Quantum state preparation is important for quantum information processing. In particular, in optical quantum computing with continuous variables, non-Gaussian states are needed for universal operation and error correction. Optical non-Gaussian states are usually generated by heralding schemes using photon detectors. In previous experiments, the temporal resolution of the photon detectors was sufficiently high relative to the time width of the quantum state, so that the conventional theory of non-Gaussian state preparation treated the detector's temporal resolution as negligible. However, when using various photon detectors, including photon-number-resolving detectors, the temporal resolution is non-negligible. In this paper, we extend the conventional theory of quantum state preparation using photon detectors to the finite-temporal-resolution regime, analyze the cases of single-photon and two-photon preparation as examples, and find that the generated states are characterized by the dimensionless parameter $B$, defined as the product of the temporal resolution of the detectors $\mathrm{\Delta }t$ and the bandwidth of the light source $\mathrm{\Delta }f$. Based on the results, $B\sim 0.1$ is required to keep the purity and fidelity of the generated quantum states high.

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of nonstationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical nonlinear and nonstationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differ from those of stationary ones.

The binding and trapping of particles usually rely on conservative forces, described by unitary quantum dynamics. We show that both can also arise solely from spatially dependent dephasing, the simplest type of decoherence. This can be based on continuous weak position measurements in only selected regions of space, for which we propose a practical realization. For a single particle, we demonstrate a quantum particle in a box based on dephasing. For two particles, we demonstrate their binding despite repulsive interactions, if their molecular states are dephased at large separations only. Both mechanisms are experimentally accessible, as we show for an example with Rydberg atoms in a cold gas background.

This Research Letter reports on the observation of superradiance decoherence caused by long-range dipole-dipole interactions between Rydberg atoms. A cold atom cloud is prepared in the mode volume of a weakly driven optical cavity and excited to a Rydberg state. The cavity transmission monitors the Rydberg dynamics in real time and detects superradiant enhancement of the transition rates between neighboring Rydberg states. The observed enhancement is reduced for increasing Rydberg atom density: a signature of atom pair interactions. The observations are explained within a model based on the idea of Rydberg blockade reducing the atom number participating in the Dicke state, responsible for superradiance.

A comparative study of a qutrit (three-level atomic system) coupled to a classical field in a typical Markovian reservoir (free space) and in a photonic-band-gap (PBG) crystal is carried out. The aim of the study is to assess the collective impact of a structured environment and classical control of the system on the dynamics of quantum coherence, non-Markovianity, and estimation of parameters that are initially encoded in the atomic state. We show that the constructive interplay of PBG material as a medium and a classical driving field as a part of the system results in a significant enhancement of all the quantum traits of interest, compared to the case when the driven qutrit is in a Markovian environment. Our results supply insights for preserving and enhancing quantum features in qutrit systems, which are promising alternative candidates to be used in quantum processors instead of qubits.

The inference of a hidden variable's historical value, based on observations before and after the fact, is a controversial subject in quantum mechanics. Here I address the controversy by proposing a formalism that unifies and generalizes some of the previous proposals for the task, including the quantum minimum-mean-square-error estimators proposed by Ohki, the generalized conditional expectation proposed by Accardi and Cecchini, the quantum smoothing theory proposed by Tsang, the optimal observables for parameter estimation proposed by Personick, Belavkin, and Grishanin, and the weak values proposed by Aharonov, Albert, and Vaidman. The formalism is based on Ohki's suggestion of a distance between two observables in the Heisenberg picture, which remains well defined for incompatible observables and serves as a more general foundation for quantum inference than Belavkin's nondemolition principle.

We address the effects of dissipative defects giving rise to a localized particle loss, in one-dimensional noninteracting lattice fermionic gases confined within a region of size $\ell$. We consider homogeneous systems within hard walls and inhomogeneous systems where the particles are trapped by space-dependent external potentials, such as harmonic traps. We model the dissipative particle-decay mechanism by Lindblad master equations governing the time evolution of the density matrix. The resulting quantum dynamics is analyzed in protocols starting from the ground state of the Hamiltonian for $N_0$ particles, then evolving under the effect of one dissipative particle-loss defect, for example, at the center of the system. We study the interplay between time, size $\ell$, and the number $N_0$ of initial particles, considering two different situations: (i) fixed number $N_0$ of initial particles; and (ii) fixed ratio $N_0/\ell$, corresponding to the thermodynamic limit of the initial equilibrium state. We show that the quantum evolutions of the particle number and density develop various intermediate and asymptotic dynamic regimes, and nontrivial large-time states when the dissipative mechanism acts at the center of the system.

