We investigate the second-order topological phases in a two-dimensional ring resonator array with each plaquette occupied by π gauge flux and imaginary gauge field. The real and imaginary gauge fields are induced by shifting the displacement and integrating gain or loss into the two half perimeters of the auxiliary rings. The system supports topological corner modes with their emergence being determined by the non-Bloch topological invariant due to skin effects. The bulk modes, exhibiting second-order skin effects in both trivial and nontrivial phases, are accumulated at opposite corners depending on whether clockwise or counterclockwise modes are excited. By introducing an interface with different imaginary gauge fields, we show the bulk modes exist at the interface while the topological corner modes are localized at the physical corners. Furthermore, the skin effects are also presented in the passive ring resonators. The study may find applications in lasers and broadband light trapping.

In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases that depends on the density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to both the direct Raman process and the interaction-assisted Raman process. The interaction-assisted Raman process depends on the density of atoms. These two processes have opposite effects in terms of spin-momentum locking and compete with each other. As the interaction modulation increases, the system undergoes a crossover from the direct Raman process dominated regime to the interaction-assisted Raman process dominated regime. During this crossover, for bosons, both the condensate momentum and the chirality of condensate wave function change sign, and for fermions, the Fermi surface distortion is inverted. We highlight that there exists an emergent spatial reflectional symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method may pave a way to novel phenomena in the density-dependent spin-orbit coupling gauge field with intrinsic dynamics.

Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover, and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys. Rev. Lett. 124, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.

Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many-body physics through quantum simulators. Unfortunately, the number of experimental measurements of the system required to estimate these global quantities scales exponentially with system size. Here, we consider the use of random-axis measurements for quantum state tomography and state purity estimation. We perform a general analysis of the statistical deviation in such methods for any given algorithm. We then propose a simple protocol which relies on single-pulse rotations only. We find that it reduces the basis of the exponential growth, calculating the statistical variance to scale as ${\sum }_{\mathit{a},\mathit{b}}{\left|\mathrm{\Delta }{\rho }_{\mathit{a}\mathit{b}}\right|}^2\sim 5^N/N_{\mathrm{tot}}$ for full tomography, and ${\mathrm{\Delta }\mu }^2\sim 7^N/N_{\mathrm{tot}}^2$ for purity estimation, for $N$ qubits and $N_{\mathrm{tot}}$ measurements performed.

We theoretically investigate electron-hole recollisions in high-harmonic generation (HHG) in band-gap solids irradiated by linearly and elliptically polarized drivers. We find that in many cases, the emitted harmonics do not originate in electron-hole pairs created at the minimum band gap, where the tunneling probability is maximized, but rather in pairs created across an extended region of the Brillouin zone (BZ). In these situations, the analogy to gas-phase HHG in terms of the short- and long-trajectory categorizations is inadequate. Our analysis methodology comprises three complementary levels of theory: the numerical solutions to the semiconductor Bloch equations, an extended semiclassical recollision model, and a quantum wave-packet approach. We apply this methodology to two general material types with representative band structures: a bulk system and a hexagonal monolayer system. In the bulk, the interband harmonics generated using elliptically polarized drivers are found to originate not from tunneling at the minimum band gap $\mathrm{\Gamma }$, but from regions away from it. In the monolayer system driven by linearly polarized pulses, tunneling regions near different symmetry points in the BZ lead to distinct harmonic energies and emission profiles. We show that the imperfect recollisions, where an electron-hole pair recollide while being spatially separated, are important in both bulk and monolayer materials. The excellent agreement between our three levels of theory highlights and characterizes the complexity behind the HHG emission dynamics in solids, and expands on the notion of interband HHG as always originating in trajectories tunnelled at the minimum band gap. Our work furthers the fundamental understanding of HHG in periodic systems and will benefit the future design of experiments.

