We develop a theory describing the transient transmission through noisy qubit-resonator systems with quadratic interactions as are found in superconducting and nanomechanical resonators coupled to solid-state qubits. After generalizing the quantum Langevin equations to arbitrary qubit-resonator couplings, we show that only the cases of linear and quadratic couplings allow for an analytical treatment within standard input-output theory. Focussing on quadratic couplings and allowing for arbitrary initial qubit coherences, it is shown that noise characteristics can be extracted from input-output measurements by recording both the averaged fluctuations in the transmission probability and the averaged phase. Our results represent an extension to the field of transmission-based noise spectroscopy with immediate practical applications.

The ionization of atoms and molecules by strong laser fields has been studied extensively, both theoretically and experimentally. The strong-field approximation (SFA) allows for the analytical solution of the Schrödinger equation and accurately predicts the behavior of ionization processes in intense laser fields. Over the past decade, there has been a growing interest in the study of nondipole effects in these processes. However, such predictions have so far been limited to monochromatic driving laser fields, while experiments often employ quite short pulses. In this paper, we therefore present an extension of the SFA that also allows incorporating the more complicated temporal structure of a few-cycle pulse. By this extension, the prediction of so-called peak shifts is significantly improved, and the ability to control the laser pulse inducing above-threshold ionization is greatly enhanced. The enhanced control over the characteristics of the laser pulse results in more accurate predictions of peak shifts. Our results show better agreement with experimental investigations compared to previous theoretical studies.

We provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated electromagnetic fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-$\mathrm{\Lambda }$ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. We find that a complex-valued nonlinear coupling coefficient can lead to noises even without linear gain or loss. Finally, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

This work demonstrates the capabilities of an entangled photon-pair source at telecom wavelengths, based on a photonic integrated ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator with monolithically integrated piezoelectric frequency tuning. Previously, frequency tuning of photon pairs generated by microresonators has only been demonstrated using thermal control, however these have limited actuation bandwidth and are not compatible with cryogenic environments. Here, the frequency-tunable photon-pair generation capabilities of a ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator with a monolithically integrated aluminium nitride layer are shown. Fast-frequency locking of the microresonator to an external laser is demonstrated, with a resulting locking bandwidth orders of magnitude larger than reported previously using thermal locking. These abilities will have direct application in future schemes which interface such sources with quantum memories based on, e.g., trapped-ion or rare-earth-ion schemes.

We numerically investigate the dynamics of vortex generation in a two-dimensional, two-component Bose-Einstein condensate subjected to an oscillatory magnetic obstacle. The obstacle creates both repulsive and attractive Gaussian potentials for the two symmetric spin-$\uparrow$ and $\downarrow$ components, respectively. We demonstrate that, as the oscillating frequency $f$ increases, two distinct critical dynamics arise in the generation of half-quantum vortices (HQVs) with different spin circulations. Spin-$\uparrow$ vortices are nucleated directly from the moving obstacle at low $f$, while the spin-$\downarrow$ vortices are created at high $f$ by breaking a spin wave pulse in front of the obstacle. We find that vortex generation is suppressed for sufficiently weak obstacles, in agreement with recent experimental results by Kim et al. [Phys. Rev. Lett. 127, 095302 (2021)]. This suppression is caused by the finite sweeping distance of the oscillating obstacle and the reduction in friction in a supersonic regime. Finally, we show that the characteristic length scale of the HQV generation dynamics is determined by the spin healing length of the system.

We propose a scheme to realize an optical Bessel potential with parity-time ($\mathcal{P}T$) symmetry and investigate the existence, propagation, and manipulation of multidimensional optical solitons through the interplay among diffraction, Kerr nonlinearity, and potential confinement in a cold atomic gas under the condition of electromagnetically induced transparency (EIT). We show that the system supports not only two-dimensional stationary optical solitons but also rotary ones; the stability of such solitons can be actively controlled by the gain-loss component (imaginary part), while the rotary motions can be tuned by the refractive-index component (real part) of the $\mathcal{P}T$-symmetric potential. Moreover, we demonstrate that the system allows the existence of stable three-dimensional spatiotemporal optical solitons, i.e., optical bullets, which have ultraslow propagation velocity and display helicoidal motions with controllable propagation trajectories. Due to the Kerr nonlinearity enhanced by the EIT effect, extremely low power is needed to create these multidimensional optical solitons. The results reported here are useful not only for the generation and manipulation of high-dimensional solitons via $\mathcal{P}T$-symmetric potentials, but also for promising applications in optical information processing and transmission.

