In the usual quantum tunneling, a low-energy quantum particle penetrates across a physical barrier of higher potential energy, by traversing a classically forbidden region, and finally escapes into another region. In an analogous scenario, a classical particle inside a closed regular region in the phase space is dynamically bound from escaping to other regions of the phase space. Here, the physical potential barrier is replaced by dynamical barriers which separate different regions of the phase space. However, in the quantum regime, the system can overcome such dynamical barriers and escape through them, giving rise to dynamical tunneling. In chaotic Hamiltonian systems, dynamical tunneling refers to quantum tunneling between states whose classical limits correspond to symmetry-related regular regions separated by a chaotic zone between which any classical transport is prohibited. Here, an experimental realization of dynamical tunneling in spin systems is reported using nuclear magnetic resonance (NMR) architecture. In particular, dynamical tunneling in quantum kicked tops of spin-1 and spin-3/2 systems using two- and three-qubit NMR registers is investigated. By extracting time-dependent expectation values of the angular momentum operator components, size-dependent tunneling behavior for various initial states is systematically investigated. Further, by monitoring the adverse effects of dephasing noise on the tunneling oscillations, we assert the importance of quantum coherence in enabling dynamical tunneling.

Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of noisy intermediate-scale quantum computers. These methods use an optimization algorithm executed in a classical computer, fed with values of the objective function obtained in a quantum processor. A proper choice of optimization algorithm is essential to achieve good performance. Here, we review the use of first-order, second-order, and quantum natural gradient stochastic optimization methods, which are defined in the field of real numbers, and propose stochastic algorithms defined in the field of complex numbers. The performance of all methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation. In general, complex number optimization algorithms perform best, with first-order complex algorithms consistently achieving the best performance, closely followed by complex quantum natural algorithms, which do not require expensive hyperparameter calibration. In particular, the scalar formulation of the complex quantum natural algorithm allows to achieve good performance with low classical computational cost.

General algebraic relations are derived which provide a stringent test of the accuracy of $n$-photon electric dipole transition rates when mass-polarization effects are included. They are a generalization of the well-known equivalence of the length, velocity, and acceleration forms of the transition matrix element that follows from gauge invariance. The algebraic relations connect the coefficients in a power series in powers of $\mu /M$ for the three gauges, where $M$ is the nuclear mass and $\mu$ is the electron reduced mass. These relations also provide a stringent test of the leading infinite-mass term, a quantity that must be calculated with sufficient accuracy for the higher-order terms in powers of $\mu /M$ to be correct. As a check, the length-velocity algebraic relations are used to test the accuracy of high-precision calculations for both one-photon ($1s2p{}^{1}P-1s^2{}^{1}S$ and $1s2p{}^{3}P-1s2s{}^{3}S$) and two-photon ($1s2s{}^{1}S-1s^2{}^{1}S$) decay for the heliumlike ions with $Z=2–10$.

We study $e^{+}-\mathrm{H}(n$) and $\mathrm{Ps}\left(n\right)-p$ collisions near the three-body breakup threshold and thresholds for the charge-transfer processes. We show that classical trajectory Monte Carlo (CTMC) simulations for the three-body breakup agree reasonably well in this energy region with quantum-mechanical convergent close-coupling (CCC) calculations even if the initial hydrogen atom or positronium atom is in the ground state. The threshold behavior of the three-body breakup cross section in $e^{+}$-H($1s$) and $\mathrm{Ps}\left(1s\right)-p$ collisions agrees with the Wannier law with Klar's exponent and obeys the classical scaling laws, although some deviation from the Klar-Wannier behavior is observed in the CCC results. Below the threshold the agreement between CTMC and CCC disappears. In particular the CTMC method fails completely for the processes of H formation in $\mathrm{Ps}\left(1s\right)-p$ collisions and Ps formation in $e^{+}$-H collisions well below the three-body breakup threshold. For higher initial states the CTMC results below the threshold improve substantially, in accordance with the correspondence principle. This is explained by comparing the quantum-mechanical threshold laws with the classical laws.

We report measured and calculated values of radiative decay rates and vibrational branching fractions for the $A{}^2\mathrm{\Pi }(v=0)$ state of ${}^{24}\mathrm{Mg}{}^{19}\mathrm{F}$. The decay rate measurements use time-correlated single-photon counting with roughly 1% total uncertainty. Branching-fraction measurements are performed using two calibrated imaging systems to achieve few percent total uncertainty. We use the multireference relativistic ab initio methods to calculate the Franck-Condon factors and transition dipole moments required to determine the decay rates and the branching fractions. The measurements provide a precision benchmark for testing the accuracy of the molecular structure calculations. The determination of the decay rate and vibrational branching fractions can be used to inform future optical cycling and laser cooling schemes for the MgF molecule.

The realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact interaction on optical kagome lattices. In the strong coupling regime, the system is described by an effective spin-1 model with two- and three-body interactions between neighboring spins. By mapping out the phase diagram via the variational Monte Carlo method, we find a non-Abelian chiral spin-liquid phase in which the Ising-type anyons obey non-Abelian braiding statistics. The gapless chiral edge states can be detected by measuring the spin-spin correlation from atomic population. Furthermore, an interesting $Z_2$ QSL phase is observed exhibiting both topological order and lattice symmetry-breaking order. Our scheme can be implemented in cold quantum gases of bosonic atoms.

We theoretically calculate the dynamic structure factor of a two-dimensional Rashba-type spin-orbit-coupled (SOC) Fermi superfluid with the random phase approximation and analyze the main characters of dynamical excitation shown by both density and spin dynamic structure factors during a continuous phase transition between a Bardeen-Cooper-Schrieffer superfluid and a topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to the two-branch structure of the quasiparticle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless $DD$-type pair-breaking excitation at the critical Zeeman field $h_c$ and is imparted a finite width to phonon peak when the transferred momentum $\mathit{q}$ is around the Fermi vector $k_F$. At a much larger transferred momentum $(\mathit{q}=4k_F)$, the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.

The ranges of existence and stability of dark cavity-soliton stationary states in a Fabry-Pérot resonator with a Kerr nonlinear medium and normal dispersion are determined. The Fabry-Pérot configuration introduces nonlocal coupling that shifts the cavity detuning by the round trip average power of the intracavity field. When compared with ring resonators described by the Lugiato-Lefever equation, nonlocal coupling leads to strongly detuned dark cavity solitons that exist over a wide range of detunings. This shift is a consequence of the counterpropagation of intracavity fields inherent to Fabry-Pérot resonators. In contrast with ring resonators, the existence and stability of dark soliton solutions are dependent on the size and number of solitons in the cavity. We investigate the effect of nonlocal coupling of Fabry-Pérot resonators on multiple dark solitons, and we demonstrate long-range interactions and synchronization of temporal oscillations.

We theoretically studied the scattering of short two-photon pulses from a spatially separated array of two-level atoms coupled to the waveguide. A general analytical expression for the scattered pulse has been obtained. The contributions of various single-eigenstate and double-excited eigenstates of the array have been analyzed. We also calculated how the time, during which the incident photons are stored in the array, depends on the array period and the number of atoms. The largest storage times correspond to the structures with the anti-Bragg period, equal to the quarter of the wavelength of light at the atom resonance frequency $\lambda /4$.

Light-matter interacting systems involving multilevel atoms are appealing platforms for testing equilibrium and dynamical phenomena. Here we explore a tricritical Dicke model, where an ensemble of three-level systems interacts with a single light mode, through two different approaches: a generalized Holstein-Primakoff mapping and a treatment using the Gell-Mann matrices. Both methods are found to be equivalent in the thermodynamic limit. In equilibrium, the system exhibits a rich phase diagram where both continuous and discrete symmetries can be spontaneously broken. We characterize all the different types of symmetries according to their scaling behaviors. Far from the thermodynamic limit, considering just a few tens of atoms, the system already exhibits features that could help characterize both second- and first-order transitions in a potential experiment. Importantly, we show that the tricritical behavior is preserved when dissipation is taken into account. Moreover, the system develops a rich steady-state phase diagram with various regions of bistability, all of them converging at the tricritical point. Having multiple stable normal and superradiant phases opens prospective avenues for engineering interesting steady states by a proper choice of initial states and/or parameter quenching.

We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.

In this work, we derive Robertson-Heisenberg–type uncertainty relation for two incompatible observables in a pre- and postselected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have physical meanings which we present here. We demonstrate two unusual properties in the PPS system using our uncertainty relation. First, for commuting observables, the lower bound of the uncertainty relation in the PPS system does not become zero even if the initially prepared state, i.e., preselection, is the eigenstate of both the observables when specific postselections are considered. This implies that for such case, two commuting observables can disturb each other's measurement results which is in fully contrast with the Robertson-Heisenberg uncertainty relation. Second, unlike the standard quantum system, the PPS system makes it feasible to prepare sharply a quantum state (preselection) for noncommuting observables (to be detailed in the main text). Some applications of uncertainty and uncertainty relation in the PPS system are provided: (i) detection of mixedness of an unknown state, (ii) stronger uncertainty relation in the standard quantum system, (iii) “purely quantum uncertainty relation” that is, the uncertainty relation which is not affected (i.e., neither increasing nor decreasing) under the classical mixing of quantum states, (iv) state-dependent tighter uncertainty relation in the standard quantum system, and (v) tighter upper bound for the out-of-time-order correlation function.