A scheme of an ultrasensitive magnetometer in the cavity quantum electromagnonics is proposed, where the intracavity microwave mode is coupled to a magnonic mode via magnetic dipole interaction. It is shown that by driving both magnonic and microwave modes with external classical fields and controlling the system parameters, one can reduce the added noise of magnetic field measurement below the standard quantum limit (SQL). Surprisingly, we show that beyond the rotating wave approximation (RWA), not only can the added noise be suppressed but also the output cavity response to the input signal can be substantially amplified in order to achieve a precise magnetic-field measurement. The estimated theoretical sensitivity of the proposed magnetic amplifier-sensor is approximately on the order of ${10}^{-18}\mathrm{T}/\sqrt{\mathrm{Hz}}$, which is competitive compared to the current state-of-the-art magnetometers like superconducting quantum interference devices (SQUIDs) and atomic magnetometers. The advantages of the proposed sensor in comparison with the other magnetometers is its high sensitivity at room temperature, sensing in a wide range of frequencies up to MHz, and its capability for signal-response amplification.

The properties of atomic negative ions are to a large extent determined by electron-electron correlation which makes them an ideal testing ground for atomic many-body physics. In this paper, we present a detailed experimental and theoretical study of excited states in the negative ion of iridium. The ions were stored at cryogenic temperatures using the double electrostatic ion ring experiment facility at Stockholm University. Laser photodetachment was used to monitor the relaxation of three bound excited states belonging to the [Xe] $4f^{14}5d^{8}6s^2$ ionic ground configuration. Our measurements show that the first excited state has a lifetime much longer than the ion-beam storage time of $1230\pm 100\mathrm{s}$. The binding energy of this state was measured to be $1.045\pm 0.002\mathrm{eV}$. The lifetimes of the second and third excited states were experimentally determined to be $133\pm 10$ and $172\pm 35\mathrm{ms}$, respectively. Multiconfiguration Dirac-Hartree-Fock calculations were performed in order to extract binding energies and lifetimes. These calculations predict the existence of the third excited bound state that was detected experimentally. The computed lifetimes for the three excited bound states agree well with the experimental results and allow for a clear identification of the detected levels.

A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $\pi$ (i.e., a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $\pi$ pulse and an adiabatic chirped pulse, both of which produce population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman shift leads to an energy level shift and hence a static detuning. In both the resonant and adiabatic approaches, a small level shift does not alter the transition probability very much; however, it can significantly change the dynamical phases in the propagator. The repeated application of the same pulse greatly amplifies the changes in the dynamical phases and maps them onto the populations. Hence the effect of the level shift can be measured with good accuracy. It is found that sequences of pulses with alternating phases deliver much greater error amplification and much steeper excitation profiles around resonance, thereby providing much higher sensitivity to small energy level shifts. Explicit analytic estimates of the sensitivity are derived using the well-known noncrossing Rosen-Zener and Rabi models and the level-crossing Demkov-Kunike model. This recipe provides a simple tool for rapid and accurate sensing of weak electric and magnetic fields by using the same pulse generating an inversion quantum gate, without sophisticated tomography or entangling operations.

On-chip single-photon nonreciprocal devices with high isolation and low insertion loss become a key element in quantum information processing. Based on electromagnetically induced transparency in chiral quantum systems, a single-photon isolator and a single-photon circulator are obtained without requiring unbalanced coupling. These devices have high isolation and low insertion loss. Moreover, their bandwidths are significantly broadened with the assistance of electromagnetically induced transparency.

We present a math-physics modeling approach called canonical quantization with numerical mode decomposition for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic fields are coupled to nonuniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as nonlocal dispersion cancellation of an entangled photon pair and the Hong-Ou-Mandel effect in a dispersive beam splitter.

Although the time-dependent buildup processes of Autler-Townes splitting in attosecond transient absorption spectra have been observed in plenty of experiments, there still exists an open question of when the splitting is maximized, which tells us how fast the system responds to the pump field and how well the adiabatic following is in a slowly varying few-cycle laser pulse. In this Letter we work out a compact formula to quantify the buildup time of the Autler-Townes splitting, which is related to multiple timescales of the laser-atom system, e.g., the Rabi period, the laser cycle, and the pulse duration, according to a universal power law. This scaling law applies not only to singly excited states, but also to doubly excited states in which complex electron-electron interaction gets involved. Our findings have potential applications in calibrating the zero delay in a transient absorption spectroscopy.

Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wavelike interference patterns or particlelike anticorrelations, depending upon the (possibly delayed) choice of the experimenter. A variant known as the quantum eraser uses entangled light to recover the lost interference in a seemingly nonlocal and retrocausal manner. Although it is believed that this behavior is incompatible with classical physics, here we show that, using postselection, the observed quantum phenomena can be reproduced by adopting a simple deterministic detector model and supposing the existence of a random zero-point electromagnetic field.

