A cat state is formed as the steady-state solution for the signal mode of an ideal degenerate parametric oscillator, in the limit of negligible single-photon signal loss. In the presence of signal loss, this is no longer true over timescales much longer than the damping time. However, for sufficient parametric nonlinearity, a cat state can still exist as a transient state. In this paper we study the dynamics of the creation and decoherence of cat states in degenerate parametric oscillation, both with and without the Kerr nonlinearity found in recent superconducting-circuit experiments that generate cat states in microwave cavities. We determine the time of formation and the lifetime of a cat state of fixed amplitude in terms of three dimensionless parameters $\lambda$, $g$, and $\chi$. These relate to the driving strength, the parametric nonlinearity relative to signal damping, and the Kerr nonlinearity, respectively. We find that the Kerr nonlinearity has little effect on the threshold parametric nonlinearity ($g>1$) required for the formation of cat states and does not significantly alter the decoherence time of the cat state, but can reduce the time of formation. The quality of the cat state increases with the value of $g$. To verify the existence of the cat state, we consider several signatures, including interference fringes and negativity. We emphasize the importance of taking into account more than one of these signatures. We simulate a superconducting-circuit experiment using published experimental parameters and find good agreement with experimental results, indicating that a nonclassical catlike state with a small Wigner negativity is generated in the experiment. Interference fringes, however, are absent, requiring higher $g$ values. Finally, we explore the feasibility of creating large cat states with a coherent amplitude of 20, corresponding to 400 photons, and study finite-temperature reservoir effects.

We demonstrate numerically and analytically the optical binding between a pair of chiral nanoparticles immersed in a plane wave of linear polarization. The numerical results based on the full wave simulation show that, when the electric field of the incident wave is polarized along the pair axis (the line connecting the particle pair), the closest dimer can be formed at particle separation around $1.25\lambda$, with $\lambda$ denoting the incident wavelength, while when the electric field is polarized normal to the pair axis, the nearest dimer is formed with a separation of one wavelength. In both cases, there exist multiple stable dimer states due to the spatially oscillatory decaying behavior of the binding force with the increase of particle distance. Interestingly, there also appears a lateral optical force exerted on each particle in the direction normal to both the pair axis and light flow, when either or both particles have chirality. Analytical analysis within the dipole approximation indicates that the binding force comes dominantly from the gradient of the optical potential, irrespective of particle chirality. The lateral force, on the other hand, has multiple origins. In addition to the gradient force, the radiation force, the curl force, and the spin force may make significant contributions dependent on the particle chirality, as the particles approach each other.

We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point-source initial condition. We show that in both the propagation and Klein-tunneling regimes, the zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the zitterbewegung frequency and that the amplitude of these oscillations decays as $t^{-3/2}$. We show that the beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cutoff quantum states. We also find a time domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction-in-time phenomenon observed in nonrelativistic systems. The relative positions of these wavefronts are used to investigate the time delay of quantum waves in the Klein-tunneling regime. We show that depending on the energy difference $\mathcal{E}$ between the source and the potential step, the time delay can be positive, negative, or zero. The latter case corresponds to a super-Klein-tunneling configuration, where $\mathcal{E}$ equals half the energy of the potential step.

Interaction information, a measure of higher-order statistical correlations, is examined in quantum systems consisting of three coupled and uncoupled oscillators, in position and in momentum space. The magnitudes of the interaction information are greater than zero, and equal in both spaces, in the uncoupled case. This is interpreted as a dominance of synergic effects due to the indistinguishability of particles, and is larger for symmetric wave functions compared to antisymmetric ones. In symmetric wave functions, the magnitude of interaction information increases with the coupling strength, and the inclusion of coupling reveals differences in behavior between the spaces. With attractive potentials, interaction information is positive in momentum space (synergic) and negative in position space (redundant). This is reversed with repulsive potentials. It is now position space which yields positive values, while momentum space gives negative ones. The inclusion of spin provides antisymmetric wave functions which yield that the overall tendencies are maintained. However, there are regions for both attractive and repulsive potentials where the sign of interaction information changes, with the interpretation that the balance changes from a dominance of synergic to that of redundant interactions, and vice versa. This suggests that the nature of the interactions in these systems can be tuned with the coupling strength.

We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indicator of code quality than, say, entanglement fidelity. Yet our algorithm does not suffer from inefficiencies usually associated with the use of worst-case fidelity. Specifically, using a near-optimal recovery map, we are able to reduce the triple numerical optimization needed for the search to a single optimization over the encoding map. We can further reduce the search space by using the Cartan decomposition, focusing our search over the nonlocal degrees of freedom resilient against independent per-qubit noise, while not suffering much in code performance.

