We have experimentally demonstrated that magnetic-field-insensitive coherent-population-trapping (CPT) resonances are generated between the ground hyperfine levels on the $D_1$ line of ${}^{133}\mathrm{Cs}$ using a two-photon $\mathrm{\Lambda }$ scheme excited by lin||lin polarizations. The frequency shift of the CPT resonance is 0.04 Hz for the deviation of $1\mu \mathrm{T}$ at a “magic” magnetic field of $139\mu \mathrm{T}$ and is 50 times smaller than that of the conventional clock transition at a typical bias magnetic field for the clock operation. The amplitude of the CPT spectrum excited by lin||lin polarizations is enhanced as the excitation intensity increases and is well explained by the three-level model without trap levels. Thus, the CPT resonance on the $D_1$ line of ${}^{133}\mathrm{Cs}$ excited by a simple lin||lin scheme will be one of the best candidates for frequency reference of miniature atomic clocks.

Using genetic algorithm, we propose a method to retrieve the alignment distribution of transiently aligned ${\mathrm{CO}}_2$ molecules from the high-order harmonic generation (HHG) spectra. The retrieval method is based on the quantitative rescattering (QRS) model where averaged photorecombination transition dipole can be factored out from the parallel (or perpendicular) harmonic spectra after the propagation of the harmonic fields in the gas medium. We examine how the retrieved alignment distributions are affected by uncertainty in alignment-dependent ionization probability and on multiple orbital contribution to the HHG. We further confirm that alignment distribution is more accurately retrieved by using the minima in the HHG spectra driven by a long-wavelength laser. In addition, we show that earlier experimental data on the ratios between the perpendicular and the parallel HHG components of aligned ${\mathrm{CO}}_2$ molecules are in better agreement with the QRS model if the macroscopic propagation and multiple orbital interference are included in the theoretical calculation.

We consider a Bogoliubov–de Gennes (BdG) Hamiltonian, which is a non-Hermitian Hamiltonian with pseudo-Hermiticity, for a system of (pseudo) spin-$1/2$ bosons in a honeycomb lattice under the condition that the population difference between the two spin components, i.e., magnetization, is a constant. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry, with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We quantitatively study the topological properties of this model within the framework of the 38-fold way for non-Hermitian systems. We find, through the symmetry analysis of the Bloch Hamiltonian, that this model is classified either as two copies of symmetry class $\text{AIII}+{\eta }_{-}$ or two copies of symmetry class $\text{A}+\eta$ depending on whether the (total) system is time-reversal symmetric, where $\eta$ is the matrix representing pseudo-Hermiticity and ${\eta }_{-}$ indicates that pseudo-Hermiticity and chiral symmetry operators anticommute. We prove, within the context of non-Hermitian physics where eigenstates obey the bi-orthonormality relation, that a stable bulk is characterized by a single topological invariant, the Chern number for the Haldane model, independent of pairing interactions. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes, which is expected to be useful for models built upon copies of the Haldane model across a broad array of disciplines. We adapt the theorem in our recent work [Ling and Kain, Phys. Rev. A 104, 013305 (2021)] to pseudo-Hermitian Hamiltonians that are less restrictive than BdG Hamiltonians and apply it to highlight that the vanishing of an unconventional commutator between number-conserving and number-nonconserving parts of the Hamiltonian indicates whether a system can be made to act as a topological amplifier.

We report on a theoretical study of a ring-shaped Bose-Einstein condensate with Raman-induced spin-orbital-angular-momentum coupling. We analyze the structure of the ground state of the system depending on different physical parameters and reveal a peculiar fine structure within the stripe phase on the phase diagram. We demonstrate the existence of the predicted stripe subphases within a wide range of physical parameters, and their traceability through physical observables, and compare the results with several commonly used variational approximations. We also show that predicted subphases of the stripe phase can be observed within experimentally realizable conditions.

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of a one-dimensional system with a nontrivial band topology. An interplay of disorder and topological ordering in the SSH model is of great interest owing to experimental advancements in synthesized quantum simulators. In this paper, we investigate a special sort of a disorder when intercell hopping amplitudes are random. Using a definition for ${\mathbb{Z}}_2$-topological invariant $\nu \in \{0;1\}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\langle \nu \rangle$ averaged by random realizations. This allows to find: (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite-size fluctuations of $\nu$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for the finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green's function method for a thermodynamic limit.