A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, whereas its location on the Bloch sphere is described by the spin coherent state. An additional spin that interacts with the spin cluster plays the role of a coin, whose state determines the rotation of the spin cluster. The Wigner function is calculated to visualize the movement of the walker on the Bloch sphere with which the probability distribution and the standard deviation are also achieved. The quadratic enhancement of variance for the quantum walk on the Bloch sphere is confirmed. Compared to the ideal quantum walk on a circle, the walker's states on the Bloch sphere are generally nonorthogonal, whose drawbacks can be eliminated by increasing the number of spins in the spin cluster.

It is well known that the maximal success probability of the binary quantum communication can be improved by using a sub-Poissonian nonstandard coherent state as an information carrier. In the present article, we consider the quantum communication with $N$-ary phase-shift-keying ($N$-PSK) signal for an arbitrary positive integer $N>1$. By using nonstandard coherent state, we analytically provide the maximal success probability of the quantum communication with $N$-PSK. Unlike the binary case, there is a case that the guessing probability of $N$-PSK quantum communication can be improved by some non-sub-Poissonian, nonstandard coherent state.

The $\alpha$-Rényi entropy in the gapless models has been obtained by the conformal field theory, which is exact in the thermodynamic limit. However, the calculation of its finite-size effect (FSE) is challenging. So far only the FSE in a single interval in the $XX$ model has been understood and the FSE in the other models and in the other conditions is totally unknown. Here we report the FSE of this entropy in disjointed intervals $A={\cup }_i{A}_i$ under a uniform dilation $\lambda A$ in the $XY$ model, showing a universal scaling law as ${\mathrm{\Delta }}_{\lambda A}^{\alpha }={\mathrm{\Delta }}_A^{\alpha }{\lambda }^{-\eta }\mathcal{B}(A,\lambda )$, where $\left|\mathcal{B}\right(A,\lambda \left)\right|\le 1$ is a bounded function and $\eta =\text{min}(2,2/\alpha )$ when $\alpha <10$. We verify this relation in the phase boundaries of the $XY$ model, in which the different central charges correspond to the physics of free fermion and free boson models. We find that in the disjointed intervals two FSEs, termed as extrinsic FSE and intrinsic FSE, are required to fully account for the FSE of the entropy. Physically, we find that only the edge modes of the correlation matrix localized at the open ends $\partial A$ have contribution to the total entropy and its FSE. Our results provide some incisive insight into the entanglement entropy in the many-body systems.

The neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. A two-qubit controlled-phase gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing nontrivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing the two-qubit controlled-phase ($C_Z$) gate via single-modulated-pulse off-resonant modulated driving embedded in a two-photon transition for Rb atoms. It relies on a global driving laser pulse with a carefully calculated smooth waveform to gain the appropriate phase accumulations required by $C_Z$ gate. Combining this $C_Z$ gate with global microwave pulses, two-atom entanglement is generated with the raw fidelity of 0.945(6). After accounting for state preparation and measurement errors, we extract the entanglement operation fidelity to be 0.980(7). Our work features completing the $C_Z$ gate operation within a single pulse to avoid shelved population in the Rydberg levels, thus demonstrating another promising route for realizing a high-fidelity two-qubit gate for the neutral atom platform.

Experimental imperfections induce phase and population errors in quantum systems. We present a method to compensate unitary errors affecting also the population of the qubit states. This is achieved through the interaction of the target qubit with an additional control qubit. We show that our approach works well for single-photon and two-photon excitation schemes. In the first case, we study two reduced models: (i) a two-level system in which the interaction corresponds to an effective level shift and (ii) a three-level one describing two qubits in the Bell triplet subspace. In the second case, a double Stimulated Raman Adiabatic Passage process is presented with comparable compensation efficiency with respect to the single-photon case.

The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, probabilistically sending an unknown qubit state to two receivers, sending different qubit states to two receivers, and sending qutrit states to two receivers. Finally, we discuss some applications of these protocols.

