The phase diagram of lowest-energy vortices in the polar phase of spin-1 Bose-Einstein condensates is investigated theoretically. Singly quantized vortices are categorized by the local ordered state in the vortex core and three types of vortices are found as lowest-energy vortices, which are elliptic AF-core vortices, axisymmetric F-core vortices, and N-core vortices. These vortices are named after the local ordered state, ferromagnetic (F), antiferromagnetic (AF), broken-axisymmetry (BA), and normal (N) states apart from the bulk polar (P) state. The N-core vortex is a conventional vortex, in the core of which the superfluid order parameter vanishes. The other two types of vortices are stabilized when the quadratic Zeeman energy is smaller than a critical value. The axisymmetric F-core vortex is the lowest-energy vortex for ferromagnetic interaction, and it has an F core surrounded by a BA skin that forms a ferromagnetic-spin texture, as exemplified by the localized Mermin-Ho texture. The elliptic AF-core vortex is stabilized for antiferromagnetic interaction; the vortex core has both nematic-spin and ferromagnetic orders locally and is composed of the AF-core soliton spanned between two BA edges. The phase transition from the N-core vortex to the other two vortices is continuous, whereas that between the AF-core and F-core vortices is discontinuous. The critical point of the continuous vortex-core transition is computed by the perturbation analysis of the Bogoliubov theory and the Ginzburg-Landau formalism describes the critical behavior. The influence of trapping potential on the core structure is also investigated.

The non-Hermitian system has been widely studied recently in various fields from quantum physics to condensed matter, in which the “exceptional point” (EP) as an essential feature of the systems can be used to design sensors, for example, a mass sensor to detect the mass of nano-objects. Inspired by the LIGO gravitational wave detector by using squeezed states of light, we here aim to enhance the sensitivity of the mass sensor by a nonlinear laser drive. The system consists of two optomechanical cavities that are mechanically coupled and driven nonlinearly by detuned lasers (squeezed lasers). Compared to the case of linear drive, our results are more sensitive to the mass, and the split width of the eigenvalues at EP can be further increased by using the squeezed lasers. The sensitivity enhancement factor and optical damping of resonators are also calculated and discussed, and a great improvement is found consequently. This work would provide a wider view for the new quantum sensors in order to be applied in the fields of nanoparticle detection, precision measurement, and quantum metrology.

We present an experimental and theoretical study of the response of a dipolar supersolid to a Bragg excitation at high-energy defined by the impulse approximation regime. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein condensate to a supersolid state and ultimately to an incoherent array of droplets. Already in the supersolid regime, the observed reduction is faster than the one theoretically predicted by the Bogoliubov–de Gennes theory. By comparing experiments and theories, we are able to attribute this discrepancy to the presence of coherent phase dynamics induced by the crossing of the phase transition. The phase variations are found to change character along the phase diagram and become predominantly incoherent only when reaching the incoherent-droplet regime.

We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong the coherence time of a fiducial qubit. The qubit is part of a network of other qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of the fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona fide physical process. Even in the presence of disorder, a winding number $W$ can be defined and evaluated in real space, as long as certain symmetries are preserved. Hence we can construct the topological phase diagrams of noisy open quantum models, such as the non-Hermitian disordered Su-Schrieffer-Heeger dimer model and a trimer model that includes longer-range couplings. For finite-size systems we find that there are precisely $W$ modes localized at one end of the chain. In such topological phases the qubit's coherence lifetime is exponentially large in the system size. In the presence of competing disorder parameters, interesting reentrance phenomena of topologically nontrivial sectors are observed. This means that in certain parameter regions, increasing disorder drastically increases the coherence time of the fiducial qubit.

We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about the number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e., high fidelity of initial states. The main tool is a counter gate with which the required nonlocal information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states and generalize it to purify multiparty GHZ states.

Quantum resources and protocols are known to outperform their classical counterparts in a variety of communication and information processing tasks. Random access codes (RACs) are one such cryptographically significant family of bipartite communication tasks, wherein the sender encodes a data set (typically a string of input bits) onto a physical system of bounded dimension and transmits it to the receiver, who then attempts to guess a randomly chosen part of the sender's data set (typically one of the sender's input bits). In this work, we introduce a generalization of this task wherein the receiver, in addition to the individual input bits, aims to retrieve randomly chosen functions of the sender's input string. Specifically, we employ sets of mutually unbiased balanced functions, such that perfect knowledge of any one of the constituent functions yields no knowledge about the others. We investigate and bound the performance of (i) classical, (ii) quantum prepare and measure, and (iii) entanglement assisted classical communication (EACC) protocols for the resultant generalized RACs (GRACs). Finally, we detail the case of GRACs with three input bits and find maximal success probabilities for classical, quantum, and EACC protocols, along with the effect of noisy quantum channels on the performance of quantum protocols. Moreover, with the help of this case study, we reveal several characteristic properties of the GRACs which deviate from the standard RACs.

