We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to $d$ states, optionally reduced to the real subspace. As a dimension certificate, we use the linear independence tested by a determinant. We find the sets of preparations and measurements that maximize the chance to detect larger space if the extra contribution is very small. We discuss the practical application of the test to certify the space logical operations on a quantum computer.

Compared with a qubit, a qudit (i.e., a $d$-level or $d$-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits that are different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with $d=3$. We propose a simple method to realize a hybrid quantum controlled-sum gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary logic gates for quantum computing with qutrits. Our proposal is based on circuit QED and operates essentially by employing a SC ququart (a four-level quantum system) dispersively coupled to a microwave cavity. The gate implementation is quite simple because it only requires a single basic operation. Neither classical pulse nor measurement is needed. The auxiliary higher energy level of the SC ququart is virtually excited during the gate operation, thus decoherence from this level is greatly suppressed. As an application of this gate, we discuss the generation of a hybrid maximally entangled state of one SC qutrit and one cat-state qutrit. We further analyze the experimental feasibility of creating such a hybrid entangled state in circuit QED. This proposal is quite general and can be extended to accomplish the same task in a wide range of physical system, such as a four-level natural or artificial atom coupled to an optical or microwave cavity.

We consider the implementation of two-qubit gates when the physical systems used to realize the qubits possess additional quantum states in the accessible energy range. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space, and we analyze the effect of the additional quantum states on the gate speed. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-qubit gates significantly faster than the reference value based on simple qubits. On the other hand, a weak anharmonicity constrains the speed at which the system can be adequately controlled: according to the intuitive picture, faster operations require stronger control fields, which are more likely to excite higher levels in a weakly anharmonic system, which in turn leads to faster decoherence and uncontrolled leakage outside the qubit space. To account for this constraint, we modify the pulse optimization algorithm to avoid pulses that lead to appreciable population of the higher levels. In this case, we find that the presence of the higher levels can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal-control gate speeds with those obtained using the cross-resonance or selective-darkening gate protocol. We find that this protocol, with some parameter optimization, can be used to achieve a relatively fast implementation of the controlled-NOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting circuits. They also provide guidelines for desirable conditions on anharmonicity that would allow optimal utilization of the higher levels to achieve fast quantum gates.

Single-photon detectors are a pivotal component in photonic quantum technologies. A precise and comprehensive calibration of the inherent detection efficiency is of utmost importance to ensure the proper evaluation of the performance in view of the specific technological application of interest, such as the protection against security breaches in quantum cryptographic solutions. Here we report on a systematic study and comprehensive analysis of the estimation of the inherent detection efficiency of two commercial single-photon detectors based on single-photon avalanche diodes for various mean photon numbers and at high laser pulse repetition rates using different techniques. We observe an unexpected and significant drop in the inherent detection efficiency at detection rates of 10% and higher relative to the maximum detection rate. It is demonstrated that for data analysis a statistical model for the detection rate conveniently can be used if no time-stamped data are available. We conclude that the full characterization of single-photon detectors used in critical applications should include the sensitivity of their inherent detection efficiency to high event rates.

Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold maximum-likelihood decoders require an explicit error model for Pauli errors to decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum-weight matching are error agnostic. Here we consider an intermediate approach, formulating a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but is agnostic to error rate. Our decoder is based on counting the number and effective weight of the most likely error chains in each equivalence class of a given syndrome. We use Metropolis-based Monte Carlo sampling to explore the space of error chains and find unique chains that are efficiently identified using a hash table. Using the error-rate invariance, the decoder can sample chains effectively at an error rate which is higher than the physical error rate and without the need for thermalization between chains in different equivalence classes. Applied to the surface code and the $XZZX$ code, the decoder matches maximum-likelihood decoders for moderate code sizes or low error rates. We anticipate that, because of the compressed information content per syndrome, it can be taken full advantage of in combination with machine-learning methods to extrapolate Monte Carlo–generated data.

We propose doubly ionized lanthanum (${\mathrm{La}}^{2+}$) as a possible qubit candidate for quantum networks. Transitions between the lowest levels in the atom are in the infrared, enabling a direct matter-light interface amenable to long-distance quantum communication. These transitions could also be used to directly laser-cool trapped ${\mathrm{La}}^{2+}$ ions. The rich hyperfine structure of the ion may allow for a qubit stored in magnetic-field insensitive states as well as protocols for atom-photon entanglement.

New $(e,2e)$ differential cross-section measurements from argon are presented in the perpendicular plane, where the incident electron beam is orthogonal to both detected electrons that map out a detection plane as their angles are varied. New data were obtained at energies from 40 to 200 eV above the ionization potential (IP), with the scattered and ejected electrons having equal energies. These data are compared to previous measurements from 5 to 50 eV above the IP as well as to theoretical calculations from different models in this energy range. A significant discrepancy between the prediction of theory and experiment 50 eV above the IP was retested, and the new experiments confirmed the results from previous measurements. Additional data spanning this energy are presented which show a deep minimum in the cross section under these conditions. Results for the evolution of the cross section into the intermediate-energy regime are also discussed.