We propose an analog quantum simulator for simulating real-time dynamics of $(1+1)$-dimensional non-Abelian gauge theory well within the existing capacity of ultracold-atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a one-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on the loop string hadron formalism of $SU\left(2\right)$ lattice gauge theory, this simulation technique is completely $SU\left(2\right)$ invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable and particularly effective in simulating the theory in the weak-coupling regime, and also a bulk limit of the theory in the strong-coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of the exact spectrum and real-time dynamics of lattice gauge theory to that of the atomic Hamiltonian with an experimentally realizable range of parameters.

We consider the interplay of repulsive short-range and same-sign long-range interactions in the dynamics of dark solitons, as prototypical coherent nonlinear excitations in a trapped one-dimensional Bose gas. First, the form of the ground state is examined, and then both the existence of the solitary waves and their stability properties are explored, and corroborated by direct numerical simulations. We find that single- and multiple-dark-soliton states can exist and are generically robust in the presence of long-range interactions. We analyze the modes of vibration of such excitations and find that their respective frequencies are significantly upshifted as the strength of the long-range interactions is increased. Indeed, we find that a prefactor of the long-range interactions considered comparable to the trap strength may upshift the dark soliton oscillation frequency by an order of magnitude, in comparison to the well established one of $\mathrm{\Omega }/\sqrt{2}$ in a trap of frequency $\mathrm{\Omega }$.

The conventional optical theorem cannot consider losses of host media. As a fundamental problem of light scattering, the generalized optical theorem of an infinite cylinder embedded in a weakly absorbing host is studied in this paper. Using the analytical way, we derive the generalized far-field and distance-independent extinction efficiencies per unit length of the cylinder under normally incident p- and s-polarized waves, which reduce to the conventional formulas in the transparent host media. For large cylinders, the increasing absorption of the host medium leads to an increasing amplitude of interference oscillation and the emergence of negative extinction, which is similar to that for spheres. Furthermore, the absorption of the host medium is proved to destroy the morphology-dependent resonance structure in extinction and suppress the electric field resonance inside the cylinder. For small cylinders in a weakly absorbing host medium, we present the conditions for negative extinction and quantitatively analyze the differences in extinction between the absorbing host medium and the nonabsorbing counterpart. It is found that the ratio of the extinction from the generalized theory to conventional formulas depends only on the refraction indices of the cylinder and the host medium. The results for small cylinders are rather sensitive to the state of polarization of the light. By illustrating the significant differences between the generalized optical theorem and the conventional theory with a specific case of a Ge cylinder in polyethylene, we show the non-negligible impacts of the absorption of the host media on the optical extinction of the cylinder for the two polarizations.

We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can therefore be used as a foundation for describing any phenomenon resulting from any combination of linear coupling, scattering, and Kerr nonlinearity, such as bending and surface roughness losses, geometric backscattering, self- and cross-phase modulation, four-wave mixing, third-harmonic generation, and Kerr frequency comb generation. The theory is then applied to a translationally symmetric waveguide in order to calculate the evanescent coupling strength to the modes of a microresonator placed nearby, as well as the Kerr self- and cross-phase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetry-breaking dynamics of two counterpropagating modes of a loop resonator and prove that cross-phase modulation is exactly twice as strong as self-phase modulation only in the case that the two counterpropagating modes are otherwise identical.

We analytically derive the mean path length of light rays diffusely incident on refractive regular polygons of $n$ sides ($n$-gons), analyzed from the dynamical billiards perspective and from ray optics. In polygons with sufficiently low refractive index, the mean path length is found to be equal to that in the invariant scattering case, i.e., the product of the mean chord length with the refractive index. If the refractive index is higher than some critical value, the mean path length is lower than the scattering value due to inaccessibility of trapped modes. Regular odd $n$-gons are found to have the same mean path length as $2n$-gons, when normalized against their mean chord length. There is a discontinuity between the mean path length in high $n$-gons and that in a circle, attributed to quasitrapped modes in high $n$-gons. This difference is removed with a small amount of absorption. We extend the results to refractive prisms with a regular polygon base, for example, hexagonal ice crystals. For prisms with any ergodic shaped base, we derive a simple formula for the mean path length.