We propose a scheme for trapped-atom interferometry using an interacting Bose-Einstein condensate. The condensate is controlled and spatially split into two confined external momentum modes through a series of Bragg pulses. The proposed scheme (i) allows the generation of large entanglement in a trapped-interferometer configuration via one-axis twisting dynamics induced by interatomic interaction and (ii) avoids the suppression of interactions during the interferometer sequence by a careful manipulation of the state before and after phase encoding. The interferometer can be used for the measurement of gravity with a sensitivity beyond the standard quantum limit.

Complementarity between one-particle visibility and two-particle visibility in discrete systems can be extended to bipartite quantum-entangled Gaussian states implemented with continuous-variable quantum optics. The meaning of the two-particle visibility originally defined by Jaeger, Horne, Shimony, and Vaidman with the use of an indirect method that first corrects the two-particle probability distribution by adding and subtracting other distributions with varying degree of entanglement, however, deserves further analysis. Furthermore, the origin of complementarity between one-particle visibility and two-particle visibility is somewhat elusive and it is not entirely clear what is the best way to associate particular two-particle quantum observables with the two-particle visibility. Here, we develop a direct method for quantifying the two-particle visibility based on measurement of a pair of two-particle observables that are compatible with the measured pair of single-particle observables. For each of the two-particle observables from the pair is computed corresponding visibility, after which the absolute difference of the latter pair of visibilities is considered as a redefinition of the two-particle visibility. Our approach reveals an underlying mathematical symmetry as it treats the two pairs of one-particle or two-particle observables on equal footing by formally identifying all four observable distributions as rotated marginal distributions of the original two-particle probability distribution. The complementarity relation between one-particle visibility and two-particle visibility obtained with the direct method is exact in the limit of infinite Gaussian precision where the entangled Gaussian state approaches an ideal Einstein-Podolsky-Rosen state. The presented results demonstrate the theoretical utility of rotated marginal distributions for elucidating the nature of two-particle visibility and provide tools for the development of quantum applications employing continuous variables.

Macroscopic realism (MR) is the notion that a time-evolving system possesses definite properties, irrespective of past or future measurements. Quantum-mechanical theories can, however, produce violations of MR. Most research to date has focused on a single set of conditions for MR, the Leggett-Garg inequalities (LGIs), and on a single data set, the standard data set, which consists of single-time averages and second-order correlators of a dichotomic variable $Q$ for three times. However, if such conditions are all satisfied, then where is the quantum behavior? In this paper we provide an answer to this question by considering expanded data sets obtained from finer-grained measurements and MR conditions on those sets. We consider three different situations in which there are violations of MR that go undetected by the standard LGIs. First, we explore higher-order LGIs on a data set involving third- and fourth-order correlators, using spin-$\frac{1}{2}$ and spin-1 systems. Second, we explore the pentagon inequalities and a data set consisting of all possible averages and second-order correlators for measurements of $Q$ at five times. Third, we explore the LGIs for a trichotomic variable and measurements made with a trichotomic operator to again identify violations for a spin-1 system beyond those seen with a single dichotomic variable. We also explore the regimes in which combinations of two and three-time LGIs can be satisfied and violated in a spin-1 system, extending recent work. We discuss the possible experimental implementation of all the above results.

We present a bit encoding scheme for a highly efficient and scalable representation of bosonic Fock number states in the restricted Boltzmann machine neural network architecture. In contrast to common density matrix implementations, the complexity of the neural network scales only with the number of bit-encoded neurons rather than the maximum boson number. Crucially, in the high occupation regime its information compression efficiency is shown to surpass even maximally optimized density matrix implementations, where a projector method is used to access the sparsest Hilbert space representation available.