Interferometric power, based on the minimal quantum Fisher information in a black-box interferometer, can be used to measure general quantum correlation in a bipartite system. This paper explores the interferometric power of a two-qubit system in a common bath. It is found that, for an initially separable state, the interferometric power of the system can be produced with the time evolution, even subject to the dephasing environment. Moreover, it is asymmetric with respect to the local evolution implementing on one subsystem or another. Our result would be useful to quantum information processing beyond entanglement, especially in one-sided device-independent task.

The particle and spin transports through a quantum point contact between two Fermi gases with Raman-induced spin-orbit coupling are investigated. We show that the particle and spin conductances both demonstrate the structure of plateaus due to the mesoscopic scale of the quantum point contact. Compared with that of normal Fermi gases, the height of the plateau of the particle conductance is enhanced by the spin-orbit-coupling effect for the whole parameter space. This implies that the 0.7 anomaly observed in mesoscopic experiments is unlikely to be induced purely by the spin-orbit coupling. Furthermore, the generation of spin current is investigated in this system. We find that the spin current can be induced by only the bias of the spin difference between the two reservoirs for the case of vanishing two-photon detuning. When the two-photon detuning is nonzero, the spin current can also be generated by the bias of the total particle number between the two reservoirs.

We present a simple theoretical model used for describing the suppressing reactivity of an ultracold Fermi molecular gas in a degenerate regime via the statistical potential. The statistical potential originates from the symmetry properties of the wave function of identical particles, and is derived by using the density matrix. We use our theoretical model to well reproduce recent experimental results of a potassium-rubidium molecule gas in the deep quantum degenerate regime reported by De Marco et al. [Science 363, 853 (2019)]. The suppression of the chemical reaction rate observed in the experiment is quantitatively reproduced by using the $p$-wave scattering volume as an adjusting parameter. The strength of spatial correlation can be intuitively captured by the statistical potential.

We explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice into the topological Anderson insulator state. On the other hand, the nontrivial topology of the photonic band structure suppresses Anderson localization of modes that disorder introduces inside the band gap of the ideal lattice. Furthermore, we discover that disorder can both open a topological pseudogap in the spectrum of an otherwise topologically trivial system and introduce spatially localized modes inside it.

Continuous interest in bidirectional ultrafast fiber lasers not only reinforces the practical applications in coherent dual-comb spectroscopy but also enriches the understanding of soliton dynamics in nonlinear systems. However, the transient dynamics of bidirectional solitons are still unexplored. Here, we report on an observation of the switching dynamics in a net-anomalous-dispersion bidirectional ultrafast fiber laser which can operate in both asynchronous and synchronous operations. Transient switching dynamics between the asynchronous and synchronous states are demonstrated, which is accompanied by switchable and weak interaction between bidirectional solitons. The dynamical evolution and output properties of the asynchronous and synchronous bidirectional solitons are investigated respectively. Stable breathing solitons in the synchronous operation show opposite behaviors in both spectra and pulse energy dynamics, which vary with different pump powers. Our findings provide insight into the transient dynamics in ultrafast lasers and contribute to the understanding of nonlinear systems in general.

We investigate the spectral topology of one-dimensional lattices where the nonreciprocal hoppings within the nearest $r_d$ neighboring sites are the same. For the purely off-diagonal model without onsite potentials, the energy spectrum of the lattice under periodic boundary conditions (PBCs) forms an inseparable loop that intertwines with itself in the complex energy plane and is characterized by winding numbers ranging from 1 up to $r_d$. The corresponding spectrum under open boundary conditions (OBCs), which is real in the nearest neighboring model, will ramify and take the shape of an $(r_d+1)$-pointed star with all the branches connected at zero energy. If we further introduce periodic onsite modulations, the spectrum will gradually divide into multiple separable bands as we vary the parameters. Most importantly, we find that a different kind of band gap called a loop gap can exist in the PBC spectrum, separating an inner loop from an outer one with each composed by part of the spectrum. In addition, loop structures also exist in the OBC spectra of systems with onsite potentials. We further study the lattices with power-law decaying long-range nonreciprocal hopping and found that the intertwined loops in the PBC spectrum will be untangled. Finally, we propose an experimental scheme to realize the long-range nonreciprocal models by exploiting electrical circuits. Our work unveils the exotic spectral topology in the long-range nonreciprocal lattices.