Optical systems obeying non-Hermitian dynamics have been the subject of intense and concerted investigation over the past two decades owing to their broad implications in photonics, acoustics, electronics, and atomic physics. A vast majority of such investigations rely on a dissipative, balanced loss-gain system which introduces unavoidable noise, and consequently this limits the coherent control of propagation dynamics. Here, we show that an all-dielectric, nondissipative photonic crystal (PC) could host at least two exceptional points in its eigenvalue spectrum. By introducing optimum apodization in the PC architecture, namely 1D-APC, we show that such a configuration supports a spectrum of exceptional points which distinctly demarcates the $\mathcal{PT}$-symmetric region from the region where $\mathcal{PT}$ symmetry is broken. The analytical framework allows us to estimate the geometric phase of the reflected beam and derive the constraint that governs the excitation of topologically protected optical Tamm-plasmon modes in 1D APCs.

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [Baker et al., Nat. Phys. 17, 179 (2021)]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In our related work [Ostrowski et al., Phys. Rev. Lett. 130, 183602 (2023)] we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this paper we provide details of the calculations given in our related paper and introduce three families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, $p$, with $p=4$ corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of $p$, where for $p>3$, each family of models exhibits Heisenberg-limited beam coherence, while for $p<3$, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulas for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact $p\approx 4.15$, not $p=4$.

We perform a systematical study for the polarization of x rays emitted when a free electron is captured by Be-like highly charged ions theoretically. We focus on the dielectronic recombination of the $J=1/2\to J=1/2$ transition and its polarization is zero due to axial symmetry. Including the interference between the dielectronic and radiative recombinations, the polarization changes dramatically when the electron energy crosses the resonant energy. By comparing the simulations with or without certain interactions, we found that the Breit interaction is not important even for very high-$Z$ ions. For low-$Z$ ions, the configuration interaction of the dielectronic recombination states affects the polarization greatly, while for high-$Z$ ions the configuration interaction of the ground state of Be-like ions plays an important role.

We study the ground-state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density-matrix renormalization-group-method simulations, we construct grand-canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

Supersolid is a special state of matter with both superfluid properties and spontaneous modulation of particle density. In this paper we focus on the supersolid stripe phase realized in a spin-orbit-coupled Bose-Einstein condensate and explore the properties of a class of metastable supersolids. In particular, we study a one-dimensional supersolid whose characteristic wave number $k$ (magnitude of wave vector) deviates from $k_m$, i.e., the one in the ground state. In other words, the period of density modulation is shorter or longer than the one in the ground state. We find that this class of supersolids can still be stable if their wave numbers fall in the range $k_{c1}<k<k_{c2}$, with two thresholds $k_{c1}$ and $k_{c2}$. Stripes with $k$ outside this range suffer from dynamical instability with a complex Bogoliubov excitation spectrum at long wavelength. Experimentally, these stripes with $k$ different from $k_m$ are accessible by exciting the longitudinal spin dipole mode, resulting in temporal oscillation of the stripe period as well as $k$. Within the mean-field Gross-Pitaevskii theory, we numerically confirm that for a large enough amplitude of spin dipole oscillation, the stripe states become unstable through breaking periodicity, in qualitative agreement with the existence of thresholds of $k$ for stable stripes. Our work extends the concept of supersolid and uncovers an unconventional class of metastable supersolids to explore.

A distinguishing feature of ultracold collisions of bosonic lithium atoms is the presence of two near-degenerate two-body continua. The influence of such a near degeneracy on the few-body physics in the vicinity of a narrow Feshbach resonance is investigated within the framework of a minimal model with two atomic continua and one closed molecular channel. The model allows analysis of the spin composition of loosely bound dimers and trimers. In the two-body sector the well-established coupled-channel calculation phenomenology of lithium is qualitatively reproduced, and its particularities are emphasized and clarified. In the three-body sector we find that the Efimov trimer energy levels follow a different functional form as compared to a single continuum scenario while the thresholds remain untouched. This three-channel model with two atomic continua complements our earlier developed three-channel model with two molecular channels [Yudkin and Khaykovich, Phys. Rev. A 103, 063303 (2021)] and suggests that the experimentally observed exotic behavior of the first excited Efimov energy level (Yudkin, Elbaz, and Khaykovich, arXiv:2004.02723) is most probably caused by the short-range details of the interaction potential.

Introducing a nonstoquastic catalyst is a promising avenue to improve quantum annealing with the transverse field. In the present paper, we propose a nonstoquastic catalyst for bifurcation-based quantum annealing described by the spin-1 operators to improve the efficiency of a ground-state search. To investigate the effect of the nonstoquastic catalyst, we study the ferromagnetic $p$-spin model, which has difficulty with finding the ground state due to the first-order phase transition for quantum annealing. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated by introducing the proposed nonstoquastic catalyst with the appropriate amplitude. We also numerically calculate the minimum energy gap for a finite-size system by diagonalizing the Hamiltonian. We find that while the energy gap decreases exponentially with increasing system size for the original Hamiltonian, it decreases polynomially against the system size for the Hamiltonian with the nonstoquastic catalyst. This result implies that the proposed nonstoquastic catalyst has the potential to improve the performance of bifurcation-based quantum annealing.