Large arrowhead matrices with randomly distributed entries describe a variety of important phenomena where a degree of freedom is nonlocally coupled to a disordered continuum of modes, including central-spin problems in condensed matter, molecular junctions, and quantum emitters in cavity QED. Here we provide an exact solution of random arrowhead Hamiltonians with diagonal disorder in the thermodynamic limit. For concreteness, we focus on the problem of $N$ emitters homogeneously coupled to a nonlocal cavity mode, corresponding to the disordered Tavis-Cummings model of cavity QED in the single-excitation limit, for which we provide asymptotically exact formulas for static and dynamical quantities of interest. By varying the coupling strength, we find that the distribution of energy spacing can be continuously tuned between Poisson statistics and a distribution that is very close to semi-Poisson statistics, the latter statistics being usually associated with the critical point of Anderson localization-delocalization transitions. We show that the system has a peculiar diffusivelike behavior with an escape probability growing linearly with time for any finite coupling strength and that the escape rate can be controlled by selecting the energy of the initial site. The escape rate averaged over the disorder configurations is found to exhibit a maximum for intermediate coupling strengths, before saturating at a lower, $g$-independent value for sufficiently large $N$ in the collective strong-coupling limit, a cavity protection effect. We investigate the system in a two-terminal configuration and show that the steady-state excitation current exhibits features similar to the escape probability, thereby extending our cavity-protected transport scenario to out-of-equilibrium situations. We finally demonstrate that dark states can provide a major contribution to long-distance transport in disordered systems.

We theoretically propose a scheme to perform rotation sensing in a whispering-gallery-mode resonator setup. With the assistance of a largely detuned two-level atom, which induces the effective coupling between clockwise- and counterclockwise-propagating modes in the resonator, we realize an effective interferometry with SU(2) algebraic structure. By studying the quantum Fisher information of the system, we find that the estimated accuracy for the angular velocity of the rotation can achieve and even break the Heisenberg limit in the linear and nonlinear setup, respectively. The high performance of quantum metrology is proved to be associated with the state compressibility during the time evolution. We hope that our investigation will be useful in the design of a quantum gyroscope based on spinning resonators.

We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation $r$. At $r\lesssim \xi$, where $\xi$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\gg \xi$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/r^3$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

We investigate the relation between tripartite entanglement of the three-qubit system and the maximum steering inequality violation of the reduced two-qubit states. Firstly, it is found that a single parameter family of entangled three-qubit pure states have the maximum steering inequality violation among all of the three-qubit pure states for a fixed amount of tripartite entanglement. The tripartite entanglement is quantified by the genuinely multipartite concurrence, generalized geometric measure, and tangle. Subsequently, the complementary relation between tripartite entanglement and the maximum steering inequality violation for an arbitrary three-qubit pure state can be established. Particularly, the result also holds for three-qubit mixed states if the entanglement measure is tangle. The complementary relations indicate that the maximum steering inequality violation of the reduced two-qubit system is at the expense of tripartite entanglement.

Quantum error mitigation is essential for many computing tasks on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit overhead or requiring only one ancilla qubit. In dual-state purification, we effectively generate a purified state with increased fidelity using the erroneous state and its dual state, respectively, prepared with the noisy quantum circuit and the dual map of its inverse circuit. Combined with tomography purification, we can make sure that the final estimate of an observable is obtained from a pure state. While the absolute error increases, the numerical result, based on a depolarizing model, suggests that our protocol reduces the error compared to the case without the protocol by a rescaling factor decreasing with the qubit number and circuit depth; i.e., the relative performance of purification is better for larger circuits. On a cloud quantum computer, we successfully demonstrate the reduced error with a quantum variational eigensolver circuit.