Distilling precise estimates from noisy intermediate scale quantum (NISQ) data has recently attracted considerable attention Kandala et al., Nature (London) 567, 491 (2019). In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e., the ability to accurately distill precise observable estimates, as a hybrid quantum classical computing benchmarking task. Specifically, using Rabi oscillations as a test program, we characterize single qubit error rates on IBM's Poughkeepsie superconducting quantum hardware, incorporate control-mediated noise dependence into a generalized rescaling protocol, and analyze how noise characteristics influence Richardson extrapolation-based error mitigation. Our results identify regions in the space of Hamiltonian control fields and circuit depth which are most amenable to reliable noise extrapolation, as well as shed light on how low-level hardware characterization can be used as a predictive tool for uncertainty quantification in error-mitigated NISQ computations.

We report an absolute frequency measurement of the $2s3d{}^1{D}_2$ state in neutral ${}^9\mathrm{Be}$ using two-photon spectroscopy with a resonant intermediate state. The absolute center-of-gravity energy is determined to be 64 428.40 321(55) ${\mathrm{cm}}^{-1}$, a factor of 180 more precise than the previous experimental measurement. We also confirm our previous result for the energy of the intermediate $2s2p{}^1{P}_1$ level. Precision is limited by unresolved hyperfine structure and the complications of performing resonant two-photon spectroscopy on an atomic beam. A three-level rate-equation analysis is presented to explore, and minimize, systematic uncertainties arising from small deviations of the angle between the atomic and optical beams off-perpendicular.

We perform calculations of the $CP$-violating atomic and molecular electric dipole moments (EDMs) induced by the interaction of the nuclear Schiff moments with electrons. EDMs of atoms Eu, Dy, Gd, Ac, Th, Pa, U, Np, and Pu are of special interest since they have isotopes with strongly enhanced nuclear Schiff moments caused by the octupole nuclear deformation or soft octupole vibration mode. These atoms have open $4f$ or $5f$ shells making the calculations complicated. We use our special version of the configuration-interaction method combined with the many-body perturbation theory method adopted for an open $f$-shell case. To validate the method we perform similar calculations for simpler atoms (Xe, Hg, ${\mathrm{Tl}}^{+}$, Pb, ${\mathrm{Pb}}^{2+}$, Rn, Ra), where some earlier results are available. In addition, we present the estimates of the $CP$-violating nuclear spin–molecular axis interaction constants for molecules which may be of experimental interest, including AcF, AcN, ${\mathrm{AcO}}^{+}$, EuN, ${\mathrm{EuO}}^{+}$, ThO, PbO, and TlF. We also present updated values of the nuclear Schiff moments and atomic and molecular EDMs expressed in terms of the $CP$-violating $\pi$-meson–nucleon interaction constants ${\overline{g}}_0$, ${\overline{g}}_1$, ${\overline{g}}_2$, QCD parameter $\overline{\theta }$, and quark chromo-EDMs. The results may be used to test $CP$-violation theories and search for axion dark matter in atomic, molecular, and solid-state experiments.

Ultracold polar molecules can be shielded from fast collisional losses using microwaves, but achieving the required polarization purity is technically challenging. Here, we propose a scheme for shielding using microwaves with polarization that is far from circular. The setup relies on a modest static electric field and is robust against imperfections in its orientation.

Production of electron-positron pairs from vacuum in strong bichromatic electric fields, oscillating in time with a fundamental frequency and its second harmonic, is studied. Strong-field processes occuring in such field configurations are generally known to be sensitive to the relative phase between the field modes. Phase-of-the-phase spectroscopy has recently been introduced in the context of strong-field photoionization as a systematic means to analyze these coherence effects. We apply this method to the field-induced pair production by calculating the phase dependence of the momentum-resolved particle yields. We show that asymmetric checkerboard patterns arise in the phase-of-the-phase spectra, similarly to those found in strong-field photoionization. The physical origin of these characteristic structures, which differ between the created electron and positron, is discussed.

Bright solitary waves in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. They nonetheless behave like a compound object, staying whole in collisions, with their collision properties strongly affected by intersoliton quantum coherence. We show that separate solitary waves decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions occur predominantly repulsively and can no longer be described within mean-field theory. When considering the timescales involved in recent solitary wave experiments where nonequilibrium phenomena play an important role, these features could explain the predominantly repulsive collision dynamics observed in most condensate soliton train experiments.

