The transitions from the incoherent noise to the coherent soliton have been fully revealed in ultrafast lasers. However, the soliton transformation between different coherent states, termed as soliton metamorphosis, remains an attractive yet uncharted territory. Here, we reveal the ultrafast dynamics of the soliton metamorphosis via single-shot spectroscopy in a specially designed fiber laser capable of emitting fast-switchable dissipative solitons and stretched pulses. It is demonstrated that the soliton metamorphosis is a consecutive evolution process including the self-phase modulation stage, pulse split stage, and transient stretched pulse stage. Particularly, the long-period pulse breathing and the spectral period doubling appear in the forepart and middle part of the last stage. The metamorphosis dynamics and soliton properties are substantiated by numerical simulation based on a three-step model. This work not only unveils the transient evolution physics of the pulse in soliton metamorphosis, but also provides a simple and effective way to control operations of ultrafast lasers.

To investigate the dynamical behavior of a quantum system embedded in a memory environment, it is crucial to obtain the knowledge of the reservoir spectral density. However, such knowledge is usually based on a priori assumptions about the environment. In this paper, we put forward a method to obtain key information about the reservoir spectral density of an optomechanical resonator without additional assumptions about the spectral shape. This is achieved by detecting and analyzing the optical transmission rate of the emitted light. In the weak optomechanical single-photon coupling regime, we establish a simple relation between the output light spectrum and the reservoir spectral density. This provides a straightforward and effective way for reconstructing the spectral density profile in single or even multiple decoherence channels.

We investigate the Bose-Hubbard chain in the presence of nearest-neighbor pairing. The pairing term gives rise to an unusual gapped ${\mathbb{Z}}_2$ Ising phase that has number fluctuation but no off-diagonal long range order. This phase has a strongly correlated many-body doubly degenerate ground state which is effectively a gap-protected macroscopic qubit. In the strongly interacting limit, the system can be mapped onto an anisotropic transverse spin chain, which in turn can be mapped to the better-known fermionic sister of the paired Bose-Hubbard chain: the Kitaev chain which hosts zero-energy Majorana bound states. While corresponding phases in the fermionic and bosonic systems have starkly different wave functions, they share identical energy spectra. We describe a possible cold-atom realization of the paired Bose-Hubbard model in a biased zigzag optical lattice with reservoir-induced pairing, opening a possible route towards experimental Kitaev chain spectroscopy.

In 1962, Eugene P. Wigner [in Philosophical Reflections and Syntheses (Springer, Berlin, 1995), p. 247] introduced a thought experiment that highlighted the incompatibility in quantum theory between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner's friend scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by D. Frauchiger and R. Renner [Nat. Commun. 9, 3711 (2018)] brought attention back to the Wigner's friend and its potential of putting theories to the test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner's friend scenario did not share a time reference frame with the outer observer, and time were tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by M. P. Woods, R. Silva, and J. Oppenheim [Ann. Henri Poincaré 20, 125 (2019)] called the quasi-ideal clock. Our results have shown that this approach produces no decoherent behavior, and the disagreement between the superobserver and its friend persists even for an imprecise clock on Wigner's side. However, the Gaussian spread of this clock model can control which observables do not raise a paradox, indicating the relevance of deepening this analysis.

Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogs are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detectors, these amplifiers implement ideal measurements of the normal operator.

The adiabatic quantum information processing task requires that the evolution of a system must be kept in its instantaneous eigenstate. However, normally the adiabaticity will be ruined due to the interaction between the system and the noisy environment in its long evolution time. Here, in this paper, we show that zero-area pulse control can be used to realize the adiabatic process in a nonadiabatic regime. A concrete example is provided where one spin chain is cut into two chains. The pulse function is applied in the laboratory frame and suitable pulse conditions are obtained numerically. We find that compared with the pulse conditions obtained in the adiabatic frame, the results are similar for low-energy-level systems but tend to deviate when the system's energy level increases. We then obtain the pulse conditions theoretically by writing the control Hamiltonian in the adiabatic frame. It is found that a sequence of pulses with intensities tuned by a time-dependent energy difference is required to guarantee an effective adiabatic speedup.

Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagin's maximum principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagin's maximum principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.

A nonlinear integrodifferential equation of the “reaction-diffusion” type is derived for an optical pulse propagating in a gain resonant two-level medium with the inhomogeneous broadening of the quantum transitions. The stable exact analytical solution of this equation in the form of a dissipative optical soliton with an asymmetric temporal profile is found and analyzed. The temporal duration of this soliton is much longer than the characteristic phase relaxation time but much shorter than the energy relaxation time. It is shown that the formation of such a soliton requires the presence of linear losses, created by the equilibrium part of the medium. It is noted that the found soliton solution qualitatively coincides with the dissipative soliton recently discovered experimentally in a laser microcavity.

Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multistability. Although this exotic behavior has attracted intense research interest, the utilization of optomechanical systems in technological applications in most cases necessitates a complex, yet predictable and controllable oscillatory response. In fact, the various types of robust oscillations supported by optomechanical systems are nested in either the same or neighboring regions of the parameter space, where chaos exists. In this work we systematically dissect the parameter space of the fundamental optomechanical oscillator in order to identify regions where stable self-sustained and self-modulated oscillations exist, by utilizing bifurcation analysis and advanced numerical continuation techniques. Moreover, in cases where bistability occurs, we study the accessibility of these oscillatory states in terms of the initial conditions and their location with respect to well-defined basins of attraction. The results provide specific knowledge for parameter sets enabling the appropriate oscillatory response for different types of applications.

We propose a method for learning temporal data using a parametrized quantum circuit. We use the circuit that has a similar structure as the recurrent neural network, which is one of the standard approaches employed for this type of machine learning task. Some of the qubits in the circuit are utilized for memorizing past data, while others are measured and initialized at each time step for obtaining predictions and encoding a new input datum. The proposed approach utilizes the tensor product structure to get nonlinearity with respect to the inputs. Fully controllable, ensemble quantum systems such as an NMR quantum computer are a suitable choice of an experimental platform for this proposal. We demonstrate its capability with simple numerical simulations, in which we test the proposed method for the task of predicting cosine and triangular waves and quantum spin dynamics. Finally, we analyze the dependency of its performance on the interaction strength among the qubits in numerical simulation and find that there is an appropriate range of the strength. This work provides a way to exploit complex quantum dynamics for learning temporal data.

We propose to utilize fractional Hilbert transform (FHT) to fulfill the optical super-resolution for two unequally bright point sources. For such an asymmetric case, we compare the FHT scheme with both the direct imaging and conventional Hilbert transform schemes. We calculate the Fisher information about the separation and the relative intensity of two light sources. Based on single and multiple parameter estimation, we demonstrate that the FHT scheme has its unique advantages in estimating the separation of the unequally bright point sources. An unconditional enhancement of the measurement precision can be achieved by the FHT scheme. We believe that the FHT can be a good candidate in fulfilling the optical super-resolution in realistic scenarios.

Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level $\mathrm{\Lambda }$ systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure purely holonomic evolution. Our proposal not only improves conventional qubit-based NHQC by efficiently reducing its duration, but also provides implementations of qudit-based NHQC. Therefore, our proposal provides a further development of NHQC that can contribute significantly to the physical realization of efficient quantum information processors.

We investigate the finite-temperature charge-density-wave (CDW) transition of lattice Bose gases within optical cavities in the deep Mott-insulator limit. We find a new critical regime emerges at a temperature around one-half of the on-site interaction energy, where the first-order CDW transition at low temperatures terminates at a critical point and changes to a second-order one. By directly calculating the critical exponents and constructing the effective theory in the corresponding critical regime, we find the emergent criticality belongs to the five-dimensional Ising universality class. Direct experimental observation of the emergent criticality can be readily performed by current experimental setups operated in the temperature regime around half the on-site interaction energy.