We present a theoretical study of coherent quantum dynamics of a single magnetic fluxon (MF) trapped in Josephson-junction parallel arrays (JJPAs) with large kinetic inductances. The MF is the topological excitation carrying one quantum of magnetic flux, ${\mathrm{\Phi }}_0$. The MF is quantitatively described as the $2\pi$ kink in the distribution of Josephson phases, and for JJPAs with high kinetic inductances the characteristic length of such distribution (the “size” of MF) is drastically reduced. Characterizing such MFs by the Josephson phases of three consecutive Josephson junctions we analyze the various coherent macroscopic quantum effects in the MF quantum dynamics. In particular, we obtain the MF energy band originating from the coherent quantum tunneling of a single MF between adjacent cells of JJPAs. The dependencies of the band width $\mathrm{\Delta }$ on the Josephson coupling energy $E_J$, charging energy $E_C$ and the inductive energy of a cell $E_L$, are studied in detail. In long linear JJPAs the coherent quantum dynamics of MF demonstrates decaying quantum oscillations with characteristic frequency $f_{qb}=\mathrm{\Delta }/h$. In short annular JJPAs the coherent quantum dynamics of MF displays complex oscillations controlled by the Aharonov-Casher phase $\chi \propto V_g$, where $V_g$ is an externally applied gate voltage. In the presence of externally applied dc bias, $I$, a weakly incoherent dynamics of quantum MF is realized in the form of macroscopic Bloch oscillations leading to a typical “nose” current-voltage characteristics of JJPAs. As ac current with frequency $f$ is applied the current-voltage characteristics display a set of equidistant current steps at $I_n=2enf$.

Final projectile charge states are experimentally and theoretically analyzed after ${\mathrm{H}}^{+}$ ions collide with a ${\mathrm{C}}_{60}$ monolayer deposited on Cu(111) with an ample range of incoming energies (2–8 keV) in the low-energy regime. The three possible charge states (negative, positive, and neutral) are experimentally measured by using the low-energy ion scattering technique for two different collisional setups: 45° (90°) and 67.5° (67.5°) incoming (exit) angles, relative to the target surface plane, with a fixed backscattering angle of 135°. Experimental ion fraction magnitudes and energy dependence are practically intermediate between that found in pristine Cu(111) and a thick ${\mathrm{C}}_{60}$ film, revealing the influence of the substrate on the final charge state of the projectile. Unlike these previous systems, the positive and negative ions contribute nearly evenly to the total scattered charged particles. On the theoretical side, we applied a first-principles based model that considers the fine details of the surface under analysis and assumes a projectile trajectory corresponding to a single binary collision with the more exposed carbon atoms of the ${\mathrm{C}}_{60}$ molecule. The theoretical and experimental results are independently compared with the already reported cases: ${\mathrm{H}}^{+}$ on a thick ${\mathrm{C}}_{60}$ film, ${\mathrm{H}}^{+}$ on Cu(111), and ${\mathrm{H}}^{+}$ on graphite. A detailed analysis of the electronic surface band structure allows us to draw a conclusion about the relevance of the substrate in the present system and about the aspects to be improved in our theoretical description. The contrast between experimental and theoretical results allows us to infer that trajectories involving ion penetration and multiple scattering events are particularly relevant for the projectile-target charge exchange process studied.

The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Such a released localized state may represent a radiation mode inserted into a multimode interference device or a cold-atom system released in an optical trap, for instance. Here, without losing any generality, for simplicity, the case of a particle with a mass $m$ is considered and described by a localized state corresponding to the ground state of a square box of width $w$, which is released inside a wider cavity (with a width $L>w$). The effects of decoherence are then numerically investigated by means of a simple dynamical model that captures the essential features of the phenomenon under Markovian conditions, leaving aside extra complications associated with a more detailed dynamical description of the system-environment interaction. As it is shown, this model takes into account and reproduces the fact that decoherence effects are stronger as energy levels become more separated (in energy), which translates into a progressive collapse of the energy density matrix to its main diagonal. However, because energy dissipation is not considered, an analogous behavior is not observed in the position representation, where a proper spatial localization of the probability density does not take place, but rather a delocalized distribution. This result emphasizes the fact that classicality is reached only if both decoherence and dissipation coexist; otherwise, nonclassical traits might still persist. Actually, as it is also shown, in the position representation some off-diagonal correlations indeed survive unless an additional spatial-type factor is included in the model. This makes evident the rather complex nature of the decoherence phenomenon and hence the importance to have a familiarity with how it manifests in different representations, particularly with the purpose to determine and design reliable control mechanisms.