We study the dispersive readout of a qubit in the ultimate limit of a single-photon probe. The use of a single-photon probe avoids the errors due to nonorthogonality of coherent states. A photodetector is used in the scheme we consider. The dynamics of the system is studied using the Heisenberg-Langevin equations. We treat the counter-rotating terms in the Hamiltonian perturbatively, which leads to the Bloch-Siegert shift in the resonator frequency. It is shown how the shift can improve the readout. The theory of photon transport through the qubit and the resonator it couples to is provided while taking the effect of the counter-rotating terms into account. To calculate the readout contrast, we use two approaches. The first one neglects the qubit relaxation and allows us to derive a compact expression for the contrast. Also, we obtain simple estimates for the system parameters to maximize the contrast. The second approach accounts for the qubit relaxation, which allows us to further improve the contrast. We demonstrate that for a readout time of $1\mu \mathrm{s}$, a contrast of more than 75% can be achieved for an ideal detector and single-photon source.

We study many-particle phenomena of propagating multimode photons and phonons interacting through a Brillouin scattering type Hamiltonian in nanoscale waveguides. We derive photon and phonon retarded Green's functions and extract their spectral functions in applying the factorization approximation of the mean-field theory. The real part of the self-energy provides renormalization energy shifts for the photons and the phonons. Besides the conventional leaks, the imaginary part gives effective photon and phonon damping rates induced due to many-particle phenomena. The results extend the simple spectral functions of quantum optomechanics into continuum quantum optomechanics. We present the influence of thermal phonons on the photon effective damping rates and consider cases of specific photon fields to be excited within the waveguide and which are of importance for phonon cooling scenarios.

Hyperfine-changing collisions are of fundamental interest for the study of ultracold heteronuclear mixtures. Here, we report a state-to-state study of the hyperfine-changing-collision dynamics in a Bose-Fermi mixture of ${}^6\mathrm{Li}$ and ${}^{41}\mathrm{K}$ atoms. The collision products are directly observed and the spin-changing dynamics is measured. Based on a two-body collision model, the experimental results are simultaneously fitted from which the spin-changing rate coefficient of $1.9\left(2\right)\times {10}^{-12}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ is gained, which is consistent with the multichannel quantum defect theory calculation. We further show that the contact parameter of a ${}^6\mathrm{Li}\text{−}{}^{41}\mathrm{K}$ mixture can be extracted from the measured spin-changing dynamics. The obtained results are consistent with the first-order perturbation theory in the weakly interacting limit. Our system offers great promise for studying spin-changing interactions in heteronuclear mixtures.

We report on spectroscopy of cold dysprosium atoms on the $1001\text{−}\mathrm{nm}$ transition and present measurements of the excited-state lifetime which is at least $87\left(7\right)\mathrm{ms}$ long. Due to the long excited-state lifetime we are able to measure the ratio of the excited-state polarizability to the ground-state polarizability at $1064\mathrm{nm}$ to be 0.83(0.13) by parametric heating in an optical dipole trap. In addition we measure the isotope shifts of the three most abundant bosonic isotopes of dysprosium on the $1001\text{−}\mathrm{nm}$ transition with an accuracy better than $30\mathrm{kHz}$.

We have measured characteristic $K$ x rays in coincidence with the scattered particles from collisions of hydrogenlike Ge ions with Kr atoms. The ions were first accelerated to 8.6 MeV/amu, post-stripped to H-like charge state, and decelerated to around 2.5 MeV/amu. From the measurements the probabilities for K-shell to K-shell charge transfer as a function of collision impact parameters were obtained. The probabilities show an onset of oscillations which are interpreted as quantum interference between the $K$-shell to $K$-shell electron transfer amplitudes in two spatially separated coupling regions in the incoming and outgoing parts of the collision. The probabilities of $K$-shell vacancy distribution created by the collision are calculated within a relativistic independent electron model using the coupled-channel approach with atomlike Dirac-Fock-Sturm orbitals. A reasonable agreement between the theoretical results and the experimental data is found.

We show that a quantum dynamical localization effect can be observed in a generic thermalization process of two weakly coupled chaotic subsystems. Specifically, our model consists of the minimal experimentally relevant subsystems that exhibit chaos, which are 3-site Bose-Hubbard units. Due to the high dimensionality of the composite 6-site system, the quantum localization effect is weak and cannot be resolved merely by the breakdown of quantum-to-classical correspondence. Instead, we adopt an intrinsic definition of localization as the memory of initial conditions, which is not related to the underlying classical dynamics. We discuss the dynamics in the chaotic sea, and in the vicinity of the mobility edge, beyond which ergodization is suppressed.

In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized $\mathrm{\Lambda }$ system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic evolution can be viewed as a conventional Hamiltonian dynamics in an appropriately chosen extended Hilbert space. In contrast to the existing approaches, our method does not require the calculation of the non-Abelian Berry connection and can be applied without any parametrization of the dark subspace, which becomes a challenging problem with increasing system size.

Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non-trace-preserving character of the evolution. We illustrate our results with two different systems, one where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture of the correction to the trace of the density matrix as a detailed balance equation.