Optically pumped magnetometers usually rely on optical pumping using circularly or linearly polarized light. We study here zero-field magnetometers pumped with elliptically polarized light, preparing both atomic orientation and alignment with complementary geometries. We start by extending the three-step approach for elliptically polarized pumping. This allows us to study the Hanle effect in elliptical polarization by comparing the analytical absorption signals with experiments made on ${}^4\mathrm{He}$ metastable state. We then study parametric resonance magnetometers based on elliptical polarization by using the dressed-atom formalism with one and two radio-frequency fields. The results show good agreement with the experimental measurements and interesting perspectives for magnetometry where symmetry breaking by pumping light is mitigated.

The effect of the spatial inhomogeneity on the photoelectron momentum distributions (PMDs) is recently identified [Chen et al., Phys. Rev. A 104, 043107 (2021)]. As an important parameter of the laser field, the wavelength cannot be ignored. We theoretically investigate the wavelength dependence of the PMDs in a spatially inhomogeneous field. The results show that the PMDs gradually move to the negative direction with the increase of the laser wavelength compared with the case of the spatially homogeneous field. However, a critical value of the wavelength appears, where the PMDs are just separated. Then, the PMDs can be clearly separated into two regions and the rescattering energy of the electron is tremendously enhanced. We illustrate that the holographic interference structure can be isolated in the relative high-energy region and the holographic interference structure for the shorter wavelength is more obvious. A prominent high-energy peak appears in the critical wavelength and the high-energy peak is sensitive to the initial transverse momentum of the rescattering electrons after tunneling. Moreover, we also demonstrate that the critical wavelength will change with the inhomogeneity parameters.

It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudospin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present-day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as ${}^{87}\mathrm{Rb}$, ${}^7\mathrm{Li}$, ${}^{41}\mathrm{K}$ (Newton-Cartan), and ${}^{23}\mathrm{Na}$ (Einstein-Hilbert).

We study superfluidity of a cigar-shaped Bose-Einstein condensate by stirring it with a Gaussian potential oscillating back and forth along the axial dimension of the condensate, motivated by experiments of Raman et al. [Phys. Rev. Lett. 83, 2502 (1999)]. Using classical-field simulations and perturbation theory, we examine the induced heating rate, based on the total energy of the system, as a function of the stirring velocity $v$. We identify the onset of dissipation by a sharply increasing heating rate above a velocity $v_c$, which we define as the critical velocity. We show that $v_c$ is influenced by the oscillating motion, the strength of the stirrer, the temperature, and the inhomogeneous density of the cloud. This results in a vanishing $v_c$ for the parameters similar to the experiments, which is inconsistent with the measurement of nonzero $v_c$. However, if the heating rate is based on the thermal fraction after a $100\mathrm{ms}$ equilibration time, our simulation recovers the experimental observations. We demonstrate that this discrepancy is due to the slow relaxation of the stirred cloud and dipole mode excitation of the cloud.

The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behavior of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way toward the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena.

Magneto-optical materials have found wide applications in optical-functional devices and topological photonics due to their magneto-optical activity and time-reversal symmetry breaking. However, there are rare kinds of magneto-optical materials in nature and their working frequencies are mostly limited to the microwave regime which largely limits the applications. In this work, we propose a scheme to realize an effective magneto-optical near-zero-index metamaterial, that is, using an array of spinning cylinders. The material of the cylinder can be arbitrary and the strength of the magneto-optical effect parameter can be tuned according to the spinning speed. Therefore, the operating frequency can go beyond the microwave regime and in principle cover much higher frequencies, which largely expands the range of operating frequency of magneto-optical materials. The results are verified by numerical full-wave simulations.

In this paper, we theoretically study the Faraday (FR) rotation effect excited by a transverse-magnetic (TM)-polarized wave passing through a bulk Weyl semimetal (WSM). Results show that the FR angle maintains a large value $(\sim \text{–}{21}^{\circ })$ with high transmission $\left(\right|t_{pp}|\sim 87\%)$, which is caused by the close transmission coefficient of $|t_{ps}|$ $|t_{ps}|$ and $|t_{pp}|$. What is more important, the FR angle can be further enhanced at the epsilon-near-zero (ENZ) frequency, where a maximum FR rotation angle (absolute value) of 45° has been obtained due to the sharp decreases of $|t_{pp}|$. Remarkably, the ENZ frequency of the WSM can be regulated by varying the Fermi energy and tilt degree, resulting in the tunable and enhanced FR angle at the different ENZ frequencies. Particularly, it is demonstrated that the incident angle should be declined with the increase of WSM thickness for enhancing the FR angle at the ENZ frequency. We also examine the effect of Weyl node separation on the FR angle. Our studies provide a simple and effective method to enhance and control the FR effect with a WSM or other topological semimetals.

When an atom is ionized by a strong laser pulse, the field can drive the released electron back to the parent ion and trigger the emission of a high-order harmonic photon with a frequency that is a function of the time of ionization. The attractive Coulomb potential causes a slowdown of the outgoing electron that must be compensated by an earlier release into the accelerating field to produce the same harmonic frequency as without the Coulomb force. By numerical solution of the time-dependent Schrödinger equation for a helium model atom, we demonstrate that such a subtle time shift of about 35 attoseconds is measurable by streaking with a weak, orthogonally polarized field combined with a complex-time trajectory interpretation. A comparison of results for high and low streaking frequency shows that only the high-frequency method measures the Coulomb shift well. This is confirmed by a classical trajectory model and by the analytical $R$-matrix theory.