We propose a universal magnetic-free scheme to achieve phase nonreciprocity. The scheme requires only two tunable phase shifters and a proper length of the delay line. The phase shifter can be tuned to provide phase shifts $\delta$ and $\delta +\pi$ over a wide bandwidth. When passing through the two phase shifters, in the forward direction, signals acquire the same phase shift, $\delta$ or $\delta +\pi$. However, in the backward direction, signals acquire different phase shifts; one is $\delta$, and the other is $\delta +\pi$. We use superconducting elements to build up such a gyrator and use it as the nonreciprocal path in a circulator. The circulator can achieve 15-dB isolation across the 4.92–8.76-GHz band. We can cascade two such circulators to get an isolator of more than 20-dB isolation in the frequency range of 4.16–9.33 GHz. The scheme can be easily applied to other platforms such as rf communication systems and nanophotonics.

The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schrödinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and ($2+1$)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.

We propose a scheme to simulate the extended Su-Schrieffer-Heeger (SSH) model by using the hybrid cavity magnonics system. We consider a hybrid cavity-magnon array with $N$ sites, where each site contains two cavity modes and one magnon mode, and the cavity modes at the neighboring site couple to each other with controllable tunneling rates. Under large detuning conditions, we adiabatically eliminate the cavity field and obtain periodic interactions between the magnons depending on the phase between adjacent cavity fields. After setting the relationship of the phases, we obtain the magnon version of the extended SSH model. Employing this model, we investigate the distribution of edge states and the topological phase transition. Moreover, our scheme can be easily extended to the SSHm model with the jump period $m$ by setting different phase shifts. Finally, considering the noninteger cell case, we find that an arbitrary magnon entangled state can be encoded by two edge states and transferred from the left site end to the right site end via the adiabatic channel. Our work provides a pathway for realizing quantum information transmission and offers an idea for implementing quantum simulations based on cavity magnonics systems.

The deterministic quantum computation with one-clean-qubit model (DQC1) complexity class, or power-of-one qubit model, is examined as an open quantum system. We study the dynamics of a register of qubits carrying out a DQC1 algorithm and show that, for any algorithm in the complexity class, the evolution of the logical qubit can be described as an open quantum system undergoing a dynamics which is unital. Unital quantum channels respect the Tasaki-Crooks fluctuation theorem, and we demonstrate how this is captured by the thermodynamics of the logical qubit. As an application, we investigate the equilibrium and nonequilibrium thermodynamics of the DQC1 trace estimation algorithm. We show that different computational inputs, i.e., different traces being estimated, lead to different energetic exchanges across the register of qubits and that the temperature of the logical qubit impacts the magnitude of fluctuations experienced and quality of the algorithm.

There are many approaches when it comes to exploring the potential of the random access code (RAC) communication protocol. Given its versatility, the RAC is particularly useful when the communication between parties is restricted. In previous works, it has been proven that $2^{\left(d\right)}\to 1$ quantum random access codes (QRAC), in the absence of noise, outperform their classical counterpart (the $2^{\left(d\right)}\to 1$ CRAC) for any dimension $d$. Here, building upon these works, we showed that noisy channels can significantly decrease the performance of $2^{\left(d\right)}\to 1$ QRAC. In order to mitigate noise-driven efficiency losses, we employed the see-saw optimization algorithm with semidefinite programming (SDP) to find the best quantum encoding and decoding strategies for the QRAC given a known quantum channel.

The Dirac equation for ${{\mathrm{H}}_2}^{+}$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27 to 32 digits) is achieved, either with the dual kinetic balance, which provides the fastest convergence, or without imposing any kinetic balance condition. An application to heavy molecular ions is also illustrated. The calculation of relativistic sum rules shows that this method gives an accurate representation of the complete Dirac spectrum, making it a promising tool for calculations of QED corrections in molecular systems.

We measure the thermalization dynamics of a lattice Bose gas that is Stark localized by a parabolic potential. A nonequilibrium thermal density distribution is created by quickly removing an optical barrier. The resulting spatiotemporal dynamics are resolved using Mardia's $B$ statistic, which is a measure sensitive to the shape of the entire density distribution. We conclude that equilibrium is achieved for all lattice potential depths that we sample, including the strongly interacting and localized regime. However, thermalization is slow and nonexponential, requiring up to 500 tunneling times. We show that the Hubbard $U$ term is not responsible for thermalization via comparison to an exact diagonalization calculation, and we rule out equilibration driven by lattice-light heating by varying the laser wavelength. The thermalization timescale is comparable to the next-nearest-neighbor tunneling time, which suggests that a continuum, strongly interacting theory may be needed to understand equilibration in this system.