Searching for nonthermalized dynamics in interacting quantum systems is not only of fundamental theoretical interest in nonequilibrium quantum physics but also of immense practical significance in quantum information processing. In this paper, we study quantum quench dynamics in a hard-core bosonic model with nearest-neighbor hopping and infinite-range interactions, which have been realized in recent high-finesse cavity experiments. We show that the long-time dynamics of this model can exhibit either undamped oscillations or thermalization depending on the choice of initial states. The long-range nature of the interactions rather than conserved quantities are responsible for such nonergodic dynamical behavior.

Motivated by recent experimental advances in ultracold atomic gases placed in cavities, we study the influence of the atom-cavity coupling on the Fermi gases trapped in optical lattices. By adiabatic elimination of the cavity photon field, the atom-cavity coupling gives rise to effective long-range interactions. It results in a variety of two-body scattering processes, during which the atomic pairs can acquire an additional center-of-mass momentum. This reveals the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids in which the atomic pairing momentum is nonzero. By inspecting the phase diagram at the mean-field level, we confirm that the FFLO superfluid phase coexists with the zero-momentum pairing, and is the ground state that hosts the lowest energy. Furthermore, the order parameter characterizing the non-zero-momentum pairing does not vanish as long as the cavity-induced interaction is present.

Flat-top-soliton (or platicon) dynamics in coherently pumped normal dispersion microresonators is important for both fundamental nonlinear physics and microcomb generation in the visible band. Here we numerically investigate the platicon generation that is initiated via Raman assisted four wave mixing instead of mode interaction. To show the possibility of generating coherent combs in the visible band, we design an aluminum nitride (AlN) microresonator with normal dispersion and investigate the comb generation dynamics in simulations. Stable platicon Kerr combs can be generated in this AlN microresonator using a 780-nm pump. Moreover, we also observe a breather platicon dynamics induced by the narrow Raman gain spectrum of crystalline AlN, which shows distinct dynamics from the dark soliton breathers reported in previous work that are dominated by Kerr effect. A phase diagram bearing the influence of the pump detuning and pump power on the breathing dynamics of the breather platicon is also computed. Furthermore, a transition to chaotic breathing is numerically observed.

Floquet theory combined with the generalized Van Vleck nearly degenerate perturbation theory has been widely employed for studying various two-level systems that are driven by external fields via time-dependent longitudinal (i.e., diagonal) couplings. However, three-level systems strongly driven by time-dependent transverse (i.e., off-diagonal) couplings have rarely been investigated, due to the breakdown of the traditional rotating wave approximation. Meanwhile, the conventional perturbation theory is not directly applicable, since a small parameter for the perturbed part is no longer apparent. Here we develop a double-unitary-transformation approach to deal with periodically modulated and strongly driven systems, where the time-dependent Hamiltonian has large off-diagonal elements. The first unitary transformation converts strong off-diagonal elements to diagonal ones, and the second enables us to harness the generalized Van Vleck perturbation theory to deal with the transformed Floquet matrix and also allows us to reduce the infinite-dimensional Floquet Hamiltonian to a finite effective one. For a strongly modulated three-level system, with the combination of the Floquet theory and the transformed generalized Van Vleck perturbation theory, we obtain analytical results of the system, which agree well with exact numerical solutions. This method offers a useful tool to analytically study multilevel systems with strong transverse couplings.

Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum measurements for a $d$-dimensional Hilbert space. These experimental requirements are compounded by the complexity of processing the collected data, which can take several orders of magnitude longer than the experiment itself. In this paper we propose an alternative self-guided algorithm for quantum process tomography, tuned for the task of finding an unknown unitary process. Our algorithm is a fully automated and adaptive process characterization technique. The advantages of our algorithm are the following: it has an inherent robustness to both statistical and technical noise; it requires less space and time since there is no postprocessing of the data; it requires only a single input state and measurement; and it provides on-the-fly diagnostic information while the experiment is running. Numerical results show our algorithm achieves the same $1/n$ scaling as standard quantum process tomography when $n$ uses of the unknown process are used. We also present experimental results wherein the algorithm and its advantages are realized for the task of finding an element of SU(2).

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough understanding of their relations is still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The infinite-dimensional case from quantum optics is then recovered in the large-spin limit.

