We employ an all-particle multireference Fock-space relativistic coupled-cluster (FSRCC) theory to study the $5s^2{}^1{S}_0-5s5p{}^{3}P_0^o$ clock transition in both fermionic and bosonic isotopes of Sr. We compute the excitation energies for several low-lying states, E1 and M1 transition amplitudes, hyperfine reduced matrix elements, and isotope shifts using FSRCC theory. Further, using our results on E1, M1, and hyperfine structure (HFS) reduced matrix elements, we calculate the lifetime of the metastable clock states for ${}^{87}\mathrm{Sr}$ and ${}^{88}\mathrm{Sr}$. Furthermore, we employ perturbed relativistic coupled-cluster (PRCC) theory to compute the ground state electric dipole polarizability of Sr. To improve the accuracy of our results, we incorporate the corrections from the relativistic and quantum electrodynamical (QED) effects, and perturbative triples to all our calculations. Moreover, we employ large bases to ensure the convergence of the computed properties. Our computed excitation energies are in good agreement with the experimental data for low-lying excited states. Our results for E1, M1, and HFS reduced matrix elements are within the experimental error bars, however, with slight difference from the previous calculations due to more accurate treatment of electron correlations in FSRCC theory. Our computed lifetime of the clock state for ${}^{87}\mathrm{Sr}$ is within the error bars of the available experimental results, whereas for ${}^{88}\mathrm{Sr}$ it is an order of magnitude smaller than the only available calculation [R. Santra et al., Phys. Rev. A 69, 042510 (2004)] using model potential. Our PRCC result for the ground state polarizability is in good agreement with the experiment, and smaller than previous calculations. Our results on isotope shift factors are consistent with available experimental results for intercombination transitions. From detailed analysis of the results, we find that the corrections from the Breit interaction, QED effects, and perturbative triples are crucial to get accurate clock transition properties in Sr. Moreover, valence-valence electron correlation is important to get accurate energies and properties of Sr.

Laser-induced tunneling ionization underlies a broad class of strong-field phenomena in attosecond physics. A key quantity in this process is the transverse tunneling exit position, which influences both the phase of the continuum wave packet and the subsequent electron dynamics. In this work, we show that the intracycle interference between directly ionized electron wave packets provides a sensitive probe of the transverse tunneling exit position in molecules. By numerically solving the time-dependent Schrödinger equation for the aligned ${\mathrm{N}}_2$ molecule, we observe a pronounced, alignment-dependent asymmetry in the intracycle interference pattern of the photoelectron momentum distribution. Analysis based on adiabatic theory reveals that this asymmetry originates from the transverse shift of tunneling exit position. The exit position is reconstructed from the interference patterns with picometer-scale precision and is consistent with the result obtained from the electron density distribution of the molecular orbital.

Non-Hermitian cavity magnomechanics, which incorporates the magnon-photon and magnon-phonon interactions simultaneously, enables rich physical phenomena, including exceptional-point-enhanced sensing, and offers pathways toward topological transitions and nonreciprocal quantum transformation. These interactions exert a pivotal influence on the optical response of a weak probe field and pave the way for novel applications in quantum technologies. In this work we consider a yttrium-iron-garnet (YIG) sphere coupled to a microwave cavity. The magnon mode of the YIG sphere is directly excited through microwave field coupling, whereas the cavity mode is probed via a weak-field interrogation scheme. The direct interaction of a traveling field with the magnon mode induces gain in the system, thereby establishing non-Hermitian dynamics. The parity-time ($\mathcal{PT}$)-symmetric behavior of a hybrid non-Hermitian cavity magnomechanical system is designed and investigated. Eigenvalue spectrum analysis demonstrates that a third-order exceptional point (${\mathrm{EP}}_3$) emerges under tunable effective magnon-photon coupling when the traveling field is oriented at an angle of $\pi /2$ relative to the cavity's $x$ axis. The photonic spin Hall effect (PSHE) in a reflected probe field is subsequently examined in such a system. Under balanced gain and loss conditions and in the presence of effective magnon-phonon coupling, tunable effective magnon-photon coupling enables coherent control of the PSHE across the broken $\mathcal{PT}$-symmetric phase, at the ${\mathrm{EP}}_3$ and in the $\mathcal{PT}$-symmetric phase. Investigation reveals that the PSHE can be significantly enhanced or suppressed via effective magnon-photon coupling. The influence of intracavity length on the PSHE is further explored, providing an additional parameter for fine-tuning the transverse shift. These findings establish a direct correspondence between the PSHE and the underlying non-Hermitian eigenvalue spectrum. They further demonstrate that non-Hermitian cavity magnomechanical platforms provide a pathway to tunable photonic functionalities, with immediate prospects for quantum switching and precision sensing.