We deduce formulas for the angular position of singular optic axes in homogeneous optical media. The angular position of singular optic axes for a given general (complex, nonsymmetric) dielectric tensor is the same for its transposed and complex conjugated tensors as well as for a (complex) multiple. For the case of a symmetric dielectric tensor, the four axes fulfill a connecting relation, meaning that the singular optic axes of a nonsymmetric dielectric tensor do not relate to those of any (effective) symmetric tensor. For the symmetric case, we provide analytical solutions for the angular positions of singular optic axes of triclinic, monoclinic, and orthorhombic crystals.

We study the optical forces experienced by a dielectric microsphere placed in a nonparaxial vector self-accelerating beam. Following the beam's peak intensity (or the main lobe), where the dominant transverse trapping appears, the longitudinal optical force is found to switch from a purely pushing case to an impure case involving pulling forces. The pulling forces tend to appear away from the optimal transverse trapping position, particularly for large particles but populate largely within the transverse trapping potential. In terms of magnitude, such forces can be comparable to the transverse ones when manipulating small particles. The cases of both Mie and Rayleigh particles are discussed. Our work opens the possibility to uncover the pulling effect in nonparaxial accelerating beams, which may lead to applications in optical trapping and manipulation.

Local tensor methods are a class of optimization algorithms introduced in [Hastings, arXiv:1905.07047v2] as a classical analogue of the quantum approximate optimization algorithm. These algorithms treat the cost function as a Hamiltonian on spin degrees of freedom and simulate the relaxation of the system to a low-energy configuration using local update rules on the spins. Whereas the emphasis in Hastings' work was on theoretical worst-case analysis, we here investigate the underlying dynamics of the algorithm, and find that the local tensor method closely follows discretized, imaginary-time dynamics of the system under the problem Hamiltonian. Then, we study practical performance through benchmarking experiments on instances of the MaxCut problem. Through heuristic arguments we propose formulas for choosing the hyperparameters of the algorithm which are found to be in good agreement with the optimal choices determined from experiment. We observe that the local tensor method is closely related to gradient descent on a relaxation of MaxCut to continuous variables but consistently outperforms gradient descent in all instances tested. We find that time to solution achieved by the local tensor method is highly uncorrelated with that achieved by a widely used commercial optimization package; on some MaxCut instances the local tensor method beats the commercial solver in time to solution by up to two orders of magnitude and vice versa.

We explore the classical dynamics of a non-Hermitian compound optomechanical system. By resorting to the method used in laser theory, we derived the classical dynamical equations of the system which incorporate the gain saturation effect of the gain medium. By simulating the classical evolutions of the system, we find that as long as the initial state of the cavities is not in the vacuum state the gain medium will amplify the light energy stored initially in the system and drive the mechanical oscillator into self-sustained oscillation although there is no extra optical drive for the system. Self-sustained oscillation can be formed in both the nonlinear $PT$ symmetry and $PT$ symmetry-broken phase. We also find that the oscillation amplitudes of the mechanical oscillator are more sensitive to the gain saturation of the gain medium than the gain coefficient. Multistability of the self-sustained oscillation also appears in our model. Our paper provides a deeper insight into the influence of non-Hermiticity on the dynamics of optomechanical systems and a tool for device applications.

We propose a model including a one-dimensional harmonic chain of oscillators whose two ends coupled two cavity-optomechanical systems for studying one-dimensional thermal conductivity in statistical physics. In this model, the cavity-optomechanical systems function as two laser-engineerable thermal reservoirs. When the effective temperatures of the two reservoirs are not equal, a heat flux through the chain can be generated, and moreover the classical and quantum features of the heat flux have been studied. We further show that the heat flux does not obey the Fourier's law in this model. The thermal switching phenomenon could be induced by controlling the on-site vibrational frequency. Finally, we propose to apply the correlation between two mechanical oscillators to measure the heat flux through the chain.