In a practical continuous-variable quantum-key-distribution (CVQKD) system, a strong local oscillator (LO) signal in a quantum channel may be manipulated by eavesdropper Eve to steal information about secret keys through general attacks (e.g., entangling cloner attack or intercept-resend attack) without being detected, which is an effective quantum hacking strategy, i.e., LO attacks. To guarantee the practical security of the system, a general monitoring scheme has been previously demonstrated to resist this quantum hacking attack, where the channel transmittance was regarded as a fixed value related to transmission distance. However, practical communication environments are complex, which may result in the time-varying transmittance. This deviation may affect the effectiveness of this monitoring scheme. In this paper, we investigate the monitoring of CVQKD systems running in complex communication environments. We first model the LO attacks on practical CVQKD systems in complex environments, where the channel transmittance is assumed to obey a fixed distribution. Then, the low bound of intensity disturbance of the LO signal for Eve successfully concealing herself is obtained based on this model, where we consider all noise that can be used by Eve in complex communication environments. Simultaneously, we obtain an optimal monitoring condition to resist the LO attacks. Our numerical analysis confirms that the proposed monitoring scheme can effectively resist the LO attacks on practical CVQKD systems in complex environments. Subsequently, the feasibility of this way is again demonstrated by using a quantitative example. It is important that this monitoring scheme can also be extended to resist other quantum hacking attacks.

A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with bounded amplitude. The coupling between the bath and the qubit is modeled by a Lindblad master equation. Dissipation typically drives the system to the maximally mixed state; consequently, there generally exists an optimal evolution time beyond which the decoherence prevents the system from getting closer to the target state. For some specific dissipation channel, however, the optimal control can keep the system from the maximum entropy state for infinitely long. The conditions under which this specific situation arises are discussed in detail. The numerical procedure to construct the time-optimal protocol is described. In particular, the formalism adopted here can efficiently evaluate the time-dependent singular control which turns out to be crucial in controlling either an isolated or a dissipative qubit.

We employ quantum optimal control theory to realize quantum gates for two protected superconducting circuits: the heavy-fluxonium qubit and the 0-$\pi$ qubit. Utilizing automatic differentiation facilitates the simultaneous inclusion of multiple optimization targets, allowing one to obtain high-fidelity gates with realistic pulse shapes. For both qubits, disjoint support of low-lying wave functions prevents direct population transfer between the computational-basis states. Instead, optimal control favors dynamics involving higher-lying levels, effectively lifting the protection for a fraction of the gate duration. For the 0-$\pi$ qubit, offset-charge dependence of matrix elements among higher levels poses an additional challenge for gate protocols. To mitigate this issue, we randomize the offset charge during the optimization process, steering the system towards pulse shapes insensitive to charge variations. Closed-system fidelities obtained are 99% or higher and show slight reductions in open-system simulations.

The QED contribution to the dipole polarizability of the ${}^4\mathrm{He}$ atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to 0.048 557 2(14) in atomic units, confirms the small magnitude of this quantity found in the only previous calculation [G. Łach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004)], but differs from it by about 5%. The origin of this difference is explained. The total QED correction of the order of ${\alpha }^3$ in the fine-structure constant $\alpha$ amounts to $30.6671\left(1\right)\times {10}^{-6}$, including the $0.1822\times {10}^{-6}$ contribution from the electric-field derivative of the Bethe logarithm and the $0.01112\left(1\right)\times {10}^{-6}$ correction for the finite nuclear mass, with all values in atomic units. The resulting theoretical value of the molar polarizability of helium-4 is $0.51725408\left(5\right){\mathrm{cm}}^3/\text{mol}$ with the error estimate dominated by the uncertainty of the QED corrections of order ${\alpha }^4$ and higher. Our value is in agreement with but an order of magnitude more accurate than the result $0.5172544\left(10\right){\mathrm{cm}}^3/\text{mol}$ of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].

Chemical reaction dynamics is known to be influenced by quasibound states (unstable electron standing waves) that exist in the positive-energy continuum in the spatial neighborhood of molecules. These unstable spatial structures give rise to resonances in the scattering dynamics between molecules or between electrons and molecules. Here we analyze the quasibound states associated with both an attractive and a repulsive molecule-size tetrahedral structure by using Wigner-Eisenbud $R$-matrix theory. Our results indicate that quasibound states typically exist in the neighborhood of all small molecules and other small quantum objects.

We investigate the photoelectron angular emission distributions obtained by strong-field dissociative ionization of ${\mathrm{H}}_2$ using cold target recoil ion momentum spectroscopy. In the case of employing laser light with an ellipticity close to 0.9 and an intensity of $1.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, we find that the most probable release time of the electron does not generally coincide with the time when the laser field maximizes. The release time is affected by the molecular orientation. In addition, we observe that the width of the release-time distribution depends on molecular orientation. We attribute this observation to the two-center interference.

