The concept of cross-spectral purity of light, established by Mandel for stationary optical fields, is extended to nonstationary fields. Separability conditions that ensure the cross-spectral purity of nonstationary light are derived in the space-frequency and space-time domains. It is also shown that the property of cross-spectral purity is not strictly preserved on propagation of fields with any appreciable spectral bandwidth. Further, we introduce a method for generating cross-spectrally pure (stationary and nonstationary) fields from spatially incoherent light sources by means of achromatic Fourier-transform systems.

Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a unique coordination game. In the simplest case, Alice and Bob, each having two random variables, attempt to maximize the area of a rectangle and the rectangle's area is represented by a certain parameter. This parameter, which is a function of the correlations between their random variables, is shown to be a Bell parameter, i.e., the achievable bound using only classical correlations is strictly smaller than the achievable bound using nonlocal quantum correlations We continue by generalizing to the case in which Alice and Bob, each having now $n$ random variables, wish to maximize a certain volume in $n$-dimensional space. We term this parameter a multiplicative Bell parameter and prove its Tsirelson bound. Finally, we investigate the case of local hidden variables and show that for any deterministic strategy of one of the players, the Bell parameter is a harmonic function whose maximum approaches the Tsirelson bound as the number of measurement devices increases. Some theoretical and experimental implications of these results are discussed.

The Page-Wootters mechanism questioned the fundamental nature of time in quantum physics. The mechanism explored the notion that a given physical quantity is always defined and measured relative to a reference frame, in general, not explained in the theoretical description of quantum physical experiments. Recently, the resource theory of asymmetry deals explicitly with the physical conditions necessary for a quantum system to serve as a good reference frame. Nonetheless, to quantify a quantum reference frame in relation to another one, it is important to establish an internal description of quantum theory, i.e., without the need for a classical reference frame. In this work, we address this issue with the concept of mutual asymmetry and use this machinery in the Page-Wootters mechanism by identifying the concept of mutual asymmetry as mutual or internal coherence. To do so, the notion of quantum coherence in relation to a quantum reference frame is revisited and a quantifier is proposed in this scenario. Also, this opens space to investigate the link of internal coherence and correlations, as proposed by Page and Wootters, under a resource theory approach.

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories.

Given any two quantum states $\rho$ and $\sigma$ in Hilbert spaces of equal dimension satisfying the majorization condition $\rho \succ \sigma$, it is always possible to transform $\rho \mapsto \sigma$ by a unital quantum map. In fact, any such transformation can be achieved just by means of noisy operations, i.e., by access to maximally mixed ancillary states and unitary transformations that act jointly in the system-ancilla space. Here, we investigate the possible transitions between states (i.e., the induced preorder of states) when one restricts the unitary control to the quantum system alone and replaces the maximally mixed ancillas with a Markovian master equation, represented by a unital Lindbladian. As a main result, we find necessary and sufficient conditions for the Lindbladian dissipation to have the same converting power as that of noisy operations, i.e., any transformation $\rho \mapsto \sigma$ is possible if and only if $\rho \succ \sigma$.

The viability of nonstoquastic catalyst Hamiltonians to deliver consistent quantum speedups in quantum adiabatic optimization remains an open question. The infinite-range ferromagnetic $p$-spin model is a rare example exhibiting an exponential advantage for nonstoquastic catalysts over its stoquastic counterpart. We revisit this model and note how the incremental changes in the ground-state wave function give an indication of how the nonstoquastic catalyst provides an advantage. We then construct two new examples that exhibit an advantage for nonstoquastic catalysts over stoquastic catalysts. The first is another infinite range model that is only 2-local, but also exhibits an exponential advantage, and the second is a geometrically local Ising example that exhibits a growing advantage up to the maximum system size we study.