Composite pulse sequences, which produce arbitrary predefined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to 8 orders of experimental errors in the pulse amplitude and the pulse duration. Composite sequences for three basic quantum gates, X (not), Hadamard and arbitrary rotation, are derived. Three classes of composite sequences are presented: one symmetric and two asymmetric. They contain as their lowest members two well-known composite sequences: the three-pulse symmetric SCROFULOUS pulse and the four-pulse asymmetric BB1 pulse, which compensate first- and second-order errors, respectively. The shorter sequences are derived analytically, and the longer ones numerically (instead by nesting and concatenation, as usually done hitherto). Consequently, the composite sequences derived here match or outperform the existing ones in terms of either speed or accuracy, or both. For example, we derive a second-order composite sequence, which is faster (by about 13%) than the famous BB1 sequence. For higher-order sequences, the speedup becomes much more pronounced. This is important for quantum information processing as the sequences derived here provide more options for finding the sweet spot between ultrahigh fidelity and high speed.

Counterfactual communication protocols are analyzed using three approaches: a classical argument, the weak trace criterion, and the Fisher information criterion. It is argued that the classical analysis leads to contradiction and should therefore be abandoned. The weak trace and Fisher information criteria are shown to agree about the degree of counterfactuality of communication protocols involving postselection. It is argued that postselection is a necessary ingredient of counterfactual communication protocols. Coherent interaction experiments, as well as a recently introduced modification of counterfactual communication setups which eliminates the weak trace, are discussed.

We explore the spatial enantioseparation of gaseous chiral molecules for the cyclic three-level systems coupled with three electromagnetic fields. Due to molecular rotations, the specific requirements of the polarization directions of the three electromagnetic fields lead to the space-dependent part of the overall phase of the coupling strengths. Thus, the overall phase of the coupling strengths, which differs with $\pi$ for the enantiomers in the cyclic three-level model of chiral molecules, varies intensely in the length scale of the typical wavelength of the applied electromagnetic fields. Under the induced gauge potentials resulting from the space-dependent part of the overall phase and the space-dependent intensities of coupling strengths, we further show spatial enantioseparation for typical parameters of gaseous chiral molecules.

The Wigner function $W_N(\mathbf{x},\mathbf{p})$ is a useful quantity to characterize the quantum fluctuations of an $N$-body system in its phase space. Here we study $W_N(\mathbf{x},\mathbf{p})$ for $N$ noninteracting spinless fermions in a $d$-dimensional spherical hard box of radius $R$ at temperature $T=0$. In the large-$N$ limit, the local-density approximation predicts that $W_N(\mathbf{x},\mathbf{p})\approx 1/{\left(2\pi \hslash \right)}^d$ inside a finite region of the $(\mathbf{x},\mathbf{p})$ plane, namely, for $\left|\mathbf{x}\right|<R$ and $\left|\mathbf{p}\right|<k_F$, where $k_F$ is the Fermi momentum, while $W_N(\mathbf{x},\mathbf{p})$ vanishes outside this region, or droplet, on a scale determined by quantum fluctuations. In this paper we investigate systematically, in this quantum region, the structure of the Wigner function along the edge of this droplet, called the Fermi surf. In one dimension, we find that there are three distinct edge regions along the Fermi surf and we compute exactly the associated nontrivial scaling functions in each regime. We also study the momentum distribution ${\widehat{\rho }}_N\left(p\right)$ and find a striking algebraic tail for very large momenta ${\widehat{\rho }}_N\left(p\right)\propto 1/p^4$, well beyond $k_F$, reminiscent of a similar tail found in interacting quantum systems (discussed in the context of Tan's relation). We then generalize these results to higher $d$ and find, remarkably, that the scaling function close to the edge of the box is universal, i.e., independent of the dimension $d$.

Metal nanoparticles (MNPs) possess the intriguing property of enhancing and limiting the energy of light field to subwavelength scale, which have attracted extensive attention in physics, chemistry, and life sciences. Meanwhile, squeezing is a general concept in quantum optics and can be used to engineer matter interaction scenarios. Here we consider an artificial hybrid molecule consisting of an MNP interacting with a semiconductor quantum dot (QD), combining with a squeezed reservoir. Using experimentally realistic parameters for the MNP-QD architecture and fully quantized approach, we theoretically explore the optical properties of the hybrid molecule driven by an external applied laser field via probing the resonance fluorescence in the steady state. We show that in this way it is possible to engineer and control the peak-value magnitudes, widths, and shapes of the resonance fluorescence spectra under the influence of the squeezed vacuum field without the need for the strong-coupling condition between the MNP and QD. In particular, some interesting phenomena in rich spectral responses are attainable, including Fano-type resonance fluorescence, fluorescence quenching, fluorescence narrowing, and fluorescence enhancement. Our method can also be extended to other nanoscopic structures, such as a plasmonic nanoantenna coupled to an emitter. These unique line shapes obtained here may have potential applications in developing quantum plasmonic platforms and sensitive on-chip devices such as optical switches and sensors.