The successful application of quantum optimal control (QOC) over the past decades has unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular, making them unsuitable for direct experimental implementation. In this paper, we propose a method to reshape those unattractive optimal controls. The approach is based on the fact that solutions to QOC problems are not isolated policies but constitute multidimensional submanifolds of control space. This was originally shown for finite-dimensional systems. Here, we analytically prove that this property is still valid in a continuous variable system. The degenerate subspace can be effectively traversed by moving in the null subspace of the Hessian of the cost function, allowing for the pursuit of secondary objectives. To demonstrate the usefulness of this procedure, we apply the method to smooth and compress optimal protocols in order to meet laboratory demands.

We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance and uncover that the random walk of droplets for the minor component plays a fundamental role in the relaxation process. Our numerical simulations based on the binary Gross-Pitaevskii model reveal the emergence of the dynamical scaling during the relaxation, which is a hallmark of scale-invariant dynamics, in a correlation function for the minor condensate. Tracking exponents characterizing the dynamical scaling in time, we find a crossover phenomenon that features the change in power exponents of the correlation length. To understand the fundamental mechanism inherent in the scale-invariant relaxation dynamics, we construct a random-walk model for droplets. Employing the model, we analytically derive the $1/3$ and $1/2$ power laws and predict the crossover of the scaling. These exponents are in reasonable agreement with the values obtained in the numerical calculations. We also discuss a possible experimental setup for observing the scale-invariant dynamics.

In this paper, we study two-body bound states in two-component Bose gas with a one-dimensional spin-orbit coupling induced by Raman lasers. The finite Raman coupling strength generates coupling among three spin channels, resulting in the reconstruction of three bound-state bands. In addition, multiple resonances can be induced at finite scattering lengths. By tuning the interaction in one intraspecies channel, one bound-state band can be lifted and three resonances can be achieved, which can be observable under current experimental conditions in ${}^{87}\mathrm{Rb}$ atoms. This induced resonance is helpful for imaging the density modulation in the stripe phase.

The form of the eigenstates of an atom coupled to a cavity mode displaying a three-dimensional periodic profile are obtained. It is shown that the quantized motion leads to degenerate states where the atomic degrees of freedom are masked, that is, upon detection of one component of this composite system the others remain in an entangled state. When the system is extended to include drive and dissipation it is found to undergo a dissipative quantum phase transition at a critical drive amplitude. Unlike other phase transitions reported in the literature, the degeneracy prepares the system in a superposition of incompatible states upon detection of the electromagnetic field. Probing the field hints at an order above the transition point that, due to state masking, allows for atomic coherence to survive at long times.

The origin of spin-orbit interaction of light at a conventional optical interface lies in the transverse nature of the photon polarization: The polarizations associated with the plane-wave components experience slightly different rotations in order to satisfy the transversality after reflection or refraction. Recent advances in topological photonic materials provide crucial opportunities to reexamine the spin-orbit interaction of light at the unique optical interface. Here, we establish a general model to describe the spin-orbit interaction of light in the photonic Dirac metacrystal. We find a giant photonic spin Hall effect near the Dirac points when a Gaussian beam impinges at the interface of the photonic Dirac metacrystal. The giant photonic spin Hall effect is attributed to the strong spin-orbit interaction of light, which manifests itself as the large-polarization rotations of different plane-wave components. We believe that these results may provide insight into the fundamental properties of the spin-orbit interaction of light in topological photonic systems.

We propose a method to predict the existence of topologically protected electromagnetic chiral modes between continuous media described by Maxwell's equations. The number and character of these modes is related to topological charges (Berry monopoles) in parameter space. Unlike the approaches proposed so far, our description does not require a regularization parameter at large $\mathbf{k}$ nor the materials to be topological on their own. The predictions of the theory are confirmed by additional numerical simulations of interfaces of gyrotropic media.

Here we propose an analytical solution for semiclassical dynamical equations through a renormalized perturbation theory, applicable to many-body systems. The many-atom emission of a dilute cloud of two-level atoms is addressed as a nontrivial example. We show that, as a result of secular terms elimination, an effective many-body spectrum emerges in the temporal solutions, which depends on initial conditions. It allows us to detect a cooperativity reduction in the semiclassical total power radiated that cannot be described by a classical model from linear optics. The second-order cooperative emission remains accurate over several single-atom lifetimes and for interacting regimes stronger than those permitted in conventional perturbation theory. We can compute the semiclassical dynamics of a few hundred thousand interacting atoms with ordinary computational resources, which makes our formalism particularly promising to probe the nonlinear dynamics of quantum many-body systems that result from cumulant expansions.