We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process was originally devised for heavy-helium-like ions. In this work, we study this process in the nuclear clock isotope ${}^{229}\mathrm{Th}$ in the $2+$ charge state. For this purpose we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low-lying isomeric state in ${}^{229}\mathrm{Th}$ is a circular process starting with a two-step pumping stage followed by NETP. The ideal intermediate steps in this process depends on the supposed energy $\hslash {\omega }_N$ of the nuclear isomeric state. For each of these energies, the best initial state for NETP is calculated. Special focus is put on the most recent experimental results for $\hslash {\omega }_N$.

Raman-Ramsey interference has proved a very effective technique to implement compact and high performing vapor cell frequency standards. In this paper, we theoretically characterize Raman-Ramsey resonances in an optically thick atomic vapor. Specifically, some parameters of interest for frequency standards applications, like contrast and linewidth of the central Raman-Ramsey fringe, are evaluated at different temperatures for ${}^{133}\mathrm{Cs}$ and ${}^{87}\mathrm{Rb}$ vapor cells with buffer gas. Density narrowing and broadening effects are described and explained in terms of a three-level theory where laser field propagation through the atomic medium is taken into account. Also, we investigate light shift both in low and high atomic density regimes. Light shift, which potentially degrades the medium- to long-term stability of Raman-Ramsey clocks, is composed of two contributions. The first is a pulling effect exerted by the wide Rabi profile enclosing the interference pattern on the central Raman-Ramsey fringe. The second light-shift term is strictly related to the detection time. Calculations derived from our model well describe already existing experimental results and new behaviors are predicted.

We compare the continuous and discrete truncated Wigner approximations of various spin models' dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a recently introduced geometric correlation matrix visualization technique [Mukherjee et al., Phys. Rev. A 97, 043606 (2018)]. We find that at modestly short times, the dominant error in both approximations is to substantially suppress spin correlations along one direction.

The fermionic, time-reversal-invariant Hofstadter-Hubbard model with a population difference between the two spin states is investigated. In the strongly interacting regime, where the system can be described by an effective spin model, we find an exotic spin structure by means of classical Monte Carlo calculations. Remarkably, this spin structure exhibits a transverse net magnetization perpendicular to the magnetization induced by the population imbalance. It is thus inherently different from canted antiferromagnetism. We further investigate effects of quantum fluctuations within the dynamical mean-field approximation and obtain a rich phase diagram including ferromagnetic, antiferromagnetic, ferrimagnetic, and transverse magnetization phases.

Existence of a spectral singularity (SS) in the spectrum of a Schrödinger operator with a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, $\mathcal{PT}$-symmetric potentials. We illustrate all these opportunities with examples. We also describe splitting of a second-order SS under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.

In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.

A pure quantum state of $N$ subsystems with local dimension $d$ is called a $k$-uniform state if every reduction to $k$ qudits is maximally mixed. Based on a special class of combinatorial design, namely irredundant orthogonal arrays, we show the existence of 2-uniform $N$-qudit states when $N\ge 4$ and $d$ is a prime power other than 2. In addition, given any Hadamard matrix of order greater than 4, we demonstrate how it can be used to construct 3-uniform multiqubit states. In fact, we find that there exists some 3-uniform $N$-qubit when $N\ge 8$ except case $N=9$. These give an answer to a question posed by Goyeneche et al. [Phys. Rev. A 90, 022316 (2014)]. Furthermore, starting from a minimal support $k$-uniform state, we show how to generate an orthogonal basis consisting of $k$-uniform states. At last, we derive a series of $(k-1)$-uniform $(N-1)$-qudit states from a single $k$-uniform $N$-qudit state. The $k$-uniform states are good candidates among the multipartite entangled states.