We consider the phenomenon of resonant radiation emitted by solitonlike wave packets in quadratic crystals and demonstrate the key role of the group-velocity dispersions, at the fundamental frequency and second harmonic, respectively, without any contribution from higher-order dispersions. In particular our approach allows us to predict a mechanism of primary resonance around the fundamental frequency component. Our theoretically predicted resonances are found to be in excellent agreement with numerical simulation of the propagation in a wide range of parameter values.

We investigate superradiant quantum phase transitions in a Dicke trimer model consisting of two types of hoppings, i.e., photon hoppings and atom hoppings. In the superradiant regime, the system can exist in two distinct phases: normal and frustrated superradiant phases, which are governed by both types of hoppings. Particularly, the interplay between these hoppings gives rise to interesting effects, such as triggering superradiance with much lower coupling strengths when both hoppings exhibit the same tendency. In contrast, with opposite tendencies, the competition between hoppings leads to a first-order phase transition between two different superradiant phases with translational symmetry broken. These findings enable the system to undergo a sequence of transitions across three phases by changing the coupling strength. Our work provides deep insights into competing interactions and quantum phase transitions in multicavity systems with geometric structures.

We propose the concept of amplified quantum nondemolition measurement of a quadrature amplitude of optical field. Similarly to standard quantum nondemolition measurement, it does not introduce a backaction noise into the measured quadrature. At the same time, it provides a noiseless amplification of this quadrature. We propose a possible practical implementation of this concept based on the nondegenerate optical parametric amplifier. We show that, assuming demanding but realistic values of the optical squeezing and losses, a sensitivity several times better than the standard quantum limit can be achieved.

Identifying the precise moment when a quantum channel undergoes a change is a fundamental problem in quantum information theory. We study how accurately one can determine the time at which a channel transitions to another. We investigate the quantum limit of the average success probability in unambiguous discrimination, in which errors are completely avoided by allowing inconclusive results with a certain probability. This problem can be viewed as a quantum process discrimination task, where the process consists of a sequence of quantum channels; however, obtaining analytical solutions for quantum process discrimination is generally extremely challenging. In this paper, we propose a method to derive lower and upper bounds on the maximum average success probability in unambiguous discrimination. In particular, when the channels before and after the change are unitary, we show that the maximum average success probability can be analytically expressed in terms of the length of the channel sequence and the discrimination limits for the two channels.

Quantum memristors (QMs) have emerged as a promising frontier in neuromorphic computing and quantum information processing. In this paper, we propose a different methodology for defining three coupled ion-trap-based QMs on a single ${}^{171}\mathrm{Yb}^{+}$ ion, with the flexibility to operate any two of them as a coupled pair at a given time, opening possibilities for scalable multilayer quantum perceptrons which require fewer trapped ions for the same architectural complexity. Our study systematically evaluates the efficacy of coupled and noncoupled QM-based models in an image classification machine learning task. Numerical simulations reveal that coupling QMs preserves their performance quality, supporting the adoption of coupled QMs in scalable neural architectures. Our results demonstrate that QM-based models maintain stability in compact neural networks and achieve a high recognition accuracy, making them viable candidates for efficient neuromorphic computing systems.