We design a strategy for the real-time calibration of nuclear velocities in ultrafast molecular reactions in strong laser fields by simulating the four-dimensional time-dependent Schrödinger equation. Taking $\mathrm{H}{\mathrm{D}}^{+}$ as the prototype, an attosecond pump pulse initiates the molecular dissociation, and the other time-delayed attosecond probe pulse, polarized in the plane perpendicular to the molecular axis, ionizes the dissociating $\mathrm{H}{\mathrm{D}}^{+}$. During the dissociation, two nuclei with different masses acquire different velocities, which imprint on the photoelectron kicked off by the probe pulse. The expected photoelectron momentum along the molecular axis can be used to precisely calibrate instantaneous nuclear velocities at ionization. This strategy works widely in general heteronuclear molecules and paves the way for making high-definition molecular movies.

Investigating the boundary between a quantum mechanical description and a classical realistic view is of fundamental importance. The Leggett-Garg (LG) inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multilevel system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using a nitrogen-vacancy center in diamond by ideal negative result measurements. The experimental maximum value of the Leggett-Garg function is $K_3^{\text{expt}}=1.625\pm 0.022$, which exceeds the Lüders bound with a $5\sigma$ level of confidence.

The effect of nuclear polarization on the nonlinearities of a King plot for isotope shift in ${\mathrm{Ca}}^{+},$ ${\mathrm{Sr}}^{+},$ and ${\mathrm{Yb}}^{+}$ ions is studied. These ions are currently used in search for the manifestation of new interaction via nonlinearities of the King plot. The role of relativistic effects is also studied. The best way to achieve separation of electronic and nuclear variables (which is necessary for the linearity) is to present the field shift as $F^{″}\delta \langle r^{\lambda }\rangle ,$ where the value of $\lambda$ is the result of numerical relativistic calculations $[2\gamma <\lambda <2,$ $\gamma =\sqrt{1-{(Z/137.036)}^2}]$. Using this ansatz, we demonstrate that the contribution of the relativistic effects to the nonlinearity in spherical nuclei is very small.

We study the ground state of $N\gg 1$ noninteracting fermions in a two-dimensional harmonic trap rotating at angular frequency $\mathrm{\Omega }>0$. The support of the density of the Fermi gas is a disk of radius $R_e$. We calculate the variance of the number of fermions, ${\mathcal{N}}_R$, inside a disk of radius $R$ centered at the origin for $R$ in the bulk of the Fermi gas. We find rich and interesting behaviors in two different scaling regimes, (i) $\mathrm{\Omega }/\omega <1$ and (ii) $1-\mathrm{\Omega }/\omega =O(1/N)$, where $\omega$ is the angular frequency of the oscillator. In the first regime we find that $\mathrm{Var}{\mathcal{N}}_R\simeq (AlnN+B)\sqrt{N}$ and we calculate $A$ and $B$ as functions of $R/R_e$, $\mathrm{\Omega }$, and $\omega$. We also predict the higher cumulants of ${\mathcal{N}}_R$ and the bipartite entanglement entropy of the disk with the rest of the system. In the second regime, the mean fermion density exhibits a staircase form, with discrete plateaus corresponding to filling $k$ successive Landau levels, as found in previous studies. Here, we show that $\mathrm{Var}{\mathcal{N}}_R$ is a discontinuous piecewise linear function of $\sim (R/R_e)\sqrt{N}$ within each plateau, with coefficients that we calculate exactly, and with steps whose precise shape we obtain for any $k$. We argue that a similar piecewise linear behavior extends to all the cumulants of ${\mathcal{N}}_R$ and to the entanglement entropy. We show that these results match smoothly at large $k$ with the above results for $\mathrm{\Omega }/\omega =O\left(1\right)$. These findings are nicely confirmed by numerical simulations. Finally, we uncover a universal behavior of $\mathrm{Var}{\mathcal{N}}_R$ near the fermionic edge. We extend our results to a three-dimensional geometry, where an additional confining potential is applied in the $z$ direction.

An arbitrary conical angle is introduced to the circular Airy beam (CAB) beyond the paraxial approximation, with the possibility to demonstrate its obvious tunability for the propagation properties of the CAB. The expressions are worked out to describe the electric field based on the angular spectrum representation, where a closed-form approximation of the angular spectrum is derived by using the stationary phase method. It is found that the nonparaxiality becomes obvious for large conical angles. In particular, the field intensity at the focal point can be enhanced about 10 times with respect to the conventional CAB by simply tailoring the conical angle. Meanwhile, the longitudinal component of the field is enhanced and gradually plays a leading role as the conical angle is increased. Moreover, the longitudinal gradient of the field intensity is also enlarged for large conical angles, suggesting a stable optical trapping for microparticles, which may find many applications in optical manipulations.