We consider the analogy between gravitational fields and optical media within the framework of geometrical optics in curved spacetime in order to describe how light can acquire orbital angular momentum (OAM) when it traverses the gravitational field of a massive rotating compact object; in particular, we analyze the interplay between OAM and polarization. Kerr spacetimes are known not only to impose a gravitational Faraday rotation on the polarization of a light beam, but also to set a characteristic fingerprint in the orbital angular momentum distribution of the radiation passing nearby a rotating black hole (BH). Kerr spacetime behaves like an inhomogeneous and anisotropic medium, in which light can acquire orbital angular momentum and spin-to-orbital angular momentum conversion can occur, acting as a polarization and phase changing medium for the gravitationally lensed light, as confirmed by the data analysis of the M87* black hole.

We investigate the collective scattering of coherent light from a thermal alkali-metal vapor with temperatures ranging from 350 to 450 K, corresponding to average atomic spacings between $0.7\lambda$ and $0.1\lambda$. We develop a theoretical model treating the atomic ensemble as coherent, interacting, radiating dipoles. We show that the two-time second-order correlation function of a thermal ensemble can be described by an average of randomly positioned atomic pairs. Our model illustrates good qualitative agreement with the experimental results. Furthermore, we show how fine-tuning of the experimental parameters may make it possible to explore several photon statistics regimes.

We investigate the dynamics of a giant atom (or atoms) in a waveguide QED scenario, where the atom couples to the coupled resonator waveguide via two sites. For a single-giant-atom setup, we find that the atomic dissipation rate can be adjusted by tuning its size. For the two-giant-atom system, the waveguide will induce the controllable individual and collective dissipation as well as effective interatom coupling. As a result, we can realize theoretically the robust entangled state preparation and nonreciprocal excitation evolution. We hope our study can be applied in quantum information processing based on a photonic and acoustic waveguide setup.

Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself, rather than the state. Here we develop a Markovian master equation for the process matrix of an open system interacting with a reservoir, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum coherent-control scenarios, such as optimal decoherence suppression, gate simulation, and passive and indirect control of the reservoir, in all of which we aim to simulate a given terminal process at a given final time.

The past two decades have witnessed a surge of interest in borrowing tools from quantum information theory to investigate quantum phase transitions (QPTs). The best-known examples are entanglement measures whose nonanalyticities at critical points were tied to QPTs in a plethora of physical models. Here, focusing on the $XXZ$ model, we show how QPTs can be revealed through the quantum steering ellipsoid (QSE), which is a geometric tool capable of characterizing both the strength and type of quantum correlations between two subsystems of a compound system. We find that the QSE associated with the $XXZ$ model changes in shape with the QPTs; that is, it is a needle in the ferromagnetic phase, an oblate spheroid in the gapless phase, and a prolate spheroid in the antiferromagnetic phase. This finding offers an example demonstrating the intriguing possibility of unveiling QPTs in a geometrically visible fashion. Some connections between our results and previous ones are discussed.

Universal quantum gates play a critical role in quantum information processing. Here, based on the scattering property of photons off single emitters in one-dimensional waveguides, we present some heralded protocols for realizing controlled-not, Toffoli, and Fredkin gates on hybrid systems. The control qubit of our gates is encoded on a flying photon, and the target qubits are encoded in the degenerate ground states of the emitter. In our schemes, the faulty scattering processes between emitters and photons caused by system imperfections can be transformed into the detection of photon polarization. That is, our three quantum gates are accomplished in a heralded way. Moreover, the quantum circuits for the three gates are versatile and compact, and no additional qubits are required. With current technique on manipulating the emitter-waveguide system, our protocols may be experimentally feasible. This work provides an effective avenue for implementing quantum logic gates.

We present numerical simulations of the time delay in photoemission of asymmetric diatomic molecules using the technique of reconstruction of attosecond beating by interference of two-photon transitions (RABITT) by solving the time-dependent Schrödinger equation. Our results show an obvious time delay between photoelectrons emitted to the left and right and this relative time delay oscillates as the photoelectron energy changes. More interestingly, the amplitude of this oscillation increases when the asymmetry degree of diatomic molecules decreases. With the method of the selected continuum wave functions, we calculate the Wigner time delay in photoionization. The obtained stereo Wigner time delay also oscillates with photoelectron energy. This oscillation is traced back to two-center interferences and it could explain the relative time delay in the RABITT measurement. Furthermore, our results indicate that the continuum-continuum time delay in photoemission of heteronuclear molecules is asymmetric.

In the context of dynamical control, non-Hermitian systems offer unique opportunities and challenges. In the simplest case of two interacting levels with gain and/or loss, the existence of an exceptional point (EP) of degeneracy in the chiral complex eigenvalue landscape fundamentally changes how the system responds to adiabatic changes in the coupling $\gamma$ and energy separation $\delta$ of the bare levels. In particular, previous studies have shown that selective population transfer can be achieved by adiabatically steering the system around closed paths that encircle the EP with the proper helicity in the $\gamma$ vs $\delta$ parameter space. Here we show that efficient state-selective population transfer can, in some cases, be achieved even with control loops that do not enclose the EP.