We present a general theoretical framework for evaluating multiphoton processes in periodically driven quantum systems, which have been identified as a versatile tool for engineering and controlling nontrivial interactions in various quantum technology platforms. To achieve the accuracy required for such applications, the resulting effective coupling rates, as well as any drive-induced frequency shifts, must be determined with very high precision. Here, we employ degenerate Floquet perturbation theory together with a diagrammatic representation of multiphoton processes to develop a systematic and automatable approach for evaluating the effective dynamics of driven quantum systems to arbitrary orders in the drive strength. As a specific example, we demonstrate the effectiveness of this framework by applying it to the study of multiphoton Rabi oscillations in a superconducting fluxonium qubit, finding excellent agreement between our theoretical predictions and exact numerical simulations, even for large driving amplitudes.

We present a theoretical study of the phase-of-the-phase spectroscopy in the few-cycle regime and analyze its explicit dependence on the carrier-envelope phase (CEP) and the pulse length. The process of above-threshold detachment of negative ions driven by ultrashort two-color laser pulses is investigated within the strong-field approximation formulated for few-cycle pulses with two carrier frequencies. While the CEP effects are known to be difficult to extract from the photoelectron yield of direct electrons, we demonstrate that the CEP leaves a clear and robust imprint on the phase of the phase, even when only direct electrons are considered. We analyze two-color configurations with parallel and orthogonal polarizations of the driving and perturbation pulses and identify characteristic CEP-dependent structures in both momentum-resolved and energy-averaged phase-of-the-phase spectra. The role of symmetry and its reduction in orthogonally polarized configurations is discussed in detail. Importantly, we show that the CEP dependence of the phase of the phase survives focal averaging and becomes particularly smooth under realistic experimental conditions. In addition, we demonstrate that the phase of the phase exhibits a pronounced sensitivity to the pulse length in the few-cycle regime, while converging for longer pulses, indicating its potential for characterizing ultrashort pulse durations. Our results establish phase-of-the-phase spectroscopy as a sensitive and experimentally viable tool for extracting information about strong-field processes driven by few-cycle laser pulses.

We consider an autonomous system of two coupled single-mode cavities, one of which interacts with a multimode resonator. We demonstrate that for small coupling strengths between single-mode cavities, the Loschmidt echo oscillates periodically in time and spontaneous breaking of time translation symmetry takes place. The Loschmidt echo behavior is an indication of the nonergodic nature of the system when its evolution is time reversible and the system retains a memory of the initial state under the action of small perturbations. This behavior reveals the presence of a time crystalline order in the autonomous system. In this regime, the system is an autonomous discrete time crystal. An increase in the coupling strength leads to a transition from periodic oscillations to an exponential decay in time of the Loschmidt echo. This corresponds to the transition from nonergodic behavior to ergodic in the system, and is accompanied by the disappearance of time crystalline order. We demonstrate that at the transition point the time-averaged variance of the number of photons reaches a maximum, which serves as a signature of the transition. We show that such a transition can also be observed when changing the number of degrees of freedom in the resonator, which is achieved by changing its length.

Giant atoms are artificial atoms that can couple to a waveguide nonlocally. Previous works have shown that two giant atoms in a braided configuration can interact through one-dimensional (1D) infinite and chiral waveguides, with both individual and collective atomic relaxation being fully suppressed. In this paper, however, we show that the decoherence-free interaction (DFI) between two giant atoms can be realized in both braided and nested configurations when the waveguide is semi-infinite. This protected interaction fails to appear in semi-infinite waveguide systems containing two separate giant atoms or two small atoms. We also study the entanglement generation between two giant atoms coupled to a 1D semi-infinite waveguide. The results show that the maximally entangled state is generated in both braided and nested configurations due to the formation of DFI, and in the separate configuration, the maximally achievable entanglement can exceed 0.5. Finally, we generalize the discussion on DFI and entanglement generation to the case involving multiple giant atoms coupled into a semi-infinite waveguide. This study presents a new scheme for realizing DFI and generating maximally entangled states in giant-atom waveguide-QED systems.

Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open: first, determining the complexity of deciding if a theory admits a noncontextual ontological model; second, determining the complexity of deciding if such a model is possible for a specific dimension $k$; and, third, efficiently computing the smallest such model when it exists, given that finding the smallest ontological model is NP-hard. We address the second problem by presenting an algorithm derived from a geometric formulation and its reduction to the intermediate simplex problem in computational geometry. We find that the complexity of deciding the existence of a noncontextual ontological model of dimension $k$ is at least exponential in the dimension of the theory and at most exponential in $k$. This, in turn, implies that computing the smallest noncontextual ontological model is inefficient in general. Finally, we demonstrate the fundamental difference between finding the smallest noncontextual ontological model and the smallest ontological model using an explicit example wherein the respective minimum ontic sizes are five and four.

