-assisted open optical microcavity to host EPs up to order four. The scattering-matrix formalism has been used to analyze the microcavity numerically. With the appropriate modulation of the gain-loss profile in the same cavity geometry, we have encountered multiple different orders of EPs by investigating the simultaneous interactions among four coupled cavity states via level-repulsion phenomena. Besides affirming the second-order and third-order branch-point behaviors of the embedded EP2s and EP3s, the fourth-order branch-point functionality of an EP4 has been manifested by encircling three connecting EP2s simultaneously in the closed gain-loss parameter space. We have established a unique successive state-switching phenomenon among four coupled states by implementing such an EP4-encirclement scheme in the system's parameter space. The proposed scheme indeed offers potential applications in state-switching and control in quantum-inspired integrated photonic circuits, where the presence of an EP4 serves as a new light manipulation tool.

We show that a system of three parallel waveguides, among which the central one is dissipative, leads to an ultrabroadband power splitting associated with an overall 50% power loss. The present approach is reminiscent of non-Hermitian systems in quantum mechanics and does not require a perfect effective index matching between the external and the central waveguides. The present concept does not need any slow adiabatic evolution of the waveguide parameters and may therefore be realized over very short device lengths, especially in the case where the central waveguide is of the plasmonic type.

Interband semiconductor lasers subject to optical feedback usually produce rich nonlinear dynamics. However, it is hard to destabilize quantum cascade lasers using common optical feedback, because of its ultrashort carrier lifetime and small linewidth broadening factor. In this work, we show that optical feedback with a tilted angle can destabilize quantum cascade lasers, which produce three types of nonlinear dynamics. We observe periodic oscillations with small tilted angles, quasiperiodic oscillations with moderate angles, and low-frequency oscillations with large angles, respectively. In contrast, this type of dynamics does not occur with well-aligned optical feedback.

The dynamics of an isolated quantum system is coherent and unitary. Weak coupling to the environment leads to decoherence, which is traditionally modeled with a Lindblad equation for the system's density matrix. Starting from a pure state, such a system approaches a steady state (mixed or otherwise) in an underdamped or overdamped manner. This transition occurs at an eigenvalue degeneracy of a Lindblad superoperator, called an exceptional point (EP), where corresponding eigenvectors coalesce. Recent years have seen an explosion of interest in creating exceptional points in a truly quantum domain, driven by the enhanced sensitivity and topological features EPs have shown in their classical realizations. Here, we present Floquet analysis of a prototypical qubit whose drive or dissipator strengths are varied periodically. We consider models with a single dissipator that generate global loss (phase damping) or mode-selective loss (spontaneous emission). In all cases, we find that periodic modulations lead to EP lines at small dissipator strengths and a rich EP structure in the parameter space. Our analytical and numerical results show that extending Lindblad Liouvillians to the Floquet domain is a potentially preferred route to accessing exceptional points in the transient dynamics towards the Lindblad steady state.

The asymmetric quantum Rabi model (AQRM) has a broken ${\mathbb{Z}}_2$ symmetry, with generally a nondegenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the ${\mathbb{Z}}_2$-symmetric quantum Rabi model are recovered, however, without any obvious paritylike symmetry. This unknown “symmetry” has thus been referred to as hidden symmetry in the literature. Here, we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunneling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunneling.

We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the complex plane. The main characteristic eigenstates are explored using entanglement entropy as a distinguishing feature. We show that the rich interplay of order, chaos and localization found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localized states unique to three-photon systems such as bound trimers, corner states, and trimer edge states.

Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favorable prefactor to the error scaling versus bond dimension. This is illustrated by time evolving a matrix product state using very large time steps, and by constructing a robust algorithm for finding ground states of two-dimensional Hamiltonians using projected entangled pair states as fixed points of two-dimensional transfer matrices.

In $3\text{D}+t$ numerical simulations, we propose an experiment wherein a mixture of gases is used for the continuous transition from $\mathsf{X}$- to $\mathsf{O}$-shaped angle-wavelength spectrum of a femtosecond infrared filament. The mixture consists of transparent nitrogen at 40 bar pressure and $85{}^{\circ }\mathrm{C}$ temperature as well as absorbing water vapor at 0–0.36 bar, with the rovibrational resonance at a wavelength slightly longer than the $1.3\mu \mathrm{m}$ center of the pump pulse driving the filament. The continuous increase in the water vapor density results in the gas mixture dispersion changing from normal to anomalous and transformation of the short-wavelength conical emission onto on-axis propagating radiation.

We present a systematic approach for obtaining lower bounds on the failure probability of unambiguous state discrimination by introducing an ancillary degree of freedom. Specifically, the lower bounds are obtained by introducing a suitable homogeneous function of the off-diagonal entries of the reduced matrix in the ancillary degree of freedom. A series of lower bounds on the failure probability of unambiguous discrimination of both pure states and mixed states are derived using the $l_r$-norm of the off-diagonal entries. Our method adds insights into the problem of unambiguous state discrimination. In particular, since we have related the lower bound with off-diagonal entries of density matrices, e.g., the $l_1$-norm coherence, our work suggests that unambiguous state discrimination may provide further applications in quantifying coherence, and vise versa.