We demonstrate the discrimination of ground-state hyperfine manifolds of a cesium atom in an optical tweezer using a simple probe beam with $99.{91}_{-0.02}^{+0.02}$% detection fidelity and 0.9(2)% detection-driven loss of bright-state atoms. Our detection infidelity of $0.{09}_{-0.02}^{+0.02}$% is an order of magnitude better than previously published low-loss readout results for alkali-metal atoms in optical tweezers. We achieve these results by identifying and mitigating an extra depumping mechanism due to stimulated Raman transitions induced by trap light in the presence of probe light. In this work, complex optical systems and stringent vacuum pressures are not required, enabling straightforward adoption of our techniques on contemporary experiments.

It has been well established that the Jastrow correlation factor can effectively capture the electron correlation effects, and thus, the efficient optimization of the many-body wave function including the Jastrow correlation factor is of great importance. For this purpose, the transcorrelated $+$ variational Monte Carlo ($\mathrm{TC}+\mathrm{VMC}$) method is one of the promising methods, where the one-electron orbitals in the Slater determinant and the Jastrow factor are self-consistently optimized in the TC and VMC methods, respectively. In particular, the TC method is based on similarity transformation of the Hamitonian by the Jastrow factor, which enables the efficient optimization of the one-electron orbitals under the effective interaction. Through test calculations of some closed-shell atoms, He, Be, and Ne, we find that the total energy is in many cases systematically improved by using better Jastrow functions. We find that even a one-shot $\mathrm{TC}+\mathrm{VMC}$ calculation, where the Jastrow parameters are optimized at the Hartree-$\mathrm{Fock}+\mathrm{VMC}$ level, can yield partial benefits from orbital optimization. It is also suggested that one-shot $\mathrm{TC}+\mathrm{VMC}$ can be a good alternative method for complex systems. Our study provides important insights for optimizing many-body wave function including the Jastrow correlation factor, which would be of great help for development of highly accurate electronic structure calculations.

The dissociative single ionization of the LiH molecule using a two-color UV-UV pump-probe scheme is simulated in ab initio calculations demonstrating how the dynamics initiated on intermediate Rydberg states of diatomic molecules can be imaged by such experiments. The theoretical treatment combines nuclear motion with highly correlated descriptions of electronic continua and bound electronic states. Nuclear dynamics on Rydberg states are only weakly reflected by changes in photoelectron energies ejected by time-delayed ionizing pulses if the Rydberg potential curves parallel those of the ion states being produced. However, coincidence measurements guided by knowledge of the photoionization amplitudes as a function of internuclear distance can still reveal intermediate-state dynamics in pump-probe experiments.

We studied the single-particle momentum distribution of mass-imbalanced Efimov states embedded in noninteger dimensions. The contact parameters, which can be related to the thermodynamic properties of the gas, were extracted from the tail of the single-particle momentum densities. We studied the dependence of the contact parameters on the progressive change in the noninteger dimension, ranging from three ($D=3$) to two ($D=2$) dimensions. Within this interval, we move from the $D=3$ regime where the Efimov discrete-scale symmetry drives the physics to close to the critical dimension, which depends on the mass imbalance, where the continuum-scale symmetry takes place. We found that the two- and three-body contacts grow significantly in magnitude with the decrease of the noninteger dimension towards the critical dimension, impacting observables of resonantly interacting trapped Bose gases.

In recent years, optically levitated systems have emerged as an important platform for conducting fundamental physics studies and precision measurements. The internal temperature of the levitated nanoparticles plays a critical role in determining the measuring sensitivity and decoherence of the system. In this study, we perform experiments on the internal temperature of a rare-earth-doped nanoparticle $\alpha -{\mathrm{NaYF}}_4$:${\mathrm{Yb}}^{3+}/{\mathrm{Er}}^{3+}$ levitated in an intermediate vacuum. To determine the internal temperature of the nanoparticle, we measure the luminescence intensity ratio of the thermally coupled levels of the doped ${\mathrm{Er}}^{3+}$ ions. Our results show that the internal temperature of the optically levitated nanoparticle increases as the air pressure decreases and that there is a coupling between the internal temperature and center-of-mass motion of the nanoparticle levitated in vacuum. We also find a correlation between the slow rise in internal temperature and the abrupt loss of the levitated nanoparticle, which can be used to guide stabilization of the optical trap.