In this paper we study transitions of atoms between energy levels of several number-theory-inspired trapping potentials under the effect of time-dependent perturbations. First, we simulate in detail the case of a trap whose single-particle spectrum is given by the prime numbers. We investigate one-body Rabi oscillations and the excitation line shape for two resonantly coupled energy levels, and we show that quantum control is a faster method for state preparation than periodic perturbation. Next, we investigate cascades of such transitions, particularly whether one can construct a quantum system where the existence of a continuous resonant cascade from a given initial energy eigenstate is predicated by the validity of a given statement in number theory. We find that such resonance cascades, in a suitably designed one-body system, can be used to illustrate that the sequence of natural numbers is closed under multiplication. We further present ideas for two more resonance cascade experiments designed to illustrate certain statements within the Diophantus-Brahmagupta-Fibonacci identity and the Goldbach conjecture.

Entanglement between remote quantum mechanical systems enables a range of quantum information tasks in communication, computation, and distributed sensing. Large numbers of entangled subsystems also require experimentally accessible and practically feasible methods of verifying the genuine, i.e., simultaneous, entanglement of all subsystems. We have derived a class of entanglement witnesses suitable for $W$ states, which are states where a single excitation is coherently distributed across subsystems initially in their ground state or a state with low thermal occupation, e.g., via detection of a Raman-scattered photon. The entanglement is witnessed through violation of an inequality involving number statistics, which can be measured via detection of subsequent Raman-scattered photons. Unlike conventional, partially tomographic, witnesses, our method is experimentally accessible for both multipartite and continuous variable systems. The thermal robustness of the method is quantified by the initial thermal occupations for which violation occurs. As an alternative approach, we have derived an inequality which tests the nonlocal, or quantum coherent, nature of the photon measurement backaction which produces the $W$ state. Violation of this alternative inequality implies the entanglement of the resulting state given the assumption of a separable initial state, under less stringent thermal constraints than the general entanglement witness. Our results are applicable to all Raman-scattering systems which can exhibit sufficient degrees of quantum indistinguishability.

We derive a geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a nonunitary Schrödinger equation. Based on the angular distance between the normalized evolving state and the initial state, we obtain a lower bound on the evolution time, expressed as the ratio between this geometric distance and the time-averaged energy dispersion. The present bound explicitly incorporates the norm-non-conserving nature of imaginary-time evolution and is applicable to time-dependent or time-independent Hamiltonians. It is saturable when the evolution direction is aligned with the geodesic on projective Hilbert space. We analytically evaluate this bound for several examples. For a two-level system, we obtain a closed-form expression for the minimal evolution time required to reach a target ground state. For the imaginary-time Grover's quantum search, our QSL reproduces the well-known logarithmic scaling $T=\mathcal{O}(lnN)$, in agreement with previous results by Okuyama and Ohzeki. We further show that the equality condition of the bound is exactly satisfied for imaginary-time evolutions generated by time-dependent but mutually commuting Hamiltonians, demonstrating that the derived QSL provides both a rigorous and achievable limit for nonunitary quantum dynamics.

We investigate the formation of bound states between dark-antidark solitary waves in two-component dipolar Bose-Einstein condensates. The excitation spectrum contains density and spin branches and a rotonic feature of the spin branch enables long-range soliton interactions, giving rise to multiple bound states for a single pair, each with a distinct separation. We show that these bound states originate from periodic modulations of the intersoliton potential, while individual solitons are surrounded by spatial spin-density oscillations. Both features provide direct signatures of the spin roton. Collisions between unbound solitons probe this potential, with dipolar interactions enforcing universal bouncing at low velocities, independent of soliton sign, whereas nondipolar solitons may either transmit or bounce. This distinct behavior offers a realistic path to confirming spin rotons experimentally.