We discuss the Chern number spectrum of ultracold fermions in square optical lattices as a function of artificial magnetic, Zeeman, and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase transitions induced by Zeeman and spin-orbit fields, where the total number and chirality of edge states change for fixed magnetic flux ratio, thus leading to topological-insulator phases which are different from those found at zero Zeeman and spin-orbit fields. We construct phase diagrams of chemical potential versus Zeeman field or spin-orbit coupling and characterize all insulating phases by their topological invariants. Lastly, we obtain a staircase structure in the filling factor versus chemical potential for various Zeeman and spin-orbit fields, showing the existence of incompressible states at rational filling factors derived from a generalized Diophantine equation.

Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the appearance of classically forbidden probability flux when a matter-wave packet, initially confined to a semi-infinite line, expands in free space.

Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect that characterizes the ability to remotely control quantum states of one system via local measurements on another distant system entangled with the controlled one. Entanglement swapping is an effective way to realize distant entanglement, which is useful for building quantum networks. Previous studies show that the presence of entanglement of subsystems in mixed states is merely necessary for achieving entanglement swapping. In this paper, we find that for Gaussian entanglement swapping with two pairs of entangled modes ${\widehat{a}}_j$ and ${\widehat{b}}_j(j=1,2)$, the existence of directional EPR steering from the modes ${\widehat{b}}_j$ under homodyne detection to the other modes ${\widehat{a}}_j$ is a sufficient and necessary condition for achieving swapped entanglement between modes ${\widehat{a}}_1$ and ${\widehat{a}}_2$, and moreover this achievement is independent of the reverse steering from modes ${\widehat{a}}_j$ to ${\widehat{b}}_j$. We further reveal that this is because the steering in that direction enables the amplitude and phase squeezing of the two composite modes of modes ${\widehat{a}}_1$ and ${\widehat{a}}_2$ via homodyne detection, which is necessary and sufficient for swapped entanglement. As a concrete example, we next investigate light-mechanical steering in a dispersively or dissipatively coupled optomechanical system, and we consider the generation of entanglement between two distant optomechanical oscillators via entanglement swapping by utilizing steering. It is interesting to find that even without the constraint that the cavity linewidth should be smaller than the mechanical frequency, robust mechanical entanglement can be obtained in the steady-state regime.

Spontaneous vortex nucleation is a universal feature of open and nonlinear physical systems. We investigate theoretically vortex rings and vortex lines emerging during propagation of self-trapped wave beams in nonlocal nonlinear media. We demonstrate how radially perturbed fundamental solitons exhibit extremely robust and long-lived oscillations with the spontaneous generation of a regular set of vortex rings at the wave beam periphery. We find numerically a class of cylindrically symmetric higher-order spatial solitons and investigate their stability and nonlinear dynamics. The formation of external vortex rings, similar to fundamental soliton, is accompanied by emergence of additional internal vortex-antivortex pairs nucleating from the edge-ring phase dislocation of perturbed higher-order soliton.

We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser driven in the resolved blue-sideband regime. To keep our results tractable, we switch to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows steering of the mechanical degree of freedom to the desired Fock state by directing the optical excitations dynamically towards the target phonon state. The numerical results, including decoherence on both the mechanical and the optical degrees of freedom, prove to be quite robust in the good- and bad-cavity regimes, with fidelities exceeding 95%. Finally, characterization of the achieved nonclassicality, as well as the limitations and feasibility of our protocol under experimental parameters, is also discussed.

Few-photon optomechanical effects not only are important physical evidence for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum technology. Here we study the few-photon optomechanical effects including photon blockade and generation of the Schrödinger cat states under the assistance of a cross-Kerr interaction, which is an inherent interaction accompanied by the optomechanical coupling in a generalized optomechanical system. By exactly diagonalizing the generalized optomechanical Hamiltonian and calculating its unitary evolution operator, we find the physical mechanism of the enhancement of photon blockade and single-photon mechanical displacement. The quantum properties in this generalized optomechanical system are studied by investigating the second-order correlation function of the cavity field and calculating the Wigner function and the probability distribution of the rotated quadrature operator for the mechanical mode. We also study the influence of the dissipations on the few-photon optomechanical effects.