Crosstalk and several forms of coherent noise are invisible when a qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of a full quantum circuit applying entangling gates to several qubits simultaneously. Unitary crosstalk noise, such as an unwanted Z-Z coupling, limits the state fidelity during the execution of cross-resonance controlled-not (cnot) gates in superconductor quantum computers. This work presents (1) a method of tracing coherent errors by exploiting their sensitivity to the arrangement of cnot gates in the circuit and (2) a correction scheme that modifies the original circuit by inserting carefully the chosen compensating gates (single- or two-qubit) to possibly undo coherent errors. On two vastly different types of IBMQ processors offering quantum volume 8 to 32, our experimental results show up to 25% reduction in the infidelity of $\left[\right[7,1,3\left]\right]$ code $|+\rangle$ state (Clifford circuits) and five- to 15-qubit $W$ states (non-Clifford circuits). Our experimental circuits aggressively deploy forced commutation of cnot gates to obtain low-noise state-preparation circuits. An encoded state initialized with fewer errors marks an important step towards successful demonstration of fault-tolerant quantum computers.

The preparation of ground states of spin systems is a fundamental operation in quantum computing and serves as the basis of adiabatic quantum computing. This form of quantum computation is subject to the adiabatic theorem which in turn poses a fundamental speed limit. We show that by employing diabatic transitions via counterdiabatic driving, a less strict requirement on adiabaticity applies. We demonstrate a scaling advantage from local and multispin counterdiabatic driving in the ground-state fidelity compared to their adiabatic counterpart, for different Ising spin models.

We study theoretically the bound states of one and two boron atoms in the exohedral and endohedral ${\mathrm{C}}_{60}$ fullerene. The optimal position of one boron atom is found above the midpoint of the ${\mathrm{C}}_{60}$ double bond in the exohedral complex, and at the center of ${\mathrm{C}}_{60}$ or below a carbon atom in the endohedral complex. However, the optimal position of a boron atom is often altered when the second boron atom is added to the molecular complex. For two boron atoms outside the cage the optimal arrangement is realized when the ${\mathrm{B}}_2$ molecule is attached by one boron atom to a double bond midpoint of ${\mathrm{C}}_{60}$ or when two boron atoms are above two double bond midpoints on opposite sides of ${\mathrm{C}}_{60}$. Two endohedral boron atoms can lie on the line joining either two opposite double bond midpoints or two centers of opposite pentagons. The latter case corresponds to the optimal geometry of the ${\mathrm{B}}_2$@${\mathrm{C}}_{60}$ complex provided that two boron atoms are close enough to form the ${\mathrm{B}}_2$ molecule. In case one boron atom is inside while the other is outside the cage, the optimal locations of atoms are above and below two neighboring carbon atoms belonging to the same hexagon of ${\mathrm{C}}_{60}$. Remarkably, all these optimal arrangements have different spin states: in the exohedral complex ${\mathrm{B}}_2{\mathrm{C}}_{60}S=1$, in the endohedral ${\mathrm{B}}_2$@${\mathrm{C}}_{60}S=2$ (as in the isolated ${\mathrm{B}}_2$ molecule), whereas for one boron atom inside and the other outside the cage $S=0$. The effective (Bader) charge of boron in these configurations varies appreciably—from $0.06e$ at the center of ${\mathrm{C}}_{60}$ to $2e$ in the ${\mathrm{B}}_2{\mathrm{C}}_{58}$ molecule with two boron atoms substituting for two carbon atoms in ${\mathrm{C}}_{60}$. We also discuss various conformations in the exohedral and endohedral molecular complexes.

Clouds of cold neutral atoms driven by a coherent light beam in a ring cavity exhibit self-structured states transversely with respect to the beam axis due to optomechanical forces and the backaction of the atomic structures on the beam. Below the instability threshold for extended hexagonal structures, localized solitonlike excitations can be stable. These constitute peaks or holes of atom density, depending on the linear susceptibility of the cloud. Complex rotating and spiraling motion of coupled atom-light solitons, and, hence, atomic transport, can be achieved via phase gradients in the input field profile. We also discuss the stability of rotating soliton chains in view of soliton-soliton interactions. The investigations are performed in a cavity scheme but expected to apply to other longitudinally pumped schemes with diffractive coupling.